Catalogue no XIE. Survey Methodology

Transcription

1 aalogu o -00-XIE Survy Mhodology 005

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4 SURVEY METHODOLOGY Joural ublshd by Sass aada Survy Mhodology s absrad Th Survy Sasa Sasal Thory ad Mhods bsras ad SRM Daabas of Soal Rsarh Mhodology Erasus Uvrsy ad s rfrd h urr Id o Sass ad Joural os Qualav Mhods MGEMET ORD hara D Roy as har GJ raso R la Mbrs J Gabo J Kovar H Mal EDITORIL ORD Edor M Sgh Sass aada Duy Edor H Mal Sass aada ssoa Edors DR llhous Uvrsy of Wsr Oaro D dr Sass aada JM r Wsa I awll US urau of h sus JL Elg US urau of Labor Sass W Fullr Iowa Sa Uvrsy J Gabo Sass aada M Hdroglou Off for aoal Sass G Kalo Wsa I Ko aoal grulural Sass Srv J Kovar Sass aada Lahr JSM Uvrsy of Marylad G aha Hbrw Uvrsy D fffra Hbrw Uvrsy JK Rao arlo Uvrsy TJ Rao Ida Sasal Isu sssa Edors EDITORIL OLIY E Raour (roduo Maagr D Roy M Sgh J-F auo D ad W Yug Sass aada J Rr Du Uvrsy L- Rvs Uvrsé Laval Shr aoal r for Halh Sass FJ Shur aoal Oo Rsarh r J Sr Uvrsy of Souhao E Sasy Oho Sa Uvrsy D Sl Uvrsy of Wollogog L Sos Souhr Mhods Uvrsy M Thoso Uvrsy of Warloo Y Tllé Uvrsé d uhâl R Valla JSM Uvrsy of Mhga VJ Vra Uvrsà dgl Sud d Sa J Wasbrg Wsa I KM Wolr Iowa Sa Uvrsy Zaslavsy Harvard Uvrsy Survy Mhodology ublshs arls dalg wh varous ass of sasal dvlo rlva o a sasal agy suh as dsg ssus h o of raal osras us of dffr daa sours ad ollo hqus oal survy rror survy valuao rsarh survy hodology srs aalyss sasoal adus dograh suds daa grao sao ad daa aalyss hods ad gral survy syss dvlo Th hass s lad o h dvlo ad valuao of sf hodologs as ald o daa ollo or h daa hslvs ll ars wll b rfrd Howvr h auhors ra full rsosbly for h os of hr ars ad oos rssd ar o ssarly hos of h Edoral oard or of Sass aada Subsso of Mausrs Survy Mhodology s ublshd w a yar uhors ar vd o sub hr arls Eglsh or Frh lro for rfrably Word o h Edor Dr M Sgh sgh@saaa (Houshold Survy Mhods Dvso Sass aada Tuy s asur Oawa Oaro aada K 0T6 For forag sruos las s h gudls rovdd h Joural Subsro Ras Th r of Survy Mhodology (aalogu o -00-X s D $58 r yar Th r luds aada sals as ddoal shg hargs aly for dlvry ousd aada: Ud Sas D $ ($6 ssus; Ohr ours D $30 ($5 ssus Subsro ordr should b s o Sass aada Dssao Dvso rulao Maag 0 ardal vu Oawa Oaro aada K 0T6 or by dallg by fa or by E-al: ordr@saaa rdud r s avalabl o brs of h ra Sasal ssoao h Iraoal ssoao of Survy Sasas h ra ssoao for ubl Oo Rsarh h Sasal Soy of aada ad l ssoao ds sass sass du Québ

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9 Survy Mhodology Ju 005 Vol 3 o - Sass aada aalogu o -00-XIE I Ths Issu Ths ssu of Survy Mhodology s ddad o Gordo J raso who rly rrd fro Sass aada H was sssa hf Sasa for h Iforas ad Mhodology fld ad had b hara of h Survy Mhodology aag board s 987 Hs ouous suor o h oural has b ard by gra sgh ad ovad by a osa dsr o fosr hgh sadards of hodology ras Furhr h also auhord svral arls ha aard h oural W wsh o rss our r graud o Gordo J raso Th urr ssu oas gh rgular ars o a vary of os ad hr shor ouaos s od h rvous ssu of h oural w ar rodug a w Shor ouaos so Survy Mhodology Ths so wll oa shorr ars yally aroud four ags ossbl os of shor ouaos lud rsao of w das whou h full dvlo of a rgular ar brf rors of ral wor ad dsussos or suls rlad o ohr ars ublshd h oural For h as four yars h Ju ssu of Survy Mhodology has ludd a vd ar hoour of Josh Wasbrg Sarg hs yar hs aual vd ar wll b ublshd h Dbr ssu of h oural brgg or l wh h assoad Wasbrg addrss dlvrd a Sass aada s aual hodology syosu h auu Th auhor of hs yar s Wasbrg ar s JK Rao ad hs ar wll b o h Irlay w Sal Survy Thory ad Mhods: a rasal I h og ar of hs ssu Wgl Valla ad Shur rs a w sulao aroah o sao of rror ras for hrshold slo rord lag For ah oal ahd ar hr s a vor of oarso ouos ha drs h lag wgh uloal odl s assud for ah oarso ouo wh dffr uloal dsrbuos for ru ahs ad ru o-ahs Th dsrbuos ar sad fro a sal ad h usd o sula h dsrbuos of h lag wghs for ru ahs ad ru o-ahs Th hod s llusrad a as sudy usg daa fro h US Mdal Edur al Survy (MES Krws Dwa Wag arl Zls ad Mall vsga h ffs of rord lag rrors boh fals osvs ad fals gavs o rs sas ohor suds Thy show aalyally how lag rrors rodu boh bas ad addoal varably o obsrvd ad d ubrs of dahs as wll as o sas of sadardzd oraly raos ad rlav rs rgrsso offs Thy dsuss hr rsuls hr olusos ad o o furhr wor ha ds o b do hs ara Th ar by va d ral ad Rss addrsss h robl of sg hyohss bw dffr survy laos suh as dffr qusoar dsgs wh a ol salg dsg s usd dsg-basd hory s dvlod for ass whr h survy laos ar assgd o subsals hrough olly radozd ral dsgs or radozd blo ral dsgs Th hory also as us of asur rror odls Dsg-basd Wald sass ar usd o oar h dffr survy laos Tsuhya aroahs h log-sadg robl of asg rsods ssv qusos a rsg fasho Isad of usg h radozd rsos aroah ha allows ll orol for h rsarhr h rooss ha h ou hqu b adad for ssv qusos Th ou hqu rss h rsod wh a ls of svral hrass fro whh h rsod sls all ha aly o h Th rsarhr osrus h ls wo ways: h frs ls oas h ssv hras whl h sod ls dos o Tsuhya rss varous saors for hs hqu ad gvs a rsg al rlad o h Jaas aoal harar I h ar by DZo Guarra ad Luz f ur odls ar usd o d rrors ha ar du o a orr u of asur a h ollo sag of h survy I a ulvara o ad assug ha h daa ar ulvara oral h rodur a dfy whh varabls ar rror for a gv sald u Th auhors also rovd dagoss for rorzg ass o b vsgad or dly hrough lral rvw Th roosd hodology s llusrad hrough a al wh sulad daa ad a al wh ral daa Sass aada aalogu o -00-XIE

10 I Ths Issu hu Yul Zauo ad Zaslavsy rs a hod for ull uao of ssg oual varabls for us rgrsso aalyss For ah rord ssg h varabl ad for a sal of ol rords ahd ass ar sld basd o a s of ahg varabls Th sal of ol rords s h usd o sa a rgrsso adus for ohr varabls o ludd aog h ahg varabls Th oual varabls for h ol rords ar h ully ud Th auhors h show a alao o a oloral ar sudy ad us sulaos o oar hr aroah o hr ohr orsos adus hods adra ad ho a h ora robl of ogorabl orsos sall-ara sao of a halh saus varabl Wh ofrod wh a al whr h usual saors ar basd baus of h ssv ubr of orsods hy a o aou for h dffrs hrough odlg adra ad ho us wo ogorabl orsos hrarhal ays odls a slo odl ad a ar odl o aalyz h halh daa ora osdrao o hr odlg s h ororao of h u fro doors org h orsos ar ad h ouo varabl Th rsuls gv a aura o-rsos adus ad a br asur of rso ar ad Fullr roos a hod o rdu h robably of obag gav sao wghs wh usg a rgrsso saor Thr hod osss of frs aroag luso robabls odoal o Horvz-Thoso sas for a vor of aulary varabls ad h usg hs aroa odoal luso robabls as al wghs a rgrsso saor Thr hod s show o wor wll a sulao sudy Th wghs obad fro hs hod ar also oard o wghs fro quadra rograg h rag rao h log rodur ad au llhood I h frs of hr shor ouaos ludd hs ssu drsso ad Thorbur show ha h oal rgrsso saor a b rssd as a albrao saor wh a aroraly hos dsa fuo Th rsulg oal saor s asyoally or ff ha h usual Gralzd Rgrsso (GREG saor sall sulao sudy llusras svral suaos whr h oal saor f sgfaly or ff ha h GREG saor Ly ad Gablr d h rsuls of Gablr Hadr ad Lahr (volu o Ksh s rsso for h dsg ff du o lusrg Thy gv a raal aroah o sag Ksh s quay a h sal dsg sag wh oly h oal ubrs of obsrvaos ad of lusrs ar dd Mza ad Lahr a h laos of a sadard rgrsso odl slo rro Mallows sas for sd rror rgrsso odls Thy show ha whl a sraghforward alao of Mallows sas ay rsul ff odl slo hods a suabl rasforao of h daa ay b h aswr Fally w would l o for you ha Harold Mal wll ow hold h w oso of Duy Edor Harold has b ar of h Edoral oard for h las 5 yars Hs ddao o h oural has b oabl ad hs ouous volv h doral ross has b srual surg ha Survy Mhodology ras a hgh qualy ublao M Sgh Sass aada aalogu o -00-XIE

11 Survy Mhodology Ju Vol 3 o 3- Sass aada aalogu o -00-XIE as Sudy Rord Lag M Wgl R Valla ad F Shur bsra Rord lag s a ross of arg rords fro wo fls ad ryg o sl h ars ha blog o h sa y Th bas frawor uss a ah wgh o asur h llhood of a orr ah ad a dso rul o assg rord ars as ru or fals ah ars Wgh hrsholds for slg a rord ar as ahd or uahd dd o h dsrd orol ovr lag rrors urr hods o dr h slo hrsholds ad sa lag rrors a rovd dvrg rsuls ddg o h y of lag rror ad h aroah o lag Ths ar rss a as sudy ha uss sg lag hods o l rord ars bu a w sulao aroah (SRa o hl dr slo hrsholds ad sa lag rrors SRa uss h obsrvd dsrbuo of daa ahd ad uahd ars o gra a larg sulad s of rord ars assgs a ah wgh o ah ar basd o sfd ah ruls ad uss h wgh urvs of h sulad ars for rror sao Ky Words: Fl ahg; Lag rror ras; Mah wgh; Slo hrshold; Mdal rords Iroduo Th bas rord lag frawor by wob Kdy ford ad Jas (959 ad Fllg ad Sur (969 uss a ah wgh o asur h llhood of a orr ah ad a dso rul o lassfy rord ars Th oal dso rul uss wo ah wgh hrsholds for slo (a ur hrshold abov whh a l s rad as a ah ad a lowr hrshold blow whh a l s rad as a oah Th ho of hs hrsholds dds o h aabl r-s lag rror ra ad h rqur o z h ubr of ls wh dra saus bw h wo hrsholds owadays raors of ourzd lag syss of us a sgl slo hrshold o avod aual rvo of h dra ls Lag dsos ar yally ad auoaally afr h sys s ud o ahv r-s rror lvls Th hallg s ha urr hods o dr h slo hrshold ad o sa lag rrors a rodu dvrg rsuls ddg o h y of lag rror h ho of oarso sa ad h sao hod Ths ar shars our r wh fllow raors who d a hod o gud lag slo ad rror sao Our as sudy usd dal v fls fro h US Mdal Edur al Survy (MES MES olls dal dur daa fro boh houshold rsods ad hr dal rovdrs Th uros s o ob h daa fro boh sours for suorg aual saos of dal ulzao ad durs (s gy for Halhar Rsarh ad Qualy 00 for or dals o MES Hr w dsuss h lag wh hr ss of aual dal v fls MES 996 MES 997 ad MES 998 Eah s ossd of a houshold fl oag vs rord by houshold rsods for a gv yar ad a dal rovdr fl oag h orrsodg vs rord by dal rovdrs of h houshold rsods O avrag aroaly dal vs wr rord for los o 0000 rsos ad aroud 5000 rso-rovdr us ah yar W usd wo odl-basd alravs for lag rror sao O of hs uss sulao o dvlo a dsrbuo of h wghs for varous lvls of agr Ths hqu alld SRa bgs by grag wgh dsrbuos for ahd ad uahd rord ars Usg hs SRa a h rovd sas of lag rror ras for dffr hrshold lvls Th rror ras a h b usd as a gud o ao ad a way o asur suss SRa s orasd wh a sod odlg aroah rad by l ad Rub (995 s w ho o show hr s a rol for boh aroahs; ah has srghs as llusrad h oarsos Mur Modls ad Sra roahs Th ur odlg hod of lag rror sao as rsd l ad Rub (995 has svral arav faurs I s flbl a ss ha h wgh rao ross dos o hav o b osdrd drly H hs hod a b alabl o ay dffr ways of rag wghs O a odl s sfd rror M Wgl Wsa Sasal Grou 650 Rsarh oulvard Rovll MD US; R Valla Jo rogra for Survy Mhodology Uvrsy of Marylad ad Uvrsy of Mhga; F Shur OR Uvrsy of hago

12 4 Wgl Valla ad Shur: as Sudy Rord Lag ras a b ad for a ouu of oal hrshold valus ad ofd bads a b osrud o oor h rso of rror sas (s so 7 Mur odlg dos hav laos Whl h hod rovds a arular d of rror ra h rooro of ld rords ha ar aually uahd ars ovrall fals osv ad fals gav rror ras ao b sad s old ars ar o osdrd Th rror ra ha s sad s odoal o h s of ld ars of rords Furhror odl arars ay b hard o sa f h wgh dsrbuos for h ahd ad uahd ss ar o sarabl (s Wlr 994 y assuo h l Rub aroah s ha s ossbl o rasfor h dsrbuos of h wghs h ahd ad uahd ss o a h oral ow a ral dffuly ss hr ha h rasford wghs ay b far fro oral wh h wgh dsrbuo for hr h ahd or uahd ss s ulodal ohr ral rqur s o hav a rag daa s whos hararss ar vry slar o hos ha ar o b ahd Whou a good rag daa s h u arar sas for h ur odl ay b oor affg h fal sad rror ras obad asd o our alao usg aual dal v daa rad ovr hr yars h arars wr o sabl ovr Ths sably ssad a rag s for ah yar ag h l Rub aroah raal our alao baus of h os ad rqurd Th sulao aroah SRa l ur odlg has h ably o a dffr hrsholds allowg h usr o oor boh h ssvy ad sfy of h dso rul for slg ld ars s log as h ross usd o ra ah wghs a b ralsally odld usozd hods of wgh assg l h o usd h urr as sudy a b aoodad Th hod dos rqur h grao of ars of rords usg h dsrbuo of hararss for h ahd ad uahd ss So ffor s dd o ralsally gra h oulaos of ars I our wor w hav b sussful wh uloal odls for grag hs oulaos 3 Thrshold Wgh ad Lag Error Esao Svral hods ar avalabl h lraur for slg ru ahs ad for sag lag rrors (g arl Krws Wag ad Zls 993 rsrog ad Mayda 993 l 993 l ad Rub 995 ad Wlr S Fllg (997 for a ovrvw of voluos rord lag Tg (968 ad Lars ad Rub (00 for ohr lg hods ad Shur (983 for a aur-raur hod o sa osso rror oarso of sas fro h dffr aroahs s olad by h fa ha ah aroah ds o fous o dffr rror oos I fa h hods usd h lag lraur o osru lag rror ras ar sowha oss W llusra hs robl blow Tabl shows a ogy abl abulag h ubrs of ru ahd ad uahd ars ad dlard ld ad old ars sld by lag syss Esas of lag rror ras a b osrud rlav o h ru oals show h olus sa of fals osv lag rror ra udr h Fllg ad Sur frawor s μˆ ( U / ad ha of fals gav lag rror ra s λˆ ( 3 M / (s also rsrog ad Mayda 993 Ths ar h ras ha SRa s dsgd o sa Thy aswr h quso Of h s of ru ahd (or uahd ars wha rooro s o orrly dfd? Tabl ogy Tabl for Evaluag Lag Errors Tru s Dlard s Mah (M Uah (U Dlard oal L ( ol ( 3 ru osv fals osv fals gav ru gav Tru oal So lag valuaos hav also osdrd ras rlav o h dlard oals h rows For sa Goaa arr r ad Mhll (00 usd / ad labld h osv rdv owr of h lag sys Ohrs howvr hav labld hs as h fals ah ra (l ad Rub 995 or fals osv dlard ra (arl al 993 Ras osrud hs ar aswr h quso Of h dlard ld (or old ars wha rooros ar wrog? oh qusos ar ora slg ahd ars ad should b addrssd Tha s o of h aals loyg boh SRa ad l Rub f ossbl 4 Sra Wgh Dsrbuo Mhods o Esa Lag Error How o bs sa h lag rrors gv a ld budg ad shdul s a dfful quso ura sao of lag rrors should dd o a las wo faors h owr of h dfyg flds o uabguously dfy vs ha ar ru ahs ad h lag hod usd Ta oghr s h ossbl a gv sg o sfy lag agors sa agr robabls ad dr ah wghs Sass aada aalogu o -00-XIE

13 Survy Mhodology Ju Followg wob ad Kdy (96 ad Jaro (989 w ado a wgh dsrbuo aroah our alao ha a a all hs faors o osdrao Th bas s s o frs ou h ah wgh ad ordr all ossbl ofguraos of agr ad dsagr ouos of h oarso flds by ah wgh Th w lo h uulav dsrbuo fuo of h wghs for ahd ad uahd ars ad us h rsulg wgh har o dr hrsholds o aa dsrd lvls of fals osv ad fals gav rror ras dal hod o dvlo hs urvs gh b o bg wh a s of rord ars for whh h ruh s ow If rsours ar avalabl w ould us a larg s of ru ahd ars ordr h by ah wgh ad obsrv wha rooro s abov or blow a gv hrshold Slarly w ould a a larg s of ars ow o b ru uahd ars ordr h by wghs ad aga abula h rooro o hr sd of h hrshold Th rooro of ru ahd ars wh wghs blow h hrshold ad h rooro of ru uahd ars wh wghs abov h hrshold would h b sas of h rror ras assoad wh h way whh h ahg algorh s ld O hod o aroa hs dal aroah (s also arl al 993 s o sal rord ars ad us aual rvw o dr h ru ah saus O h ru ars ar ow w a aah h ah wghs fro whavr lag sys s bg usd ad h dvlo uulav wgh dsrbuos as dsussd abov Ths hod s of ours sub o h wll-ow ad ohr rsour laos of aual rvw ad s sldo raal wh a larg sal alrav hod s o gra h uulav wgh dsrbuos hrough sulao Tha s h har of h SRa aroah To la so dal do a rord ar by r ad a oarso fld by v ( v K V flds Th oarso ouo suaos our alao ludd aral agrs ad ull ouo agors byod h bas agr ad dsagr agors (s also wob 988 Thrfor w do ha ah fld v has K v ouo agors Th ouo daor s y rv ( yrv K yrv v a vor of daors showg h agory o whh ar r falls O of h valus of y rv wll b ad h ohrs 0 for ah fld Th arular hory suorg h SRa aroah s o assu ha y rv has o uloal dsrbuo f ar r s a ahd ar ad a dffr uloal dsrbuo f s a uahd ar W a h odl h y rv vors as havg a uloal dsrbuo wh arars v ( v K v f h ar s a ahd ar v ad arars u u K u f h ar s a v ( v vv uahd ar Th h robably v (fld v agory agrs ar r r M s h odoal robably of agr for fld v agory I gv ha h rord ar r s h s M of ru ahd ars I oras h robably u v (fld v agory agrs ar r r U s h odoal robably of agr for fld v agory I gv ha h rord ar r s h s U of ru uahd ars ssug dd of h ahg varabls v K V w a sfy h o robably of y y K y f a ar r s a ah as r ( y ( r rv V r r M v v Th orrsodg robably of h sa ofgurao of daa f h ar s rally a uahd ar s ( y r r U V v v SRa uss Mo arlo sulao hods o gra a larg ubr of ralzaos of ahd ars ad uahd ars usg sas of h robabls v ad u v For ah sulad ar a ah wgh w r whh als o a gv ofgurao of daa s alulad For a gv ralzao y r a wgh w r s oud for h ar by sug h wghs for h radoly grad agors ha h ar fll o Th ah wgh w r of a rord ar s yally sad as V v y r v v log v w r V v yr v uv v S so 6 o h ah wghs usd our sulao Th uulav dsrbuo of hs wghs for h sulad ahd ars s h lod as S M Slarly h rvrs uulav dsrbuo for h uahd ars s lod o gra S U (s Fgur so 8 for a al of h sulao urvs usd hs sudy Th sulad rooro of ahd ars whos wghs ar blow h uoff s h sa of h fals gav rror ra Th sulao rooro of uahd ars whos wghs ar abov h uoff s h sa of h fals osv rror ra Ths aroah rqurs ha ral sas b ad of h dsrbuos aog h ahg varabls of boh ru ahd ad ru uahd ars Ev hough h wgh algorh ay volv h assuo of dd aog ahg varabls h aual daa ay show dd s log as arfal ars a b grad ha ralsally follow h obsrvd dsrbuo of h daa (ororag ay dds h hs hod should rovd suabl rror ra sas u y v y v r v rv Sass aada aalogu o -00-XIE

14 6 Wgl Valla ad Shur: as Sudy Rord Lag I our as sudy w odld daa flds as havg dd uloal dsrbuos bu hs ay o b rasoabl ohr alaos Th SRa o a aly o ay algorh whr wghs ad a uoff o ar usd for lassfao Thus hods ohr ha Fllg ad Sur (969 l l ad Rub (995 gh also b valuad hs way If hods ar dd o dal wh dd agoral varabls h ulvara uloal dsrbuos Johso Koz ad alarsha (997 har 6 ay b arora Howvr alaos slar o ours h sls rodur for aoug for dd s o for ross-lassfaos of h varabls ha ar rlad ad o sa robabls for ah ll a ross-abl For al f wo varabls wh ad agors ar assoad h w a sa h o robably for ah ll h * abl ad us hos h sulao Sars daa wll aurally l h ubr of lls for whh hs s fasbl u h rs of sars daa h aly for odl falur us b sall 5 Rord Lag of MES Mdal Evs Rord lag of MES dal vs usd fv dfyg flds: v das (yar oh day ad day-ofw dal odo ods rodur ods global-f ods ad lghs (ubr of days of hosal say Ths flds ar dsrbd or dal Wgl Valla r ad Mahl (000 rag sal fro MES 996 was loyd o drv ah ruls ad ouo agors ad o sa h robabls of agr for ah agory allowg for aral agr ad valu sf ouos Th sa ah ruls wr rad ah yar wh or aduss of h ahg arars For h rag s w usd h lag sys uoah (Mahwar 996 ad h uqu ah algorh o sl ld ars I uqu ahg a Fl rord s oally ld o oly o Fl rord (Jaro 989 I addo w usd h ay-o-ay ah algorh o gra a rado sal of old ars o fala lag rror sao Howvr h hods for sag rror ras dsrbd blow aly o ay sofwar ha ls h lag hods basd o ah wghs Thy ar o sf o uoah Th radoff drg h slo hrshold for MES was bw gg a hgh ah ra ad lg sah lag rrors hgh hrshold wgh would z fals osv (sah rrors a h s of lowrg h ah ra ad losg valuabl daa olld fro dal rovdrs O h ohr had a low hrshold would ras fals osv rror ad ay aff h alloao of dur daa a way ha would rqur sal aaly hqus o ovro ad v h oly wh uray S boh daa sours had rord o ossbly h sa dal vs for h sa rsos ovr h sa rod h sragy was o aa a rasoably hgh ah ra ad o odu a aual rvw of a ld ubr of qusoabl ld ars afr slo o assss h aaly a of falsly ag h asd o hs dso h avrag ah ra for h aual MES dal rords fls was abou 85 r Th 996 MES rag sal M urv labld h Tra M urv was grad by alyg ah wghs o ru ahd ars for a rado sal of 500 rsos MES 996 For hs rsos h aual rvw fls oad 507 vs fro houshold rsods ad 804 vs fro dal rovdrs Kowldgabl daa aagrs rvwd h vs ad sld 50 ars W osdrd hs as h ru ahd ars hs valuao Th aually ahd ars wr assgd h wghs drvd fro our ah sfao o gra a uulav dsrbuo fuo Th 996 rag sal U urv labld h Tra U urv was grad usg a rado sal of uahd ars W usd a sl rado salg wh rla hod o sl 500 vs ah fro h ahg fls ad loyd a ay-o-ay ah algorh o gra all ossbl v ars For hs radoly sld ss of ars h ha of hr bg ay orrly ahd ars s glgbl; hus h r s was a o oss of uahd ars W ald h ah wghs fro our ahg sfao ad lod h Tra U urv qual o us h uulav dsrbuo of h wghs of hs ars Fgur so 8 shows boh h Tra M ad Tra U urvs for h 996 MES Th urvs show hs fgur wr soohd usg a oarar lowss fuo (habr lvlad Klr ad Tuy 983 S LUS 000 (999 6 Sra Ilao MES Th SRa wgh dsrbuo hod usd Mo arlo sulao hods o gra sara ss of 0000 sulad ahd ad uahd ars for rag h wgh urvs To gra h S M wgh dsrbuos w sad h robabls v fro ld ars assgd by a uqu ahg algorh W usd h ud lag sys o sl ahd ars fro h 996 aual ahg fls ad abulad h obsrvd frqus for ah ouo agory for ah of h fv ahg flds Th rooro of ars ha fll o agory of fld v was h usd as h sa ˆ v of h robably v Sass aada aalogu o -00-XIE

15 Survy Mhodology Ju For h uahd ars ad h S U urv h u v robabls for uahd ars wr sad usg h sa sal of uahd ars usd rag h Tra U urv Th dffr s ha w usd hs ars o obsrv h rlav frqus for ah ouo agory for ah of h fv ahg flds aog uahd ars Th rooro of ars ha fll o agory of fld v was h usd as h sa û v of h robably u v For a sulad ahd ar a ralzao of h uloal rado varabl y rv was grad for ah ah fld For al a ofgurao l (agr o v da agr o lgh of hosal say agr o h array of odo ods o agr by y of rodur ad valu sf agr for a global-f daor was grad usg h ah robabls ˆ v for ah ouo agory Slarly for ah uahd ar a ralzao was grad of a agory for ah of h fv flds usg h uahd robabls û v dsussd abov For a gv ralzao y r a wgh w r was oud for h ar by sug h wghs for h radoly grad agors ha h ar fll o Th aual wghs usd our sulao wr adusd os ha w sfd rahr ha os dfd drly by h ahg sofwar (s Wgl al 000 Thus w ar sulag h way whh ahg would aually b ld To do hs w alulad h ah wgh for boh h ahd ad uahd ss of 0000 ars ad lod h sulad ah wgh fuos Tabl shows als of so h aral agr agors usd for ahg v da ad h sas of ˆ v uˆ v ad w r usd SRa sulao W dfd a oal of 9 ouo agors for ahg by v da 9 agors for durao of hosal say 7 agors by dal rodurs ad 3 agors ah for dal odos ad global f For al for h ouo agory a agr o v da h sa of ˆ v was 069 ag ha 69 r of h ld ars had a agr o v da Th sa of û v for hs ouo agory was 0003 showg ha oly 03 r of h uld ar showd agr o hs fld Th ah wgh for a agr o da of v was 85 ad ha for ol dsagr (dffr of or ha wo ws aar ad o dffr day of w was 664 (s Wgl al 000 for h ah wghs by ah flds ad ouo agors W sld h ah flds ha wr aroaly dd hs as sudy For al w foud o fuoal assoao bw h da of dal vs ad ohr ah flds l dal odo ad lgh of hosal say For flds suh as h daors for surgry radology ad laboraory rodurs w usd h-squar ss ad foud so dd bw h ourr of surgry ad radology To hadl hs suao w sad h o robabls ad sfd ah ruls o ra hs rodur flags as a sgl ah fld (s so 4 abov H w ould h aly h dd uloal dsrbuo for sulao Tabl Esas of Muloal robabls for Mahd ars ˆ ad Uahd ars ( u ˆ v ad Mah Wghs ( w v for h Mah Fld Ev Da ( v Mah rul for Ev Da ˆ v û v w v Mssg Ea ah Off / day Off / 3 day Off / 5 day Off / 7 day Mah by day of w oly Dsagr Tabl 3 shows h rsuls of lag rror sas fro SRa ad h rag urvs a h hrshold wgh of w for MES 996 MES 997 ad MES 998 SRa was asy o ra ah yar Rag h aual-basd wgh urvs howvr ddd ar o aual rvw ad w had oly o rlabl rag sal ha for 996 o ha h ld ars usd SRa wll aurally gra so rag of fals osvs ad fals gavs so ahd ad uahd ars ar orr Thus h ˆ v robabls oud hs way for h dfd flds ar sub o rror I would hav b rfrabl o sa h robabls fro a ruh s whr w wr ofd ha all ahs wr orr Howvr h aually ahd rag ss w wr abl o rodu wr oo sall o yld sabl sas all of h dald ah agors ad aual slo s also rf Ths dffr ay la ar h slghly hghr ovrall rror ra sas fro SRa ha fro h rag sal wgh urvs Tabl 3 Wgh urv Mhods o Esa Lag Error Ras a Thrshold Wgh MES Mhod Error Ra SRa sulao urvs Fals gav Fals osv Trag sal urvs Fals gav* Fals osv** * Esas fro h 996 Tra M urv wr usd for all hr yars ** Esas fro h 996 Tra U urv usd sals of 500 rords fro ah ah fl ad a oal of uahd ars Th 997 ad 998 sas usd dffr Tra U urvs loyg sals of 000 rords fro ah ah fl ad a oal of uahd ars Sass aada aalogu o -00-XIE

16 8 Wgl Valla ad Shur: as Sudy Rord Lag 7 Mur Modl Ilao MES ur odlg aroah by l ad Rub (995 vws h dsrbuo of obsrvd ah wghs fro a ourzd lag sys as a ur of wghs for ru ahs ad fals ahs I rl h ur odl hod has wo arav faurs suabl for MES Frs a hadl rad alaos ffly Wh global arar sas of h rasford arars ad h rao of h varas of h wo dsrbuos ar avalabl hs sas a b ald o slar daa for sao S h MES rord lag s do aually global sas drvd fro arly rag sals ould ovably b ald for lag rror sao lar yars wh aual rvw sals wr o avalabl Th sod advaag s ha h ur odl a draw fro ull ss of arar sas fro dffr rag sals ad a rfl varaos Ths faur s sally aalg for MES baus aual rvw s a ol ross ad o ssarly always aura H a alrav s o vw h our sys slo as h ruh ad us h o rovd a alrav s of arar sas Ths ross a also b rad usg rag sals fro or ha o yar Our alao of h l Rub aroah usd h sa rag sals fro MES 996 ad a sod rag sal of h sa sz fro 997 Followg l Rub s als w ald h ur odlg hod usg aually dfd ru ad fals ah ars fro a o-o-o ahg sys (o ha suh syss rovd rlavly fw fals ah ars for sao W oud odl sas for MES 996 ad MES 997 assug h aual slo o b h ruh ad for sg h bhavor of h odl w oud a sod s of sas assug our sys sld ah ars o b h ru ars Ilao volvd wo rodurs h o ad o (964 rodur for global arar sao ad h albra rodur (l ad Rub 995 o f a ur odl for rror ra sao for alyg o o h wghs wr rsald bw ad 000 Th o o rasforao dsussd by l ad Rub (995 was Ψ γ wr ( wr γ γ w whr w r s h ah wgh for ar r w s h gor a of h w r wgh ad γ s a arar ha s dd o whhr h ar s h ahd or uahd s For h ur odl rodur o b ffv h rasford wghs should b aroaly orally dsrbud Th urasford wgh dsrbuo wh our daa showd bodaly ad alos o ovrla ah wgh bw ahd ad uahd ars (bodaly was also obsrvd l Rub 995 For al alao of hr rasforao rodur o h 996 MES sys ars rsuld arar sas of w 5857 ad γ 5 for h ru ahd ars ad w 3 ad γ 0 48 for h fals ahd ars Th rasford wghs howvr showd rlavly ll rov owards oraly S h ah wghs ar h log of a rodu or h su of logs w gh ho ha h wghs would b orally dsrbud f hr wr ay oos h su Howvr w had oly fv flds o us for ahg Th sall ubr of flds ay hav aoud ar for h la of oraly wh our rasford daa Tabl 4 shows h rsuls of alyg h l Rub ur odl o MES 996 Ths abl shows h odl sad fals ah ras h 95 r ofd rval of h sad ra ad h aual obsrvd fals ah ra a h hrshold wgh of Usg h aual rvw ars as h ru ahd ars h odl sa of h d fals ah ra a h hrshold of w was 9 r wh a 95 r ofd rval ragg bw 60 ad Th aual obsrvd fals ah rror ra howvr was 45 r whh s hghr ha h ur 95 r ofd boud o ha hs ar ras of h for / Tabl Ths ar o h sa ras sad by SRa ad h wgh urv aroah MES 996 Tabl 4 Mur Modl Lag Error Esas rag fals ah rror Ed Lowr Ur Obsrvd ra ra oud* oud* Maual ah Sys ah * Th lowr ad ur bouds ar h 95 r ofd rval of h d rror ra S aual rvw ay o always b aura a oo for h uros of valuao s o ra h our sys ld ars as h ruh ahd ars ad us h for odlg Udr hs assuo h odl sa of h d rror ra s 09 ad a 95 r ofd rval bw 06 ad Th aual obsrvd ra hs as 0 r was a hyohal ouo rag h our-ld ars as orr Of ours raly hr wll b so ozro lvl of rror so ha h ur odl ofd rval s o ssarly wrog W grad global arar sas usg boh h rag sal aual slos ad sys slos for Sass aada aalogu o -00-XIE

17 Survy Mhodology Ju MES 996 ad MES 997 ad usd h as four ss of us o rovd global sas for odlg lag rror for MES 998 Ths should b ossbl baus h daa rad slar ad rord ars wr sld usg h sa ah ruls for all 3 yars dffr was ha aual rvw was o odud for MES 998 ad w ould o us h o o rodur for global arar sao for 998 (baus hr was o sara aual daor for ru ad fals ars For hs alao w us a boosra hod h l ad Rub albra rodur o draw fro ull arar ss o rfl uras sao Ths alao howvr dd o ovrg afr 50 raos of h sao rodur W ould oly olud ha h global arar sas fro arlr rag sals fald o gralz ad rovd rror ra sas for rad lag alaos 8 oludg os ad aly Ilaos Th ross of hrshold slo ad lag rror sao s a rav ross volvg rad yls of obsrvao sao ad odlg Our as sudy loyd odlg aroahs for sag lag rrors ad for oorg h rdv owr of h lag sys oh hods rovdd valuabl forao for drg h lag slo ad for valuag h qualy of h dlard ahd ars as w foud MES Th wgh urvs aroah of sao has h aal ha o a hoos a slo hrshold o aa h aabl lag rror lvl For al Fgur shows h rag sal ad h SRa sulao wgh urvs basd o h 996 MES ahg fls vral l s draw a h slo hrshold wgh of w ; h rror lvls for 996 MES (show Tabl 3 wr h sad by h uulav rag a hrshold lvl y sldg hs hrshold o a a o z h oal lag rror by slg a hrshold a h rossg o of h M ad U urvs I hs as sudy h oal hrshold suggsd by boh ss of wgh urvs s farly oss W ludd a llhood rao sal hs fgur o rovd a rough llhood rrao of h ah wgh For al a h ah wgh of w h llhood rao sor s Ths as ha for rords wh a ah wgh of w or abov h rlav llhood of bg ru ars s a las o uulav rag ssgd Mah Wgh / 0 / Llhood Rao Fgur Wgh urvs for MES 996 usg h SRa ad Trag Sal Mhods; h dashd vral rfr l shows h hrshold valu of Sass aada aalogu o -00-XIE

18 0 Wgl Valla ad Shur: as Sudy Rord Lag Sys ars 996 ad 997 Maual ars 996 Maual ars Lowr boud (95% I Ed ra Ur boud (95% I Obsrvd ra Wgh Fgur Mur Modl Esas of Fals Mah Ras by Wgh 996 ad 997 MES Trag Sals (a vral l s draw a wgh whh s hrshold For ld ar qualy Fgur shows h dsrbuos of fals ah ra sas fro ur odlg Ths fgur shows h odl sad fals ah ra h ur ad lowr 95 r ofd bouds of h rror ra sas ad h aual obsrvd ras al shows h sas rag h our sys ld ars as h ru ahd ars als ad 3 show h sas fro h 996 MES ad 997 MES rag sals Th dffr bw als ad 3 shows h ossy of aual slo by dffr rvwrs our alao I all hr als h 95 r ofd rval of h odl sas fald o ovr h ru obsrvd valus Idally o would us boh Fgur ad Fgur oghr o gud h ho of slo hrsholds W hav foud SRa o b a forav ad flbl ool for drg slo hrsholds ad sag rror ras our alao Gv uloal or ohr odls for h ahg varabls h SRa hod rovds rror ra sas ha would b obad fro rad alao of h ahg algorh o a larg ubr of adda rord ars I s also flbl aoodag h hos of oarso ss of ars for oug ras Whl our alao ahvd h ahg ad rror ra sao goals for MES or wor gh b do ror o or durg h aalyss sag Sa dos o r us o dvlo hs h o of h urr as sudy bu wo gral aroahs gh b od Frs s ossbl o rwgh h fal rsuls ad adus for fals oahs rag h a ar aalogous o u orsos (g as Oh ad Shur 980 To hadl sahs h das Shur ad Wlr (993 ad 997 ad Lahr ad Lars (00 gh b worh osulg Whhr hs addd ss ar dd of ours dds o h fal uss o whh h ld daa wll b u owldgs Th bas lag rsarh rord o hr was odud udr oras ad sosord by h gy for Halhar Rsarh ad Sass aada aalogu o -00-XIE

19 Survy Mhodology Ju 005 Qualy ad h aoal r for Halh Sass Th auhors would l o ha Sv oh Sv Mahl ad Jol oh of h gy for Halhar Rsarh ad Qualy for hr os o varous sags of hs rsarh ad Thoas l for hs suggsos o a arlr draf Rfrs gy for Halhar Rsarh ad Qualy (00 ME Mdal Edur al Survy <h://wwwahrqgov/daa/s h> rsrog J ad Mayda JE (993 Modl-basd sao of rord lag rror ras Survy Mhodology arl S Krws D Wag Y ad Zls JM (993 Evaluao of rror ras larg sal ourzd rord lag suds Survy Mhodology 9 3- o GE ad o DR (964 aalyss of rasforaos (wh dsussos Joural of h Royal Sasal Soy Srs l TR (993 Evaluao of sours of varao rord lag hrough a faoral r Survy Mhodology l TR ad Rub D (995 hod for albrag falsah ras rord lag Joural of h ra Sasal ssoao habrs JM lvlad WS Klr ad Tuy (983 Grah Mhods for Daa alyss Dubury rss oso Fllg I ad Sur (969 hory for rord lag Joural of h ra Sasal ssoao Fllg I (997 Rord lag ad ubl oly Dya Evoluao rodgs of h Iraoal Worsho ad Eoso Fdral o o Sasal Mhodology Off of Maag ad udg Washgo D Goaa S arr R r ad Mhll G (00 ral oao of rord lag rodurs Sass Md Jaro M (989 dvas rord lag hodology as ald o ahg h 985 sus of Taa Florda Joural of h ra Sasal ssoao Johso L Koz S ad alarsha (997 Dsr Mulvara Dsrbuos w Yor: Joh Wly & Sos I Lahr ad Lars MD (00 Rgrsso aalyss wh ld daa (Draf ausr Lars MD ad Rub D (00 Irav auoad rord lag usg ur odls Joural of h ra Sasal ssoao Mahwar Thologs I (996 uomah: Gralzd Rord Lag Sys Usr s Maual Slvr Srg MD: Mahwar Thologs I wob H (988 Hadboo of rord lag: Mhods for halh ad sasal suds adsrao ad busss Oford Uvrsy rss w Yor wob H Kdy JM ford SJ ad Jas (959 uoa lag of val rords S wob H ad Kdy JM (96 Rord lag: Mag au us of h dsrag owr of dfyg forao ouaos of h ssoao for oug Mahry Oh HL ad Shur F(980 Fddlg aroud wh oahs ad sahs Suds fro Iragy Daa Lags Srs Soal Sury dsrao Ror o Shur F (983 Dsg ad sao for larg fdral survys usg adsrav rords rodg of h So o Survy Rsarh Mhods ra Sasal ssoao Shur F ad Wlr WE (993 Rgrsso aalyss of daa fls ha ar our ahd Survy Mhodology Shur F ad Wlr WE (997 Rgrsso aalyss of daa fls ha ar our ahd II Survy Mhodology S-lus 000 (999 MahSof I Daa alyss rodus Dvso Sal Washgo Tg J (968 odl for ou lag of rords Joural of h ra Sasal ssoao Wgl M Valla R r JM ad Mahl S (000 robably ahg of dal vs Joural of Eoo ad Soal Masur Wlr WE (99 oarav aalyss of rord lag dso ruls rodgs of h So o Survy Rsarh Mhods ra Sasal ssoao Wlr WE (994 dvad Mhods for Rord Lag urau of h sus Sasal Rsarh Dvso Sasal Rsarh Ror Srs RR 94/05 Wlr WE (995 Mahg ad rord lag I usss Survy Mhods (Eds G o D dr haa hrsaso MJ ollg ad S Ko w Yor: Joh Wly & Sos I Sass aada aalogu o -00-XIE

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21 Survy Mhodology Ju Vol 3 o 3- Sass aada aalogu o -00-XIE Th Eff of Rord Lag Errors o Rs Esas ohor Moraly Suds D Krws Dwa Y Wag S arl JM Zls ad R Mall bsra Th adv of ourzd rord lag hodology has falad h odu of ohor oraly suds whh osur daa o daabas ar lroally ld wh oraly daa fro aohr daabas Ths howvr rodus lag rrors du o sahg a dvdual fro o daabas wh a dffr dvdual fro h ohr daabas I hs arl h a of lag rrors o sas of dologal daors of rs suh as sadardzd oraly raos ad rlav rs rgrsso odl arars s lord I s show ha h obsrvd ad d ubr of dahs ar affd oos dro ad as a rsul hs daors a b sub o bas ad addoal varably h rs of lag rrors Ky Words: ohor sudy; ourzd rord lag; Lag rrors; Lag hrshold wgh; osso rgrsso; Rlav rs rgrsso; Sadardzd oraly rao Iroduo I r yars a ubr of hsoral ohor suds hav b arrd ou vroal dology usg sg adsrav daabass as forao sours (How ad Sasoff 986; arr ad Far 990 I gral rs hs volvs lg rords of hua osur o vroal hazards wh rords o halh saus of usg ourzd hods for ahg dvdual rords fro dffr daabass I a ohor oraly sudy h val saus of ah ohor br s drd by lag wh oraly rords aad by govr ags Ess oraly wh h ohor rlav o h gral oulao ay b du o osurs rd by h ohor brs I sf rs rord lag s h ross of brgg oghr wo or or saraly rordd s of forao rag o h sa y (arl Krws Wag ad Zls 993 rodurs for ourzd rord lag (RL hav bo hghly rfd usg sohsad algorhs o valua h llhood of a orr ah bw wo rords (Hll 988; wob 988 Sass aada has dvlod a RL sys alld LIK whh s aabl of hadlg boh sgl fl lags ad lags bw wo sara fls (How ad Ldsay 98; Sh ad Sls 98 I hs sys wghs rflg h llhood of a ah ar aahd o ars of rords Two hrsholds ar s: oal ahs wh lag wghs abov h ur hrshold ar osdrd o b ls whras oal ahs wh wghs blow h lowr hrshold ar osdrd o b ols oal ahs wh wghs bw h ur ad lowr hrsholds ar rsolvd usg addoal forao wh avalabl Ohrws a sgl hrshold s sld o dsra bw ls ad ols Th ofdaly of rords rod udr h Sass s srly aad ay sudy whh rord lag s loyd ll suds rqurg lag wh rod daa bass us sasfy a rgorous rvw ad aroval ross ror o lao followg wllsablshd rodurs for daa ofdaly (Sgh Fdr Dua ad Yu 00 ll ld fls wh dfyg forao ra h usody of Sass aada (Labossèr 986 ourzd rord lag hods hav b usd o l vroal osur daa o h aada Moraly Daa as (MD For al a sudy of aada far oraors was ad o vsga ossbl rlaoshs bw auss of dah ovr far oraors aada ad varous soo-dograh ad farg varabls arularly sd us (Jorda-Sso Far ad olqu 990 I hs sudy h MD was ld wh h 97 sus of oulao ad h 97 sus of grulur ohr ogog larg-sal sudy s basd o h aoal Dos Rgsry (DR of aada (shor ad Groga 985 shor ad Davs 989 Th DR D Krws MLaughl r for oulao Halh Rs ssss Uvrsy of Oawa Oawa Oaro aada K 65 Shool of Mahas & Sass arlo Uvrsy Oawa Oaro aada KS 56 To who orrsod should b addrssd; Dwa ld Sass U Ida Sasal Isu Kolaa Ida; Y Wag Halhy Evros ad osur Safy rah Halh aada Oawa Oaro aada K 0L; S arl Halhy Evros ad osur Safy rah Halh aada Oawa Oaro aada K 0L; JM Zls Halhy Evros ad osur Safy rah Halh aada Oawa Oaro aada K 0L; R Mall MLaughl r for oulao Halh Rs ssss Uvrsy of Oawa Oawa Oaro aada K 65 Shool of Mahas & Sass arlo Uvrsy Oawa Oaro aada KS 56

22 4 Krws Dwa Wag arl Zls ad Mall: Th Eff of Rord Lag Errors o Rs Esas oas forao o ouaoal osurs o ozg radao rd by ovr aadas dag ba o 950 Th DR has rly b ld o h MD o vsga assoaos bw ss oraly du o ar ad ouaoal osur o low lvls of ozg radao (shor Krws ad Zls 997; shor Krws Zls Jag Sw ad Léourau 998 Mor rly h DR has b ld o h aada ar Id Daabas (So Zls shor Jag Krws Far ad ad Léourau 00 orhsv ls of ohr halh suds basd o lg osur daa wh h MD has b old by Far (989 Th suss of rord lag suds dds o h qualy of daabass bg ld (Roos Sood ad Jbaa 00 Usg oulao basd logudal adsrav daa Roos al ad daa qualy ssus suds of halh ad halh ar rdal ad Es (00 osdrd sysa rrors adsrav daabass volvd sodary aalyss of halh forao lhough rord lag suds wll bf fro h us hgh qualy daa laos daa qualy ay b offs o a ra by h larg sal szs foud ay adsrav daa bass Rord lag suds hav svral advaags ovr radoal dologal suds y usg sg adsrav daabass h d o oll w daa for halh suds s ruvd ad larg sal szs a of b ahvd wh rlavly ll ffor Ddg o h aur of h daabass ulzd rord lag rovds a sv way of lorg ay ossbl assoaos dologal suds Rord lag also has ra dsadvaags Thr s grally ll orol ovr h forao olld ad hr a b arabl loss o follow-u ohr dsadvaag of rord lag s h ourr of lag rrors whh s h fous of hs ar Ivably so rords ha ah wll fal o b ld ad ohr oahg rords wll b orrly ld Rlavly ll wor has b do o dr h a of hs lag rrors o sasal frs r Mays ad Raaaha (965 usd a sl lar rgrsso odl o aalyz h a of rrors rodud durg h ahg ross Thr rsuls da ha lag rrors fla h rsdual vara ad rodu bas o h sad slo arar Wlr ad Shur (99 drvd a rsso for h bas sas of lar rgrsso offs du o lag rrors dvas h sao of lag rror ras by l ad Rub (99 abld Shur ad Wlr (993 o l a rovd bas adus rodur Lar rgrsso hods for h aalyss of our ahd daa fls ar furhr dsussd by Shur ad Wlr (997 Th uros of hs ar s o lor h a of lag rrors o sasal frs ohor oraly suds Rlav rs rgrsso odls loyd h aalyss of daa fro suh suds ar dsrbd so ad rssos for h obsrvd ad d ubrs of dahs basd o hs odls dvlod Th a of lag rrors o h obsrvd ad d ubr of dahs ad rso-yars a rs s dsussd so 3 aalyss of h a of lag rrors o sas of sadardzd oraly raos (SMRs ad rlav rs rgrsso arars s gv so 4 oh ys of rrors a aus bas ad addoal varably sas of hs arars Our olusos ar rsd so 5 Rlav Rs Rgrsso Modls Sasal hods for h aalyss of ohor oraly suds ar wll sablshd (rslow ad Day 987 Th rary obv of suh aalyss s o dr f h osur o h ag of rs rass h oraly ra aog ohor brs Moraly s hararzd by h hazard fuo whh sfs h dah ra as a fuo of Lg T do h of dah h hazard fuo a u s forally dfd as r{ u T < u Δu T u} λ ( u l Δ u 0 Δu L λ (u do h hazard fuo for a sf aus of dah a u for dvdual a ohor of sz ad l z (u rrs a orrsodg vor of ovaras sf o ha dvdual W assu ha h ff of hs ovaras s o odfy h basl hazard λ *( u aorda wh h rlav rs rgrsso odl ( λ ( u λ* ( u γ{ β z ( u} ( whr γ s a osv fuo of h ovaras ad β s a vor of rgrsso arars Two sal ass of h gral rlav rs rgrsso odl of arular rs ar h ullav ad addv rs rgrsso odls Df h fuo γ ( by ( z ρ log γ ( z (3 ρ Wh ρ h gral rlav rs rgrsso odl rdus o b h ullav rs rgrsso odl λ ( u λ* ( u{ β z ( u} (4 Sass aada aalogu o -00-XIE

23 Survy Mhodology Ju Ths rooroal hazards odl was rodud by o (97 ad s wdly usd h aalyss of oraly daa (Kalbflsh ad r 980 Th addv rs rgrsso odl λ ( * u λ ( u β z ( u (5 ours as a lg as as ρ 0 L 0 ad b h ag a h of ry o h sudy ad h ag a h of loss o follow-u (du o whdrawal fro h sudy rao of h sudy or dah for h h sub of h ohor rsvly L δ or 0 aordg o whhr h h dvdual has or has o dd a h of loss o follow-u Th logllhood fuo basd o h rlav rs odl ( ay b wr as δ log( γ{ β z ( } log L (6 * γ{ β ( } λ ( 0 z u u du Wh hr s a sgl ovara z ( u h au llhood sa of θ {β} rdus o h sadardzd oraly rao SMR OS/EX whr OS δ ad EX ar h obsrvd ad d ubrs of dahs rsvly wh * 0 λ ( u du Mazao of h llhood fuo (6 a b ouaoally burdso wh larg sal szs rslow Lub ad Lagholz (983 slfy h llhood by assug ha h ovaras a o osa valus wh sas hrough whh a sub asss durg h ours of h sudy Th sas ar dfd by rosslassfao of h ovaras of rs Sfally suos ha hr ar J suh sas { S ; J } suh ha z ( u z whvr h h sub s S a u Ths sas ar uually lusv ad hausv so ha a ay gv u ah br of h ohor wll fall o o ad oly o sa Th log-llhood fuo (6 ay h b wr as whr log L { d J log( γ{ β z } γ{ β z * λ ( u du [ z ( u S ] } } s h orbuo o h d ubr of dahs fro all rso-yars of obsrvao h sa S ad d dos h oal ubr of dahs ha sa Lg Λ ( β log( γ{ β z } h au llhood sa βˆ of β s obad as h soluo o h sor quao log L J Λ ( ˆ β { d { Λ ( βˆ } } 0 (9 β β (7 (8 3 Th Eff of Lag Errors o h Obsrvd ad Ed ubrs of Dahs Two ral ys of rrors a our wh lg daa fls RL (Fllg ad Sur 969 fals osv ours wh a br of h ohor who s alv s orrly dfd as dad ad a fals gav ours wh a dasd br s osdrd o b alv Mor sfally for h ahaal dvlo o follow a fals osv ours a arular sa wh a dvdual who ras alv hroughou hs sa s orrly lablld as dad hs sa Slarly a fals gav ours a arular sa wh a br who dd bfor or durg h soour hs sa s osdrd o b alv hroughou hs sa Wh a arular sa fals osvs ad fals gavs hus rrs sal ass of slassfao rror dsussd by drso (974 har 6 I hs so w wll dsuss h ff of hs wo ys of lag rrors o h obsrvd ad d ubrs of dahs rsvly To do hs w frs df ss of ds wh sas whh wll b usd o rrs ss of orrly ahd ad orrly ahd rords 3 Lag Errors L ad D do h s of labls for hos dvduals h ohor who ra alv hroughou sa S ad hos who ar dad S rsvly Wr D as h subs of D orrsodg o hos dvduals who hav dd S L L D L ad D L do h orrsodg ss h rs of lag rrors W furhr df D as h s of labls of hos alv S (ha s bu labld as dad S orrsodg o h fals osvs S Slarly s h s of hos dad S (ha s D bu labld as alv S orrsodg o h fals gavs S L us also wr D as h subs of D orrsodg o hos who ar labld o hav dd S ad slary as h subs of who hav dd S (ha s D Ths ss sasfy h rlaos L L ( D D ( D D ad D L ( D D Th ff of lag rrors o h llhood fuo (7 ay b dsrbd as follows L 0 do h a whh h h dvdual rs aually or by lag rror h h sa S Slarly dos h of dah (f ours aually or by lag rror for h h dvdual S ad h of lavg S aually or by lag rror o ha f ss s lss ha or qual o L us for h sa of sly assu ha f ss s 0 qual o ; ha s all h dahs a sa our a h orrsodg ry s ha sa lhough hs wll udrsa h d ubr of dahs for h Sass aada aalogu o -00-XIE

24 6 Krws Dwa Wag arl Zls ad Mall: Th Eff of Rord Lag Errors o Rs Esas uros of sudyg bas ay o b ha oboabl ssug all h dahs o our a h s of lavg h orrsodg sas also offrs slar slfao Usg (8 ad h dooso of L h d ubr of dahs L S h rs of lag rrors a b wr as whr wh L L 0 0 Δ * λ ( u du * λ ( u du * λ 0 * λ 0 D ( u du ( u du (0 * λ ( u du ad Δ 0 ( * * λ ( u du ad λ ( u du ( 0 0 D For oaoal ov l us wr T λ ( for * 0 λ ( u du wha follows Th r Δ rrss h bas h d ubr of dahs h h sa du o lag rrors I follows fro (0 ad ( ha h fals osvs d o rdu h d ubr of dahs ad h fals gavs d o ras h d ubr of dahs Usg h dooso for D L h obsrvd ubr of dahs d L h rs of lag rrors ay b wr as d L d Δ d (3 whr Δ d d a (4 wh d d ad a dog h ubr of dvduals h ss D D ad rsvly Th r Δ d rrss h dffr bw h obsrvd ubr of dahs h h sa du o lag rrors I follows fro (3 ad (4 ha h fals osvs wll ras h obsrvd ubr of dahs ad h fals gavs wll rdu h obsrvd ubr of dahs Val saus s of drd by lag wh h MD whh s grally uh largr ha h ohor of rs Wh h osur rords of a lv dvdual ar orrly assoad wh hos of a dad rso h dasd dvdual usually dos o blog o h ohor Thus h rso-yars a rs orbud by h rso rag alv wll d raurly h yar of rsud dah; h los rso-yars a rs orrsod o h rod fro h yar of rsud dah ul h d of h follow-u O h ohr had wh h osur rords of a dad dvdual ar orrly assoad wh hos of a lv rso h rso-yars a rs orbud by hs dvdual wll lud a ra rod fro h aual dah-yar o h d of h follow-u Thus fals osvs wll dfla h ubr of rso-yars a rs ad fals gavs wll fla h ubr of rso-yars a rs h ohor 3 Eaos ad Varas of Dffrs w h Obsrvd ad Ed ubrs of Dahs Th ff of lag rrors o h obsrvd ad d ubrs of dahs dds o h fals osv ad fals gav ras L ad do h fals osv ad fals gav ras rsvly S for J whh ar assud o b osa wh S ad sa for all h dvduals ad D rsvly Ths assuo s rasoabl whvr dvduals h sa sa ar hghly hoogous arularly wh rs o arbus suh as h qualy of rsoal dfrs ha flu lag rror ras lhough hs dalzd assuo s ully o b fully sasfd ra affords osdrabl slfao h subsqu valuao of h ffs of lag rrors Forally ( s h odoal robably ha a dvdual ( D s labld dad (alv S Tha s [ D ] ad [ D ] L us wr a d a ad d as h ubr of dvduals D ad D rsvly Th o ha d follows a oal ( a dsrbuo ad a follows a oal ( d dsrbuo lso d follows a oal ( a dsrbuo whr s h odoal robably ha a dvdual s labld o hav dd S Tha s [ D ] larly Slarly a follows a oal ( d dsrbuo whr s h odoal robably ha a dvdual D s labld as alv S Tha s [ D ] lhough hr s o rval rlaosh bw ad gral s rasoabl o assu hs o of lag rrors ssug ha lag rrors rlad o dffr dvduals ar dd h ao ad vara of h dffr h obsrvd ubr of dahs S gv by Δ d (4 ar E[ Δ d ] E[ d ] E[ a ] a d (5 ad V [ Δ d ] V [ d a ] V [ a ] ( d ( (6 Sass aada aalogu o -00-XIE

25 Survy Mhodology Ju S ad D oss of dffr ss of dvduals d ad a ar dd Slarly h ao ad vara of h dffr h d ubr of dahs S gv by Δ ( a b alulad as follows For hs uros s ov o wr ad rs of h followg daor varabls For df ξ { I D } ad { ξ I D } lso for D df ψ I{ } Th fro ( ad h dfos of D ad w hav ad ξ T ( (7 λ ψ T ( (8 D I arular o a wr d ξ ad a D ψ whh ar usful o drv (5 ad (6 Fro (7 ad (8 w hav ad E[ Δ V [ Δ ] E[ ] E[ ] V [ λ ] λ T ( D ] V [ ( ( ] T D λ T ( λ ( T λ ( (9 (0 s ad D oss of dffr ss of dvduals Th rsuls (5 (6 ad (9 (0 da ha rord lag rrors wll lad o bas ad addoal varao h obsrvd ad d ubr of dahs Mzg h vara rs (6 ad (0 s dfful s h wo rror ras ad ar o fuoally dd Grally drasg wll rsul a ras ad v vrsa (s so 5 for furhr dsusso of hs o lhough hs rror ras ar dd of h udrlyg rlav rs rgrsso odl γ ( h a squar rror obad by obg h ao ad vara rs ao b zd whou sfao of h basl hazard λ *( u whh aars T λ 4 Th Eff of Lag Errors o Esas of SMRs ad Rgrsso offs 4 Sadardzd Moraly Raos To dr h ff of lag rrors o h SMR w rla h aual obsrvd ad d ubrs of dahs d ad by h obsrvd ad d ubr of dahs d L ad L h rs of lag rrors h rsso SMR d / Lg SMR L do h sadardzd oraly raos h rs of lag rrors w hav Δ d Δ SMR L SMR ( d I follows fro (0 (4 ha h fals osvs wll ras h SMR whras h fals gavs wll dras h SMR y usg a frs ordr Taylor srs aroao of SMR L abou SMR h dffr ΔSMR SMR L SMR a b rssd as ΔSMR SMR Δ d d Δ ( Th h a ad vara of h rlav dffr h SMR a b aroad by ad E Δ d Δ SMR [ ] [ ] E SMR ΔSMR ~ V SMR d ~ V d V Δ d Δ d ov Δ d E Δ Δ (3 (4 rsvly Th rgh had sd of (3 a b asly alulad by usg (5 ad (9 I ordr o alula h rgh had sd of (4 o ha V Δ d V [ Δ d < ] ov[ Δ d Δd ] (5 Δ V [ Δ ] ov[ Δ Δ ] (6 < V ad ov Δ d ov[ Δ d Δ Δ ] ov[ Δ d Δ ] (7 Sass aada aalogu o -00-XIE

26 8 Krws Dwa Wag arl Zls ad Mall: Th Eff of Rord Lag Errors o Rs Esas Whou loss of graly l us assu for < ha 0 0 for h sa dvdual (alv or dad S ad S ; ha s h ry S s h sa or arlr ha ha S W h hav for < ov[ Δ d Δ d ] (8 D ov[ Δ ov[ Δ d Δ D D D ov[ Δd Δ ] D ( T ( Δ ] D ] D D ov[ Δd λ T ( T ( λ T λ ( ( Δ ( T λ ] ( T λ λ ( ( T T T T ( λ λ λ ( D λ T ( λ ( ( (9 ( ( ad T T λ λ ( ( (30 (3 (3 Usg (5 (3 h vara of h rlav dffr Δ SMR/SMR a b aroad by h rgh had sd of (4 Two olusos a b draw fro (3 ad (4 Frs lag rrors a lad o bas h sa of h SMR Sod boh ys of lag rrors rodu addoal varao o sas of h SMR o ha h frs r (3 s doad by h frs r (9 for < 05 ad h gav ovara r (8 s doad h alulao of h vara (5 Thrfor h addoal vara (4 s srly osv s boh h fals osv ad fals gav ras ar osv 4 Rlav Rs Rgrsso arars To dr h ff of lag rrors o rgrsso arar sas osdr frs h gral rlav rs rgrsso odl ( Rlag h obsrvd ad d ubrs of dahs d ad h log-llhood fuo (7 wh h obsrvd ad d ubrs of dahs h rs of lag rrors d ad w hav log L J L L { d L log( γ{ β z } γ{ β z } } (33 L βˆ ad β ~ do h au llhood sas of β basd o { d } ad { d L L } rsvly Th sor quao ~ (9 a b wr as J Λ ( β β [ d Δ { Λ ( β ~ d }( Δ ] 0 (34 ~ ssug ha Δβ β βˆ s sall a frs ordr aso ~ of { Λ ( β} aroud βˆ gvs ˆ ( ~ Λ { } ~ { ˆ } { ˆ Λ β Λ Λ } Δβ (35 β whr Λˆ Λ ( βˆ ad Λˆ / β s Λ / β valuad a β ˆβ Subsug (35 o (34 lads o J Λˆ [ d { Λˆ } ] β J Λˆ β Δ d γ{ β ˆ z } Δ ˆ { ˆ Λ γ β z } ~ Δβ 0 (36 β ˆ { ˆ Λ γ β z } Δ Δβ β Usg (9 h frs suao (36 s zro osquly s Δ Δβ s sall Δ β ay b aroad by Λˆ ˆ Λ ~ { ˆ Δβ } γ β z β β Λˆ { Δd { ˆ γ β z } Δ } (37 β I follows fro (37 ha ~ Λ [ ] { ˆ Λ Λ E Δβ } γ β z α (38 β β β whr α E[ Δd ] γ{ˆ β z } E[ Δ ] whh a b alulad fro (5 ad (9 Furhr ~ Λ Λ [ ] { ˆ V Δβ γ β z } β β Λ Λ Θ β β Λ Λ { ˆ γ β z } (39 β β wh L Sass aada aalogu o -00-XIE

27 Survy Mhodology Ju Θ ov[ Δ d γ{ β ˆ z } Δ Δ d { ˆ γ β z } ] Δ whh a also b asly obad usg (6 (0 ad ( 8 (3 I h sal as of h ullav rs odl (4 h dffr Δ β du o lag rrors ay b aroad by Δβ ( X W X X ( Δ D ΔW ~ (40 whr X ( z z J ΔD ( Δd Δd JJ W dag(( z ˆ ( ˆ β z J β J ad ΔW (( z ˆ ( ˆ β Δ z J β ΔJ o ha h wgh ar W s h Fshr forao ar for ˆβ I follows fro (38 ha ~ ( Π E [ Δβ] X W X X (4 whr Π ( J wh bg sa as α bu γ { β ˆ z } rlad by ( z β ˆ Furhr ~ ( Ψ ( V [ Δβ] X W X X X X W X (4 whr Ψ s h ar of Θ s wh γ { β ˆ z } rlad by ( z β ˆ o ha (40 (4 ar sal ass of ( 37 (39 rsvly wr ar oao Wh a sgl ovara β ˆ z X W X X ΔD d ad Δ βˆ X W Δ I hs as Δβ ~ Δ d βˆ βˆ Δ S h β ˆ SMR d / Δ SMR/SMR hs as w hav Δβ ~ Δ d d Δ (43 wh Δ β (44 Thus (44 ay b vwd as a sal as of ( Th rdg rsuls da ha boh fals osvs ad fals gavs wll rodu bas ad addoal varao o h sas of rlav rs rgrsso arars Th oly gav orbuo o hs addoal vara (39 s hrough ov[ Δ Δd ] gv by d (8 ad h frs r (3 (s Θ Usg h sa argu as so 4 follows ha hs addoal vara s srly osv 5 olusos Rord lag s ow a wll-sablshd hqu dologal suds of oulao halh rss y lg forao o dvdual osurs fro o daabas o forao o halh ouos aohr daabas s ossbl o osru larg-sal forav daabass o rss o halh of oulaos ad oulao subgrous Th suss of suh suds wll dd o a larg o h qualy of h wo daabass bg ld ludg h aou of forao o dvdual dfrs usd o l dvduals h wo daabass I os suds h auray of h lag s ad by sag h fals l (fals osv ad fals ol (fals gav ras assoad wh h lag ross I ra hs s usually do by drawg a sal of ld ad old rords ad drg h auray of h lags h sal usg aulary forao draw fro ohr sours lhough RL has b usd for so ohor oraly suds h a of lag rrors o h rlably of sasal frs draw fro suh suds has o b subd o dald vsgao Th horal rsuls rsd hs ar addrss hs ssuths rsuls show ha addo o flag h obsrvd ubr of dahs fals osvs wll d o dfla h d ubr of dahs ovrsly fals gavs fla h d ubrs of dahs ad dfla h obsrvd ubr of dahs Lag rrors wr show o rodu bas o sas of SMRs Rlav rs rgrsso offs ar also sub o bas h dro of whh dds o h aur of h rgrsso off I addo o hs bass lag rrors rodu addoal uray o sas of boh SMRs ad rgrsso offs lhough w a h slfyg assuo of 0 o a drv h rlva rssos for bas ad rasd varably whou hs assuo; howvr h rssos ar oo ol o offr addoal sgh o h ffs of lag rrors Ths s also ru of h assuo ha Thr s a hal ssu wh h dfo of for h sa(s orrsodg o h las ag rval whh s usually o u o o h rgh 0 had sd I suh sa(s h assuo ha wll b robla f h robably of dyg hs las rval s arabl Ths robl ay b ruvd by assug h hua lf sa o hav a f ur l s dsussd a h d of so 3 fals osvs our rarly wh a dvdual who s alv a h d of h follow-u rod s orrly ld wh a dad rso Howvr a rso who dd o of h sas S ay b falsly ld wh aohr rso wh a arlr dah Ths lads o a fals osv whh rsss ul h aual of dah; h aalyss so 3 allows for hs y of rror Slarly a dad rso ay b falsly ld wh aohr rso dyg a a lar who s o alv a h d of follow-u Ths as s rad as a fals gav oly u o h fals dah hs fals of dah hs wll orbu orrly o h ubr of Sass aada aalogu o -00-XIE

28 0 Krws Dwa Wag arl Zls ad Mall: Th Eff of Rord Lag Errors o Rs Esas dahs a rror whh has o b osdrd so 3 Howvr hs y of rror would o orally b dd yal rord lag suds whh a slfd aual h s usd o dfy fals osvs ad fals gavs S hs y of rror s lly o b rar h ff s d o b sall I ordr o furhr lor h oal a of lag rrors l τ b h ur ag l for h h sa S (o ha so of h τ s ay b qual Th lg α do h robably of a lag rror (of hr y h fals osv ad gav ras ad ay b wr as α [ T τ ] ad α [ T > τ ] rsvly I arular α τ < T τ ] whr τ s h [ lowr ag l for h h sa ad Thrfor h fals osv ras ay b grar ha h fals gav ras h oldr ag grous wh h rvrs hag h yougr ag grous ssug a slar ar h sz of h D s ad s so allao of rs ay a la h alulao of E[ Δ ] (9 ad E[ Δ d ] (5 Ths allao ff wll rdu h d bas h SMR ad h rlav rs rgrsso arars gv (3 ad (38 rsvly lhough w hav osdrd oly all-aus oraly hs arl aus-sf oraly a b ad by sl odfaos of h dfos of D L D ad D Ths ss should h osdr oly hos dahs fro h sf aus of rs osquly d ad should do rsvly h obsrvd ad d ubr of dahs of h sf y S Th hazard fuo ( ad ( should rla o h sf y of dah wh λ *( u bg h orrsodg basl aussf hazard ra Fally h daor δ so should da h sf y of dah Whl h rdg aalyal rsuls shd osdrabl lgh o h ffs of lag rrors ohor oraly suds s ora o vsga suh ffs udr odos as los as ossbl as ay b ourd ra To hs d w odud a our sulao sudy basd o aual daa fro h aoal Dos Rgsry of aada whh h roduo of fals ls ad fals ols wh ow robabls hav b usd o furhr valua h a of lag rrors o sas of ar rs (Mall Krws Dwa ad Zls 00 Ths sulao rsuls orrobora h horal fdgs of hs ar Whl h rsuls rord hr ay hl o larfy h a of lag rrors o sasal fr hods ha a suh rrors o aou h sasal aalyss ra o b dvlod Suh hods ay b basd o rsos rror odls loyd survy salg usd ouo wh radoal sasal hods for aalyss of ohor oraly daa Rsarh hs ara s udrway 6 owldgs Ths rsarh was suord ar by a gra fro h aoal S ad Egrg Rsarh oul of aada o D Krws who urrly holds h SER/SSHR/MLaughl har oulao Halh Rs ssss a h Uvrsy of Oawa rlary vrsos of hs ar wr rsd a h ual Jo Mg of h ra Sasal ssoao Sa Fraso ugus ad h ual Mg of h Sasal Soy of aada Moral July Th fal draf was rsd h ssso hoour of JK Rao a h Sass aada Syosu 00 hld Oawa o Oobr 8 00 Th frs auhor (D Krws s arularly graful o hav b vd o sa h ssso hoour of JK Rao who srvd as hs dooral hss survsor ay yars ago Ths wor was old whl Dwa was a Vsg Sholar a h MLaughl r for oulao Halh Rs ssss h sur of 00 ad 003 Rfrs drso TW (974 Iroduo o Mulvara Sasal alyss w Yor: Joh Wly & Sos I rdal S ad Es S (00 Daa dvs: Uovrg sysa rrors adsrav daabass rodgs: Syosu 00 hvg Daa Qualy a Sasal gy: Mhodologal rsv Sass aada Oawa shor J- ad Groga D (985 Th aoal dos rgsry of aada Radao roo Dosry shor J- ad Davs D (989 Th aoal dos rgsry: ralzd rord g sys for radao worrs aada I laos of our Thology o Radao roo IE-SR-36/58 J Sha Isu Lublyua shor J- Krws D ad Zls JM (997 roool for a ohor oraly sudy of ouaoal radao osur basd o h aoal dos rgsry of aada Euroa Joural of ar 33 S0-S shor J- Krws D Zls JM Jag H Sw R ad Léourau E (998 Frs aalyss of ouaoal radao oraly basd o h aoal dos rgsry of aada ra Joural of Edology arl S Krws D Wag Y ad Zls JM (993 Evaluao of rror ras larg sal ourzd rord lag suds Survy Mhodology 9 3- l TR ad Rub D (99 R dvlos albrag rror ras for our ahg rodgs of h 99 ual Rsarh ofr US urau of h sus rslow E Lub JH ad Lagholz (983 Mullav odls ad ohor aalyss Joural of h ra Sasal ssoao 78 - Sass aada aalogu o -00-XIE

29 Survy Mhodology Ju 005 rslow E ad Day E (987 Sasal Mhods ar Rsarh Vol : Th Dsg ad alyss of ohor Suds IR sf ublao o 8 raoal agy for rsarh o ar Lyo Fra arr M ad Far ME (Eds (990 aada Edology Rsarh ofr 989: rodgs of Rord Lag Sssos & Worsho Oawa Sl rg Oawa o DR (97 Rgrsso odls ad lf abls (wh dsusso Joural of Royal Sasal Soy Far ME (989 Suds ad Rfrs Rlag o Uss of h aada Moraly Daa as Ror fro h ouaoal ad vroal halh rsarh u Halh Dvso Sass aada Oawa Fllg I ad Sur (969 hory for rord lag Joural of h ra Sasal ssoao Hll T (988 Gralzd Irav Rord Lag Sys: GIRLS Sragy (Rlas 7 Ror fro rsarh ad gral sys foras srvs ad dvlo dvso Sass aada Oawa How GR ad Ldsay J (98 gralzd rav rord lag our sys for us dal follow-u suds ours ad odal Rsarh How GR ad Sasoff R (Eds (986 rodg of h Worsho o ourzd Lag Halh Rsarh Uvrsy of Toroo rss Toroo Jorda-Sso D Far ME ad olqu (990 aada far oraor sudy: Mhodology Halh Rors 4-55 Kalbflsh JD ad r RL (980 Th Sasal alyss of Falur T Daa w Yor: Joh Wly & Sos I Labossèr G (986 ofdaly ad ass o daa: Th ra a Sass aada rodgs of h Worsho o ourzd Rord Lag Halh Rsarh Uvrsy of Toroo rss Toroo Mall R Krws D Dwa ad Zls JM (00 sulao sudy of h ff of rord lag rrors ohor oraly daa rodgs of Iraoal ofr R dvas Survy Salg arlo Uvrsy Oawa o aar r J Mays ES ad Raaaha R (965 Th ff of sahg o h asur of rsos rrors Joural of h ra Sasal ssoao wob H (988 Hadboo of Rord Lag: Mhods for Halh ad Sasal Suds dsrao ad usss Oford Mdal ublaos Oford Roos LL Sood R ad Jbaa L (00 foraorh vro: Ld-rord syss ad daa qualy aada rodgs: Syosu 00 hvg Daa Qualy a Sasal gy: Mhodologal rsv Sass aada Oawa Shur F ad Wlr WE (993 Rgrsso aalyss of daa fls ha ar our ahd Survy Mhodology Shur F ad Wlr WE (997 Rgrsso aalyss of daa fls ha ar our ahd ar II Survy Mhodology Sgh Fdr M Dua G ad Yu F (00 rog ofdaly whl rsrvg qualy of ubl us ro daa rodgs: Syosu 00 hvg Daa Qualy a Sasal gy: Mhodologal rsv Sass aada Oawa Sh ME ad Sls J (98 Gralzd rav rord lag sys Soal Sass So rodgs of h ra Sasal ssoao 8-37 So W Zls JM shor J Jag H Krws D Far ME ad ad Léourau E (00 Frs aalyss of ar d ad ouaoal radao osur basd o h aoal dos rgsry of aada ra Joural of Edology Wlr WE ad Shur F (99 How our ahg rror ff rgrsso aalyss: Eloraory ad ofraory aalyss Thal ror Sasal rsarh dvso US urau of h sus Washgo D Sass aada aalogu o -00-XIE

30

31 Survy Mhodology Ju Vol 3 o 3-40 Sass aada aalogu o -00-XIE alyss of Ers Ebddd ol Salg Dsgs Ja va d ral ad Robbr H Rss bsra aoal sasal sus rs bddd ogog sal survys ar odud oasoally o vsga ossbl ffs of alrav survy hodologs o sas of f oulao arars To s hyohss abou dffrs bw sal sas du o alrav survy laos a dsg-basd hory s dvlod for h aalyss of olly radozd dsgs or radozd blo dsgs bddd gral ol salg dsgs For boh ral dsgs dsg-basd Wald sass ar drvd for h Horvz-Thoso saor ad h gralzd rgrsso saor Th hory s llusrad wh a sulao sudy Ky Words: Dsg-basd aalyss; Masur rror odls; robably salg; Radozd rs; Suroso Iroduo ar of survy hodology s o osdr ad s alrav survy hods o rov h qualy ad ffy of sal survy rosss a aoal sasal sus Larg-sal fld rs bddd ogog survys ar arularly arora o quafy h ff of alrav survy laos o rsos bhavor or sas of f oulao arars Sass hrlads for al h ffs of alrav qusoar dsgs dffr aroah srags or dffr adva lrs hav b vsgad o boh ds of arars s Va d ral ad Rss (998 Va d ral (00 ad Va d ral ad Va rl (00 aoal sasal sus sal survys ar grally uhagd as log as ossbl ordr o osru urrud srs of sas of oulao arars I s vabl howvr ha survy rosss ar adusd fro o Ebddd rs a b ald o d ad quafy ossbl rd dsruos hs srs du o ssary hags o a sal survy ad rovd a saf raso fro a old o a w survy dsg Rug h old ad w survys ourrly by as of a bddd r ras h ossbly of fallg ba o h old aroah for rgular ublao uross f h w aroah urs ou o b a falur laos of bddd rs h lraur ar ad a h sao of h bas or h varous vara oos oal asur rror odls Mahalaobs (946 rodud h da of bddg rs ogog sal survys robably for h frs as rrag subsalg o s rvwr dffrs udr sl rado salg ad ursrd radozao of salg us o rvwrs Fllg (964 ad Harly ad Rao (978 gralzd hs aroah o sa rsos varas udr or ol salg dsgs ad rsrd radozao of salg us Fbrg ad Taur ( dsuss h dffrs ad arallls bw h hory of ral dsgs ad f oulao salg ad how h sasal hodology loyd boh flds a b obd a usful ad aural way h dsg ad aalyss of bddd rs I hr 988 arl hy gv a orhsv ovrvw of alaos of bddd rs od h lraur Th yal suao osdrd hs ar s a fld r dsgd o oar h ff of K dffr survy laos h ras o h a sas of h f oulao arars of a urr survy To hs d a robably sal ha s draw fro a f arg oulao s radoly dvdd o K subsals aordg o a ral dsg Eah subsal s assgd o o of h K ras Th ral dsgs osdrd hs ar ar olly radozd dsgs (RD s ad radozd blo dsgs (RD s whr salg sruurs l sraa rary salg us (SU s lusrs or rvwrs ar oal blo varabls Grally o larg subsal s assgd o h rgular survy whh wll b usd for offal ublao uross ad whh wll sulaously srv as h orol grou h r Th uros of bddd rs s h sao of f oulao arars udr h dffr survy laos ad o s hyohss abou h dffrs bw sas of hos arars frs sa a sadard odl-basd aroah gh b osdrd for hs aalyss S ral us ar Ja va d ral ad Robbr H Rss Sass hrlads Dar of Sasal Mhods O o Z Hrl Th hrlads

32 4 Va d ral ad Rss: alyss of Ers Ebddd ol Salg Dsgs draw by as of a ol salg dsg whou rla fro a f oulao h alao of suh a aroah gh rsul dsg-basd arar ad vara sas Ths as h aalyss rsuls osura wh h arar ad vara sas of h ogog survy whh olas h rrao of h rsuls h dsg-basd sg of h sal survy To a h aalyss or robus o darurs fro h assud odl a dsg-basd aalyss ha aous for h salg dsg should b ald for w rs our dsg-basd aroah wo alravs ar od ha a frs gla s o b orr W brfly argu howvr ha boh alravs grally gv vald rsuls Th frs alrav s o aly a dsg-basd lar rgrsso aalyss ha aous for h salg dsg o sa ad s hyohss abou h K ra ffs h rgrsso odl Ths aroah asly rsuls howvr wrog dsg varas s h radozao of h ral dsg s gord Th a aalyss obv of bddd rs s o oar h ff of alrav survy aroahs o h a sas of h urr sal survy lar rgrsso aalyss dos rsly hs obv s h ra ffs h rgrsso odl ar grally o qual o h dffrs bw h subsal sas Th sod alrav s o aly a dsg-basd fr for oarg doa arars whh h K ras ar osdrd as K doas Th obv of a bddd r howvr s o oar sas of h sa arar udr dffr survy srags or ras whras h as of doa arars h obv s o oar sas of dffr oulao arars udr basally h sa survy sragy Th aroah rsd hs ar a b suarzd as follows asd o h K subsals a dsg-basd saor for h oulao arar obsrvd udr ah of h K ras ad a dsg-basd saor for h ovara ar of h K orass bw hs sas ar drvd Ths sao rodur aous for h robably sruur of h salg dsg h rado assg of salg us o ras du o h ral dsg ad h wghg rodur ald h ogog survy for h sao of arg arars Ths gvs rs o a dsg-basd Wald sas o s h sad hyohss abou dffrs bw sal survy sas Th a orbuo of hs ar s o rovd a gral frawor for oarg K alrav survy aroahs h rals suao of a full-sal sal survy ross Th rado slo of salg us fro a f arg oulao by as of a robably sal s usd obao wh radozao of h salg us ovr dffr ras aordg o a ral dsg Ths falas oarso of alrav survy laos o h a ouos of a sal survy ad h gralzao of h obsrvd rsuls o oulaos largr ha h sal ludd h r Th aalyss rodur roosd hs ar gralzs h aalyss of wo-ra rs bddd sal survys (Va d ral ad Rss (998 ad Va d ral ad Va rl (00 o RD s ad RD s wh K > ras ora rsul s ha h dsg-basd saor for h ovara ar of h orass bw h subsal sas has a rlavly sl sruur as f h salg us wr draw wh rla ad uqual slo robabls s a rsul hr o luso robabls or dsgovaras bw h subsal sas ar rqurd h vara sao rodur Ths rsuls a arav ad rlavly sl aalyss rodur sod advaag s ha hs rodur ss hyohss o dffrs bw h sal sas of h survy whh falas h rrao of h aalyss rsuls ay alaos dsg-basd hory for h aalyss of bddd rs s rsd so I so 3 s lad or dal why h dsg-basd lar rgrsso aalyss s lss arora I so 4 h roosd dsg-basd aalyss rodur s valuad a sulao sudy olusos ar suarzd so 5 alyss of Ebddd Ers Masur Error Modls lhough h aalyss rodur for bddd rs roosd hs so s dsg-basd so us s ad of asur rror odls Tsg sysa ffs of dffr survy hodologs o h ouos of a survy ls h s of asur rrors Th radoal oo ha obsrvaos obad fro salg us ar ru fd valus obsrvd whou rror grally assud dsg-basd salg hory s o abl suh suaos Thrfor a asur rror odl s sfd for h obsrvaos obad udr h dffr survy laos or ras of h r Ths odl ls h ra ffs o sysa dffrs bw f oulao arars osdr a f oulao U of dvduals L varabl y l do h oal rsos of h h dvdual ( K obsrvd by as of h h h ra ( K K ad h l rvwr ( l K L I s assud ha hs obsrvaos ar a Sass aada aalogu o -00-XIE

33 Survy Mhodology Ju ralzao of h asur rror odl y l u β ψ l ε Hr u s h ru rs valu of h h h dvdual β h ff of h ra ψ l h ff of h l h rvwr o h h dvdual ad ε a rror oo of h h dvdual obsrvd by as of h h ra Th rvwr ff ψ l allows for sysa lusrg ad orrlao bw h rsoss of h dvduals assgd o h sa rvwr du o fd ad rado rvwr ffs ψ l ψl ξl wh ψ l h fd ad ξ l h rado ff of h l h rvwr sds rvwrs oo faors suh as odrs ad survsors gh also du orrlao bw h rsoss of h dvduals S for ah salg u a oal rsos varabl s dfd for ah of h K dffr ras h asur rror odl a b rssd ar oao as y l u β ψ l ε ( whr y y K y β ( β K β ε l K ( l Kl ( ε K ε ad ( K L E ad ov do h ao ad h ovara wh rs o h asur rror odl Th followg odl assuos ar ad: E ( ε 0 ( ov ( ε ε : O : K (3 E ( ξ l 0 (4 τl : l l ov ( ξ l ξl (5 0 : l l ov ( ε ξl 0 (6 whr 0 s a vor of ordr K wh ah l zro ad O a ar of ordr K K wh ah l zro If ψ l 0 h a odl wh oly rado rvwr ffs s obad If τ l 0 h a odl wh oly fd rvwr ffs s obad Fro h assuos follows ha E ( y l u ψ l β (7 ad ov ( y l y l τl : τl : O : ad ad ad l l l l (8 l l y orrlao bw h rsoss of dffr dvduals a b odld by as of rado rvwr ffs y fd rvwr ffs flu h d rsos valus Fro ow o for oaoal ov h subsr l wll b od y l ad y l Hyohss Tsg Th asur rror odl for h obsrvaos obad h r abls us o rla sysa dffrs bw oulao arars o h dffr survy laos Suos ha L rvwrs ar avalabl for h daa ollo Th oulao U of sz a oually b dvdd o L grous U l of sz l l K L suh ha all dvduals wh a grou ar oally rvwd by h sa rvwr L Y ( Y Y K Y K do h K dsoal vor of oulao as of y Y ε (9 L L l l u β ψ l ξl l l Th obv of h r s o vsga whhr hr ar sysa dffrs bw h K oulao as of Y du o h K dffr survy srags or ras Ths a b aolshd by forulag hyohss abou E L l ( Y u ψl β l (0 whr h ao s a ovr h asur rror odl Ths gvs rs o h followg hyohss: H H 0 : E : E Y 0 Y 0 ( whr dos a ( K K ar wh K orass ad 0 a K vor of zros S 0 follows ha E Y β ad hyohss ( ors h ra ffs as rrsd by β h asur rror odl ( Th orass bw h oulao arars aly orrsod o hs ra ffs For h radozd rs osdrd hs ar holds ha ah ral u assgd o a rvwr l has a ozro robably of bg assgd o ah of h K ras Thrfor h bas h arar sas du o fd rvwr ffs s h sa udr ah of h K ras ad als ou h K orass bw h K arar sas Hyohss ( wll b sd by sag E Y sad of β ag o aou h salg dsg h ral dsg ad h wghg rodur of h ogog survy ald for h sao of oulao arars To s ( a robably sal draw fro a f oulao s avalabl Th salg us (ral us ar radozd ovr K subsals ad ar assgd o o of h K ras I so 3 a Sass aada aalogu o -00-XIE

34 6 Va d ral ad Rss: alyss of Ers Ebddd ol Salg Dsgs dsg-ubasd saor for E Y dod Ŷ s drvd For al Ŷ ay b h Horvz-Thoso saor or h gralzd rgrsso saor L V do h ovara ar of Ŷ (aroaly dsgubasd saor for h ovara ar of h K orass of Ŷ dod ˆ V wll b drvd so 4 ow hyohss ( a b sd by as of h followg dsg-basd Wald sas: ˆ ( ˆ W Y V Yˆ ( For ahaal ov w rfr h oras ar ( M I whr s a K vor of os ad I h ( K ( K dy ar 3 Esao of Tra Effs 3 Horvz-Thoso Esaor osdr a sal s draw by a grally ol salg dsg ha a b dsrbd by h frs ad sod ordr luso robabls ad of h h h ad salg u(s rsvly I h as of a RD sal s s radoly dvdd o K subsals s K of sz If dos h ubr of salg us s h h odoal robably ha h h salg u s sld subsal s gv ha sal s s sld s qual o / I h as of a RD h salg us ar odoally o h ralzao of s drsally dvdd o J blos s oal blo varabls ar salg sruurs l sraa lusrs SU s rvwrs ad h l Wh ah blo h salg us ar radozd ovr h K ras L do h ubr of salg us K blo assgd o ra Th J dos h sz of blo dos h sz K J of subsal s ad dos h sz of sal s Th odoal robably ha h h salg u s sld subsal s gv ha sal s s sld ad s s qual o / Eah subsal s a b osdrd as a wo-has sal whr h frs ordr luso robabls of h frs has sal ar obad fro h salg dsg ad h odoal frs ordr luso robabls of h sod has sal ar obad fro h ral dsg Fro hs o of vw h frs ordr luso robabls for h ls of s ar qual o * ( / for RD s ad * ( / for RD s f h hs salg u s assgd o h h blo I follows ha h Horvz-Thoso saor for Y basd o h obsrvaos obad fro subsal s a b dfd as: ; HT * Yˆ y y (3 whr ar K vors ha dsrb h radozao has of h ral dsg For a RD follows ha r f s (4 0 f s ad for a RD r f s (5 0 f s whr r dos h u vor of ordr K wh h h l qual o o ad h ohr ls qual o zro ad 0 dos a K vor of zros rors of h vors ar gv h ad ow s s a b osdrd as a wo-has sal holds ha E ˆ se ( Y ; HT s Y whr E s ad E do h ao wh rs o h sal dsg ad h ral dsg rsvly So gv h vor Y ˆ ( Y ˆ Yˆ HT ; HT K K ; HT s roosd as a dsgubasd saor for Y u h Ŷ HT s ubasd for E Y 3 Th Gralzd Rgrsso Esaor I f oulao salg s usoary o ras h auray of h Horvz-Thoso saor f suabl aulary forao s avalabl by as of h gralzd rgrsso saor s g hlh ad Kllr (987 ad Särdal Swsso ad Wra (99 Th gralzd rgrsso saor abls us o orora h wghg sh of h ogog survy h aalyss of bddd rs Ths gh dras h dsg vara as wll as h bas du o slv orsos ad hrfor ay ras h auray of h r I h rs o h gralzd rgrsso saor hrfor rrss a dsg-basd aalogu of ovara aalyss sadard ral dsg hodology sds h valus of h rsos varabl y w also assoa wh ah u h oulao a H vor of aulary forao Th f oulao as of hs aulary varabls ar assud o b ow ad ar dod by X I s also assud ha h aulary varabls ar rs valus ha a b obsrvd whou asur rrors ad so ar o affd by h ras Wh h odl asssd aroah of Särdal al (99 s followd h rs valus u h asur rror odl of so for ah u h oulao ar assud o b a dd ralzao of h followg lar rgrsso odl: Sass aada aalogu o -00-XIE

35 Survy Mhodology Ju u (6 whr s a H vors oag h rgrsso offs ad h ar h rsduals I h odl asssd aroah of Särdal al (99 h rs valus u ar osdrd o b a ralzao of a udrlyg suroulao odl dfd by (6 I hs as h rsduals ar dd rado varabls wh a vara ω Th s rqurd ha all ω ar ow u o a oo sal faor; ha s ω v ω wh v ow Fro a srly dsg-basd o of vw roosd by hlh ad Kllr (987 hr s o d o ado a suroulao odl I ha as h rsduals ar fd rs valus of h ls h f oulao ad o odl assuos abou h rsduals ar dd I hs ar h odl asssd aroah of Särdal s adod Ths ls ha aos wh rs o h asur odl as (7 ad (0 ar odoal o h ralzao of h rs valus u K h f oulao aordg o h suroulao odl (6 Th rgrsso offs of h lar odl (6 h f oulao ar dfd as u b (7 ω ω Th rs valus u ar o obsrvabl du o asur rrors ad ra ffs osquly (7 ao b oud v h as of a ol urao of h f oulao I h as of a h ol urao udr h ra ~ y b K K (8 ω ω dos h f oulao rgrsso offs of h lar odl (6 odoal o h ralzao of u K h ao of h f oulao rgrsso offs b ~ wh rs o h asur rror odl s gv by ~ ( u β ψl Eb b ω ω K K (9 Th f oulao rgrsso offs b ~ ad b a b sad usg h sal daa fro subsal s wh h Horvz-Thoso saor: b ˆ ω * y ω * K K ow h gralzd rgrsso saor for Y basd o h obsrvaos of subsal s s dfd as Yˆ ˆ ˆ Y b ( X Xˆ K (0 ; grg ;HT HT K whr ˆX HT dos h Horvz-Thoso saor for h oulao as of h aulary varabls X basd o h salg us of subsal s Wh rssg (0 as a fuo of ( Y ˆ ˆ ˆ ; HT b XHT h gralzd rgrsso saor a b aroad by as of a frs ordr Taylor larzao abou ( E Y b X whr b s dfd (9 Ths gvs: ˆ ˆ ˆ ˆ Y & Y b ( X X E b X K ; grg ;HT HT ;HT K wh ˆ ˆ ˆ ( ; HT ;HT HT y E Y b X s ad whr s a H K ar of whh h olus ar h H vors b ow Y ˆ ( Y ˆ Yˆ GREG ;grg K K ;grg s roosd as a aroaly dsg-ubasd saor for E Y 4 Vara Esao of Tra Effs L V do h ovara ar of Y ˆ GREG To sa h ovara rs of V vors y oag h obsrvaos of all K ras obad fro ah salg u ar rqurd S h ral dsgs udr osdrao ah salg u s assgd o o of h K ras oly o of h oos of y for s s aually obsrvd osquly a dsgubasd saor for V ao b drvd Va d ral ad dr ( rd o ovro hs robl by ug h uobsrvd oos Th usfulss of hr rsuls howvr dds o h orrss of h uao odl I h rs ar hs robl s ruvd by drvg a dsg-basd saor for V h ovara ar of h orass of Y ˆ GREG whh s suff for h Wald sas ( Erssos for h gralzd rgrsso saor ar drvd frs Rsuls for h Horvz-Thoso saor ar gv as a sal as Th ovara ar of h orass of Ŷ GREG a b aroad by h ovara ar of h orass of ˆ ˆ ˆ E ( E K L HT ; HT E K ; HT ov s ad ov do h ovaras wh rs o h sal dsg ad h ral dsg rsvly ow osdr h followg vara dooso: V ove se E ov E ( Eˆ s HT ( Eˆ HT s s E E ov ( Eˆ s HT s ( Sass aada aalogu o -00-XIE

36 8 Va d ral ad Rss: alyss of Ers Ebddd ol Salg Dsgs S E ( r (s (4 h ad follows ha E ˆ ( y ( HT E s ( s Udr h odo ha a osa H vor a ss suh ha a for all U s rov h ad ha y ε (3 ( Th sad odo lly assus ha h sz of h f oulao s ow ad s usd as aulary forao Ths odo holds for wghg odls ha oa a r or o or or agoral varabls ha aro h oulao o suboulaos Usg odl assuos ( ad (3 follows fro ( ad (3 ha ad ov E E ( Eˆ E ov E ( Eˆ s s HT εε HT s ov ε s E ( (4 (5 For h hrd r ( s rov h ad for a RD ha E E ov ( Eˆ whr D s a d J ( y b s HT s E E ( D (6 K K dagoal ar wh dagoal ls ( y b J S E (7 If h rsuls obad (4 (5 ad (6 ar srd ( h follows ha V E E D (8 odoally o h ralzao of ad s a aroaly dsg-ubasd saor for D (8 a b drvd Thrfor V a ovly b sad lly as h ao ovr h asur rror odl ad h salg dsg S Va d ral (00 for l rssos for V Gv h ralzao of s ad s h alloao of h salg us wh ah blo o h subsals s a b osdrd as sl rado salg whou rla fro blo s osquly for a RD follows ha a aroaly dsg-ubasd saor for D s gv by a K K dagoal ar Dˆ wh dagoal ls dˆ J ˆ ( y b ( y bˆ J Sˆ E (9 aroaly dsg-ubasd saor for V (8 s gv by ˆ D Rsuls for a RD follow drly as a sal as fro (7 ad (9 whr J ad s a alrav h rsduals ˆ ( y b (9 a b ulld by h orro wghs (also alld g wghs Särdal al 99 rsul 66 S V (8 s dfd lly as h ao ovr h salg dsg (9 s aroaly dsg-ubasd udr gral ol salg shs Ths vara saor oly rqurs ha h frao of salg us assgd o h dffr ras aordg o h ral dsg s fd adva Th sz of h sal as wll as h blos gh b rado wh rs o h sal dsg g h as of a RD whr lusrs or SU s ar h blo varabl Th vara saor D ˆ has a sruur as f h K subsals had b draw ddly fro ah ohr whr h salg us ar sld wh uqual robabls ( / wh rla h as of a RD or ( / wh rla wh ah blo h as of a RD (oar (9 wh ohra 977 quao (96 I s rarabl ha h sod ordr luso robabls of h salg dsg hav vashd Ths s ausd by: Th assuo of addv ra ffs h asur rror odl β for all U obsrvd udr ra Th assuo ha asur rrors bw dvduals ar dd rorly hos wghg sh suh ha h odo a for all U s sasfd 4 Th fa ha varas ar alulad for h orass bw h subsal as Th dsg vara of h frs-ordr Taylor srs aroao of h gralzd rgrsso saor osss of h rsduals ( y b Fro h roof of (3 follows ha udr a wghg sh ha sasfs h odo Sass aada aalogu o -00-XIE

37 Survy Mhodology Ju a for all U h ra ffs β vash fro h rsduals ( y b (3 I hs rsduals hr rs ra: Th rsdual of h lar rgrsso odl of h rs valu u b r org h bas du o h rvwr ffs Ths r s qual o ψ l d whr d dos h rgrsso offs fro h rgrsso fuo of h rvwr ffs o h aulary varabls (s roof of (3 h ad 3 Th asur rrors ε Th rsduals of h rs valus ad h bas du o h rvwr ffs do o dd o h dffr ras ad hrfor al ou h orass of h rsduals (3 Oly h asur rrors ε ra h orass of h rsduals (3 s a rsul h wo rs ov ˆ E se( EHT s ad E ˆ ovse ( EHT s oly oa h asur rrors ε Du o h assuo of dd of h asur rrors bw dvduals h ross rodus bw dvduals whh oa h sod ordr luso robabls (4 ad (5 vash Th ovara sruur of h hrd r of ( s aly drd by h radozao has of h ral dsg For a RD hs os dow o h slo of K subsals fro s by as of sl rado salg whou rla For a RD hs os dow o h slo of K subsals fro s by as of srafd sl rado salg whou rla whr sraa orrsod o h blos of h r I h vara of h orass of h subsal as h f oulao orros h dsg vara of h subsal as al ou agas h dsg ovara bw h subsal as s a rsul h ladg r of (6 EEsD has a sruur as f h K subsals wr draw ddly of ah ohr by as of sl rado salg wh rla h as of a RD or srafd sl rado salg wh rla h as of a RD Sod ordr luso robabls aar f h ao wh rs o h salg dsg (8 s ad l s Va d ral (00 Th u us of aulary forao s a wghg sh whr ( ad ω ω for all U Udr hs wghg sh follows ha Yˆ y ; grg * * ~ y (30 whh a b rogzd as h rao saor for a oulao a orgally roosd by Há (97 I also follows ha b ˆ ( ~ ad ha a aroaly y dsg-ubasd saor for h ovara ar of h ra ffs s gv by (9 wh ˆ b ~ y * If / ˆ h h rao saor (30 orrsods wh h rgular Horvz-Thoso saor Ths odo s sasfd h as of a RD or a RD bddd a sl rado salg dsg a RD bddd a srafd sl rado salg dsg whr sraa ar usd as blo varabls or a RD bddd a srafd sl rado salg dsg wh rooroal alloao Udr h odo ˆ rssos for h dsg vara of h Horvz- Thoso saor ar gv by (7 ad (9 whr y b ad y bˆ ar rlad by y Vara rssos for h Horvz-Thoso saor ar or olad f ˆ s Va d ral (00 5 Th Wald Ts Isrg h dsg-ubasd saors for h subsal as ad h ovara ar of h orass bw hs subsal as o ( lads o h dsg-basd Wald sas ˆ ( ˆ W Y D Yˆ (3 GREG GREG I s rov h ad ha hs rsso a b slfd o: ˆ ˆ ;grg ;grg ˆ ˆ K Y K Y W (3 d K d ˆ d For gral salg shs h asyo dsrbuo of hs s sas wll b uow Howvr f h salg dsg s sl rado salg whou rla ad h ral dsg s a RD h Lha (975 ad 8 basd o h wor of Há (960 gvs suff odos udr whh Ê HT s asyoally ulvara oral dsrbud wh a E ˆ ~ E s E ( HT s E ad ovara ar V ov s E ˆ ˆ s ( E HT s Es ov ( EHT s f ad ~ ( ˆ : ( EHT ( E V H ( E ˆ HT ~ ( E V wh E ( / ε S h ε ar uually dd rado varabls wh as qual o zro ad ovara ar w hav by h ordary ral l hor ( E ( 0 (/ obg boh l dsrbuos w oba ha uodoally Ê HT (0 V ad hus ˆ YGREG ( β V s a rsul follows udr h ull hyohss ha W s asyoally h-squard dsrbud wh K dgrs of frdo (Sarl 97 hor har For or ol salg dsgs s usually ourd ha Sass aada aalogu o -00-XIE

38 30 Va d ral ad Rss: alyss of Ers Ebddd ol Salg Dsgs ˆ YGREG ( β V Th W s sll asyoally h-squard dsrbud wh K dgrs of frdo Th valdy of hs our has b ofrd by sulao suds s so 4 ad Va d ral (00 6 oold Vara Esaors I h as of a RD h salg us of s ar dvdd o JK grous of sz For ah of hs JK subsals sara oulao varas ˆ S E hav o b sad If h ubr of ral us avalabl for h sao of hs oulao varas bos oo sall h hs sas gh bo usabl I suh suaos or sabl sas a b obad by oolg sas of h oulao varas wh h blos Th rsduals of h gralzd rgrsso saor ( y b oly dd o h h ra ff hrough h asur rrors ε Udr h assuo ha σ I (3 for all U follows ha h S E wh ah blo ar dal arars S E K S E S K E for K J Udr hs assuo s ff o us a oold saor for S ; Sˆ E ; ( or alravly Sˆ E ; ˆ ( y b ( K K ˆ ( y b K K ˆ ( y b ˆ ( y b E (33 (34 Thr ar svral sal ass whr h dsg-basd Wald sas ods wh h F sass ow fro or sadard odl-basd aalyss rodurs osdr a RD bddd a slf-wghd salg dsg whr salg us ar alload rooroally o h ras ovr h blos / ad / / for all K J Th follows fro h rsuls obad for h rao saor (30 ha Yˆ ; grg / y y ad ˆ b y Do y K / y ad y / y h follows ha K K y y y K y K K y bˆ y If h follows udr h oold vara saor (33 ha dˆ J J K ˆ y b K ( y K y ˆ y b dˆ y y (35 Do y / y Udr h oold vara saor (34 follows ha dˆ J J K ˆ y b K ( y K y ˆ y b dˆ (36 Subsug hs oold vara saors o h Wald sas (3 lads o W K ( ( ˆ y y (37 d a whr dˆ s gv by hr (35 for a or (36 for a a I a b rogzd ha W /( K (37 wh d ˆ h oold vara saor (35 orrsods wh h F sass of a OV for a wo-way layou whou raos If d ˆ (36 s srd h W /( K orrsods wh h F sass of a OV for a wo-way layou wh raos (Shffé 959 har 4 oold vara saor for a RD follows as a sal as fro (35 ad (36 Udr boh saors follows ha W /( K orrsods wh h F sass of h o-way OV (Shffé 959 har 3 7 dvaags of RD s Th a advaag of RD s s h lao of h varao bw h blos h aalyss of ra ffs Salg us fro h sa srau SU or lusr grally hav a hghr dgr of hoogy oard wh salg us fro dffr sraa SU s or lusrs Ths suggss usg salg sruurs l sraa SU s or lusrs as blo varabls a RD (Fbrg ad Taur Usg hs salg sruurs as a blo varabl a RD surs ha ah srau SU or lusr s suffly rrsd wh Sass aada aalogu o -00-XIE

39 Survy Mhodology Ju ah subsal lso rvwrs ar oal blo varabls s hs las h varao h obsrvaos du o fd or rado rvwr ffs sfd asur rror odl ( For survys whr rvwrs oll daa by as of I srad gograhal aras blog o rvwrs also las hs rgoal varao fro h arg varabl Th owr of a r s azd f salg us ar alload rooroally o ras ovr h blos / / for all K J (s Va d ral 00 har 6 Ths alloao s br rsrvd f rvwrs ar usd as h blo varabls s rsos ras bw rvwrs dffr subsaally Ursrd radozao by as of a RD s o always fasbl fro a raal o of vw For al I survys whr rvwrs oll daa gograhal aras surroudg hr las of rsd rsrd radozao of salg us wh rvwrs or gograhal rgos whh ar uos of ada rvwr rgos gh b rqurd o avod a uaabl ras h ravl dsa of h rvwrs Ths aurally lads o RD s wh rvwrs or rgos as blo varabls 3 Dsg-asd Lar Rgrsso alyss dsg-basd lar rgrsso gh b osdrd as a alrav for h aalyss of bddd rs Th obsrvaos ar assud o b h ouo of a lar rgrsso odl y wh h vor oag Q laaory varabls h vor oag h rgrsso offs ad a rsdual Ths odl s aly drd by h ral dsg ad oas h ra faors loal orol faors (g blos ad ovaras as laaory varabls (s g Mogory 00 oal ovaras ar h aulary varabls h wghg sh of h gralzd rgrsso saor Th arars of rs ar h rgrsso offs h f oulao whh ar dfd by β ( X X X y whr X s h Q dsg ar of h ral dsg ad y a vor oag h obsrvaos obad udr h dffr ras as f h r f oulao s ludd h r Th dsg ar oually dvds h oulao o K suboulaos or doas whh ar obsrvd udr ah of h K ras of h r Th sz of ah suboulao s drd by h frao of salg us assgd o ah ra h r dsg-basd saor for h rgrsso offs s gv by ˆ β ( Χ Π Χ XΠ y (Särdal al 99 so 50 Hr X s h Q dsg ar y a vor oag obsrvaos obad udr h dffr ras of h us ludd h sal ad Π a dagoal ar oag h frs ordr luso robabls of h salg dsg Th aroa ovara ar of βˆ s gv by (Särdal al 99 so 50 Var(ˆ β ( X X Λ( X X - (38 wh Λ Vars ( XΠ y XΠ Xβ Th ls of Λ ar gv by q q λqq ( q q K Q U U wh y β Hyohss abou h subs of rgrsso offs ha rfl h ra ffs ar sd wh a Wald s s g Sr (989 Th aor drawba of hs aroah s ha h sao rodur dos aou for h rado assg of salg us o ras aordg o h ral dsg I dog so h subsal sas ar rroously rad as f hy wr doa sas whh rsuls wrog dsg-varas Th ovara ar of h ra ffs (8 drvd so 4 llusras ha h suroso of h ral dsg o h salg dsg drs whh sf faurs of h salg dsg ar ullfd or rsrvd For al h ff of srafd salg or wo-sag salg o h vara of h ra ffs s ullfd udr a RD Ths ff howvr s gord by h lar rgrsso aroah s Var(ˆ β oly aous for h vara of h sal dsg Dsrgardg h ral dsg h vara sao rodur bos v or obvous udr a ol urao of h f oulao Du o h ral dsg h r f oulao s radoly dvdd o K subsals ad h arars udr h dffr ras ar sll sad wh a ozro dsg vara I hs suao follows for h lar rgrsso aroah ha β ˆ β ad ha Var(ˆ β s qual o zro baus h dsg-vara dud by h ral dsg s gord Ths orass wh (8 ha udr a ol urao sll rfls h dsg-vara du o h ral dsg I s o daly vd how h lar rgrsso aroah a b adusd o allow for h radozao du o h salg dsg as wll as h ral dsg odoally o h ralzao of h sal h ral dsg a b dsrbd by frs ad sod ordr luso robabls L s do h frs ordr luso robably ha h h salg u s assgd o h h ra ad l s do h sod ordr luso robably ha h salg u s assgd o h h h ra ad h salg u s assgd o h h ra dsg-basd saor for β ha aous for h salg dsg ad h ral Sass aada aalogu o -00-XIE

40 3 Va d ral ad Rss: alyss of Ers Ebddd ol Salg Dsgs ˆ dsg s gv by β ( XΠ X XΠ y whr Π dos h dagoal ar wh frs ordr luso robabls s aroao for h ovara ar of βˆ s gv by (38 whr Λ s obad by odog o h ralzao of h sal Λ Var E ( X Π y X Π X β E Var ( X Π s s y X Π X β Ths lads o h followg rsso for h ls of Λ : q q λ qq ( U U q q ( s s s U U whh has h vara sruur of a wo-has sal whr h frs has orrsods o h salg dsg ad h sod has o h ral dsg Th salg us ar aordg o h ral dsg assgd o oly o of h K ras s a rsul follows ha s 0 for ad whh hars h drvao of a aroaly dsg-ubasd saor for h ovara rs of Var(β ˆ s also Va d ral ad dr ( I h aalyss rodur roosd so hs robl s ruvd by drvg a dsg-basd saor for h ovara ar of h orass of ŶGREG sad of a saor for h ovara ar of Ŷ slf GREG 4 Sulao Sudy I subso 4 a sulao sudy s odud o valua h rfora of h dsg-basd saor for h ovara ar of h orass bw h subsal sas D ˆ wh dagoal ls (9 as wll as h dsg-basd Wald sas W dfd by (3 o s hyohss abou hs orass Subsquly hs dsg-basd Wald s h dsg-basd lar rgrsso aroah ad a sadard OV ar ald o h aalyss of a RD ad a RD subso 4 4 Evaluao of h Ubasdss of Dsrbuo of W D ˆ ad h I hs sulao sudy a asur rror odl whou rvwr ffs s assud y β ε (39 u arfal oulao ossg of 3 sraa 450 SU s ad SSU s s grad by radoly drawg srly osv valus for h rs valus u of a arg arar Th szs of h SU s h oulao ar uqual Th rs valus ar grad wo ss Frs a osv valu for ah SU h oulao s draw fro a ufor dsrbuo Subsquly a osv valu for ah SSU also draw fro a ufor dsrbuo s addd o h valu obad for h SU h frs s Wh ah srau dffr lowr ad ur boudars ad rval-wdhs for hs ufor dsrbuos ar ald suh ha h oulao a b srafd o hr rlavly hoogous suboulaos Th rvals of h ufor dsrbuos ha ar ald h sod s ar sallr ha h rvals of h ufor dsrbuos h frs s Ths rsuld a oulao whr h rs valus for h SSU s wh ah SU ar lusrd Th sruur of h oulao s suarzd Tabl Tabl oulao Irs valu of arg arar Srau ubr of SU s ubr of SSU s Ma Sd dv M valu Ma valu Toal Sals ar draw radly fro hs oulao by as of srafd wo-sag salg whou rla wh uqual luso robabls Th luso robabls ar hos rooroally o h sz of h arg arar Th sal szs for h dffr sraa ar suarzd Tabl For ah sal a w asur rror s grad for ah oulao l Ths asur rrors ar draw fro a oral dsrbuo wh a a qual o zro ad a sadard dvao rooroal o h sz of h rs valus Th rag of h sadard dvaos vard fro 000 for h SSU s wh h largs rs valus h frs srau o 0 for h SSU s wh h salls rs valus h hrd srau Tabl Sal Dsg Srau ubr of SU s ubr of SSU s Toal Fally h sals ar radoly dvdd o four subsals aordg o a ral dsg ah wh a sz of 945 SSU s Two dffr ral dsgs ar ald I h frs dsg h SSU s ar radozd ovr h four dffr ras aordg o a RD I h sod dsg h SSU s ar radozd ovr h four dffr ras aordg o a RD whr h hr sraa ar usd as h blo varabl Wh ah blo or srau /4 of h SSU s ar radoly assgd o ah ra Udr boh ral dsgs four dffr Sass aada aalogu o -00-XIE

41 Survy Mhodology Ju ss of ra ffs ar ald o udr h ull hyohss ad hr udr dffr alrav hyohss Ths rsuld gh dffr sulaos whh ar sfd Tabl 3 Eah sulao s basd o R rsals Obsrvaos for h arg arar ar obad by addg a asur rror ad a ra ff o h rs valus aordg o (39 Tabl 3 Suary of Sulao Sgs Tra ffs Eral dsg β β β 3 β 4 RD RD RD RD RD RD RD RD Th daa obad ah rsal ar aalyzd wh h r dd Horvz-Thoso saor (30 L y~ do h h subsal sa obad udr h ra h h r rsal Th vor wh h four subsal h sas obad h r rsal s dod by Y ~ r ~ r ~ r ~ r ( ~ r y y y3 y4 Th vor wh h hr orass h h ~ r r rsal s qual o Y wh ( M I a vor of ordr 3 wh ah l qual o o ad I h 3 3 dy ar Furhror dˆ r dos h dagoal ls of h sad ovara ar obad udr h h r rsal rsso for dˆ r s gv by (9 r wh b ˆ ~ y Th sad ovara ar of h ra ffs s qual o ˆ D r r wh Dˆ ˆ r ˆ r ˆ r ( ˆ r r ~ r dag d d d3 d4 Fally ( ( ˆ r W Y D ~ r ( Y dos h Wald sas obsrvd h r h rsal asd o h R rsals wh ah sulao h oulao arars udr h dffr ras a b aroad by R r Y Y ~ R r wh Y ( Y Y Y3 Y4 Fro (0 follows ha h ral ra ffs h asur rror odl a b aroad by Y β Furhror h a of h sad rsal ovara ars a b alulad as R ˆ r D D R r ad h a of h rsal Wald sass as R r W W (40 R r aroao of h ral ovara ar of h ra ffs s gv by R ~ r ~ r V ( Y Y ( Y Y (4 R r Th rfora of h vara sao rodur s valuad by oarg D o V If h drvd vara saor D ˆ s aroaly dsgubasd h h a of rsal ovara ars D us d o h ral ovara ar V for R rsso of h rso of h drvd vara saor s obad by alulag h sadard dvao of h ls of D ad s dod by σ ( D Th dagoal ls of D ar dod d If ˆ YGREG ( β V h follows ha W χ[ ][ ] K δ wh K h ubr of dgrs of frdo ad δ / ( β ( V ( β h oraly arar of h h-squard dsrbuo I h sulao sudy h o-raly arar udr h alrav hyohss a b alulad by srg (4 h rsso of δ Subsquly h owr of h Wald sas for a arular s of ra ffs a b alulad by ( ( W χ[ ][ ] [ ][ ] K δ > χ α K whr h χ[ α ][ K ] dos h ( α rl o of h ral h-squard dsrbuo wh K dgrs of frdo Th rfora of h Wald sas s valuad by oarg (W wh h sulad owr whh s dfd as h frao of sgfa rus obsrvd h R rsals R s r ( W I ( W > χ[ α ][ K ] R r whr I ( dos h daor varabl whh s qual o o f s ru ad qual o zro ohrws Th rsuls of h sulaos ar suarzd Tabls 4 hrough 48 Th as of h subsal sas Y udr h ull hyohss Tabls 4 ad 45 slghly ovrsa h oulao a Tabl Ths dffr a b arbud o h bas of h dd Horvz-Thoso saor Th as of h orass bw h subsal sas Y howvr alos rfly agr wh h ral ra ffs β Th as of h rsal ovara ars D d o h valus of h ral ovara ars V whh llusras ha h vara sao rodur drvd so 4 s aroaly dsg-ubasd Th rlav rso of h dagoal ls of D s abou 05% udr hs arular sal sz Th sulad owr basd o h rsal dsrbuo of h Wald sas aroas h ral owr rasoably wll O h avrag h sulad owr s slghly hghr Th d valu of h hsquard dsrbuo s qual o E( χ[ K ][ δ] ( K δ (Sarl 97 so 4h If h rsal dsrbuo of h Wald sas ds o a χ[ ][ ] K δ h h a of h rsal Wald sass W (40 us d o h d valu of h h-squard dsrbuo Idd follows fro Tabls ha W (K δ Morovr h Sass aada aalogu o -00-XIE

42 34 Va d ral ad Rss: alyss of Ers Ebddd ol Salg Dsgs hyohss ha h rsal dsrbuo of h Wald sas udr h ull hyohss s qual o h ral hsquard dsrbuo s sd wh h o-sal Kologorov-Srov s Ths hyohss s o rd a a sgfa lvl of 5% for hr h RD or h RD ad ofrs h our ha h Wald sas s asyoally h-squard dsrbud udr srafd wosag salg whou rla uqual luso robabls ad rlavly larg salg fraos If h sulaos udr a RD ar oard o a RD h follows ha blog o sraa rsuls a subsaal ras of h rso of h sad orass ad h owr of h ss hs arular suao Tabl 4 Sulao Rsuls RD β ( Subsals orass Wald sas β Y d Dagoal ls of α (W s ( W Y V D σ ( D W : δ : Tabl 4 Sulao Rsuls RD β ( Subsals orass Wald sas β Y d Dagoal ls of α (W s ( W Y V D σ ( D W : δ : Tabl 43 Sulao Rsuls RD β ( Subsals orass Wald sas β Y d Dagoal ls of α (W s ( W Y V D σ ( D W : δ : Tabl 44 Sulao Rsuls RD β ( Subsals orass Wald sas β Y d Dagoal ls of α (W s ( W Y V D σ ( D W : δ : 03 Tabl 45 Sulao Rsuls RD β ( Subsals orass Wald sas β Y d Dagoal ls of α (W s ( W Y V D σ ( D W : δ : Sass aada aalogu o -00-XIE

43 Survy Mhodology Ju oarso of Thr alys rodurs Furhror hr ossbl aalyss rodurs for bddd rs ar oard h dsg-basd Wald s roosd so a sadard OV whr all obsrvaos ar qually wghd ad assud o b d ad h dsg-basd lar rgrsso aroah dsrbd so 3 To hs d wo sals ah wh a sz of 3780 SSU s ar draw fro h f oulao sfd Tabl by as of h srafd wo-sag sal dsg whh was also usd h rvous sulao (s Tabl For o sal h SSU s ar radoly dvdd o four subsals ah wh a sz of 945 by as of a RD For h ohr sal h SSU s ar radoly dvdd o four subsals ah wh a sz of 945 by as of a RD whr h sraa ar usd as h blo varabls oh rs ar odud udr h alrav hyohss whr h ra ffs h f oulao ar qual o β ( Th dsg-basd lar rgrsso aalyss s rford wh Saa s SVYREG rodur ha aous for h srafao wo-sag salg ad h uqual slo robabls of h salg dsg (Saaor 00 Th OV s rford wh Saa s ΑΝΟVΑ rodur (Saaor 00 Th aalyss rsuls udr a RD ar suarzd for h dsg-basd Wald s Tabl 5 for h dsg-basd lar rgrsso aroah Tabl 5 ad for h OV Tabl 53 Slarly h aalyss rsuls udr a RD ar suarzd Tabls 6 6 ad 63 s haszd so 3 h lar rgrsso aroah gors h dsg vara du o h radozao of h salg us ovr h subsals wh rs o h ral dsg s a rsul h sadard rrors of h ra ffs ar sallr udr h lar rgrsso aroah ha h as of h dsg-basd Wald s ad h dsg-basd rgrsso aroah rsuls sallr -valus for h s of ra ffs Tabl 46 Sulao Rsuls RD β ( Subsals orass Wald sas β Y d Dagoal ls of α (W s ( W Y V D σ ( D W : δ : 0 36 Tabl 47 Sulao Rsuls RD β ( Subsals orass Wald sas β Y d Dagoal ls of α (W s ( W Y V D σ ( D W : 5 68 δ : 905 Tabl 48 Sulao Rsuls RD β ( Subsals orass Wald sas β Y d Dagoal ls of α (W s ( W Y V D σ ( D W : δ : 5 33 Tabl 5 Dsg-basd Wald Sas RD Subsals orass Wald sas β y~ y ~ y d d W df valu Sass aada aalogu o -00-XIE

44 36 Va d ral ad Rss: alyss of Ers Ebddd ol Salg Dsgs β Tabl 5 Dsg-basd Rgrsso RD Sour off Sd rr Wald sas df valu ra ra ra ra osa Tabl 53 Sadard OV RD y oras OV 0 80 y y Sour df MS F valu w ras Rsdual Toal 3779 β Tabl 6 Dsg-basd Wald Sas RD Subsals orass Wald sas β y~ y ~ y d d W df valu Tabl 6 Dsg-basd Rgrsso RD Sour off Sdrr Wald sas df valu lo lo lo Tra Tra Tra Tra osa Tabl 63 Sadard OV RD y oras OV y y Sour df MS F valu w blos 6773 E w ras Rsdual Toal Th sadard OV s a av aroah s gors h srafao lusrg ad slo of salg us usg luso robabls ha ar hos rooroal o h valu of h arg arar Th rsul of gorg hs ass of h salg dsg h aalyss s a svr ovr-sao of h subsal sas as wll as h sadard rrors oard o h ohr wo dsg-basd rodurs hs rsuls largr -valus for h s of ra ffs ohr ora advaag of h dsg-basd Wald s oard o h dsg-basd lar rgrsso aroah s ha h Wald s always ors h dffrs bw h subsal sas whh fala h rrao of h rsuls Ths rory s arularly ora for bddd rs ad a h quafao of rd dsruos h arars of a survy du o aduss h survy dsg I h as of a RD h lar rgrsso odl osss of o r arar ad hr offs for h ra ffs I Sass aada aalogu o -00-XIE

45 Survy Mhodology Ju hs arularly sl suao h offs for h ra ffs ar aly qual o h dffrs bw h subsal sas Ths rory howvr dos hold for h ra ffs obad udr or olad odls as for al h as of h RD 5 Dsusso ad olusos I hs ar w dsuss how h sasal hodology of radozd rs ad rado survy salg a suor h dsg ad aalyss of rs bddd ogog sal survys Th sal survy dsg fors a ror frawor for h alao of rls ow fro h hory of ral dsgs l radozao ad loal orol by as of blog o sraa SU s lusrs or rvwrs To s hyohss abou h sas of f oulao arars obsrvd udr dffr ras of h r a dsg-basd Wald sas for h aalyss of RD s ad RD s bddd gral ol salg dsgs s drvd usg h Horvz-Thoso saor ad h gralzd rgrsso saor Th alao of radozd salg fro a f oulao obao wh hs dsg-basd aalyss rodur abls us o gralz h rsuls of h r obsrvd h sf sal o h r survy oulao S w allow for gral ol salg dsgs a rahr olad rsso for h ovara ar of h ra ffs wh ozro off-dagoal rs s d Th drvd saor for hs ovara ar howvr has a sruur as f h salg us wr draw wh rla ad wh uqual slo robabls o sod ordr luso robabls or dsg-ovaras bw h ra ffs ar rqurd whh slfs h aalyss osdrably For al h as of sl rado salg whou rla hs rsul als ha h f oulao orro faor should b dsrgardd sag h vara of orass s a rsul a Wald sas drvd fro a dsgbasd rsv udr gral ol salg dsgs s obad ha sll has h aalg rlavly sl sruur of sadard odl-basd aalyss rodurs For RD s ad RD s bddd a slf-wghd salg dsg aalyzd wh h dd Horvz- Thoso saor ad a oold vara saor h Wald sas ods wh h F sas of a OV for h o-way ad wo-way layous For h aalyss of h bddd wo-ra r a dsg-basd vrso of h sas a b drvd as a sal as of h Wald sas Erssos ad or dals abou hs dsg-basd sas ad s rlaosh wh Wlh s sas ad h sadard sas a b foud Va d ral ad Rss (998 Va d ral (00 or Va d ral ad Va rl (00 Th aalyss rodur roosd hs ar s ld a sofwar aag alld X ool Ths ool wll bo avalabl as a oo of h las survy rossg sofwar aag dvlod by Sass hrlads d rors of h radozao vors For RD s ad RD s h radozao vors ar dfd by (4 ad (5 s a osqu of h radozao has of h ral dsg h vors ar rado wh h followg odoal robably ass fuos For a RD w hav r s ad ( 0 s For a RD w hav r s ad ( 0 s rors of hs vors ar drvd for a RD rors for a RD follow as a sal s a RD a b osdrd as a RD wh o blo L w r do wh robably r r w r: f s O w r: rr w r: 0 f s O w r: O O r r r r w w w w r: r: r: r: f s s ( f s s ( f s s f s s Sass aada aalogu o -00-XIE

46 38 Va d ral ad Rss: alyss of Ers Ebddd ol Salg Dsgs Sass aada aalogu o -00-XIE s s s s s s s s f r: w f r: w f ( ( r: w f ( ( r: w O r r O r r Th ao of wh rs o h ral dsg s gv by: ( ( E r 0 0 r r (4 Th followg ovaras wh rs o h ral dsg a b drvd: r r ( ( ov (43 r r ( ov (44 s s s s ad f ad f ( ( ov O r r (45 s s s s ad f ad f ( ( ( ov O r r (46 roof of forula (3 Udr h sad odo ha a osa H vor a ss suh ha a for all U ad odoal o h ralzao of u K aordg o suroulao odl (6 follows ha b ~ (8 a b valuad as ( ~ ( l u y E E β β ω ψ ω ω ω a d b a b (47 whr b dos h rgrsso offs dfd by (7 ad d dos h rgrsso offs fro h rgrsso fuo of h rvwr ffs o h aulary varabls Fro rsul (47 follows ha ( β d b S 0 ad fro asur rror odl ( ad lar rgrsso odl (6 follows ha ( ( ( QED ε β d b ε β y l u ψ roof of forula (6 for a RD Frs a rsso for ˆ ( ov HT s E s drvd L K ( K do a K vor wh ls y b osquly y o ha s s s s E E ˆ ( ov E E ˆ ( ov E E HT HT wh ˆ ˆ ( ˆ HT K; HT ; HT E E K E Fuhror o ha ( ˆ HT ; E y (48 Usg (43 ad (46 h dagoal ls of ˆ ( ov HT s E a b laborad as ( ( ( ov ( ov ov ˆ ( Var HT ; J J s s s s E (49 Usg (44 ad (45 h off-dagoal ls of ˆ ( ov HT s E a b laborad as ( ( ov ( ov ov ˆ ˆ ( ov HT ; HT ; J J s s s s E E (50

47 Survy Mhodology Ju Sass aada aalogu o -00-XIE Th rsuls (49 ad (50 a b wr ar oao; J s HT ˆ ( ov y y y y D E whr D dos a K K dagoal ar wh ls J y y d b b ordg o (3 follows ha ˆ ( ov HT J s ε ε ε ε D E (5 Th fal ar of h roof s o a h ao of ˆ ( ov HT s E wh rs o h salg dsg ad h asur rror odl Th roof s gv for RD s whr SU s ar blo varabls I a wo-sag salg sh J blos or SU s ar draw fro a f oulao of u J blos wh frs ordr luso robabls I Wh ah SU SSU s ar draw h sod sag wh frs ad sod ordr luso robabls II ad II Th frs ordr luso robabls of h dvduals h sal ar II I Furhror l ε Δ do h oulao a of h asur rrors of h dvduals of blo Th II ˆ Δ ε dos h Horvz-Thoso saor for Δ ow w hav ( ( ˆ ˆ Δ Δ Δ Δ Δ Δ II II I J J ε ε ε ε ε ε (5 L I s E do h ao wh rs o h frs sag of h salg dsg ad II s E h ao wh rs o h sod sag of h salg dsg Tag h ao wh rs o h asur rror odl ad h salg dsg of h frs ar of (5 ad usg odl assuo (3 lads o II II I J s s II I Δ Δ E E E ε ε E E II I II I J s I Δ Δ ε ε (53 o ha s II ˆ ( ˆ ( E Δ Δ Δ Δ (5 quals h dsg vara of Δˆ wh rs o h sod sag of h salg dsg blo Tag h ao wh rs o h asur rror odl ad h salg dsg of h sod ar of (5 ad usg odl assuo (3 lads o ( ( ( E ˆ ˆ E E E II I II II II II II I I J s s II I Δ Δ Δ Δ ε ε (54 Wh rsuls (5 (53 ad (54 w a labora h sod r o h rgh had sd of h qual sg of (5 as E E J s ε ε ε ε (55

48 40 Va d ral ad Rss: alyss of Ers Ebddd ol Salg Dsgs Fally follows fro (5 ad (55 ha E E ov ( Eˆ s s HT EEsD QED Th drvao for a RD whr sraa ar blo varabls follows drly as a sal as fro a RD I II whr SU s ar blo varabls wh II ad J J u Th roof for a RD whr lusrs ar blo varabls follows drly as a sal as fro a RD whr SU s ar blo varabls wh II ad II Th ao of ov ˆ ( EHT s wh rs o h salg dsg ad h asur rror odl for a RD whr rvwrs ar h blo varabls dos o follow as a sal as fro a RD whr SU s ar blo varabls S h blo varabls ar o drly ld wh h salg dsg h blos should b osdrd as doas whr h blo sz s rado wh rs o h salg dsg Th drvao follows h sa ss as h roof for blog o SU s ad s gv by Va d ral (00 roof of forula (3 Mar Dˆ a b arod as follows: ˆ ˆ d 0 D ˆ 0 D* ordg o arl s dy (Morsso 990 har follows ha: ˆ ˆ ˆ ˆ ( ( ˆ ˆ D d D* D* D* D* ra( ˆ D Fro hs rsul follows ha ˆ ˆ ˆ ( ˆ D D* D* D* ra( ˆ D ˆ ˆ ˆ D D D ra( ˆ D Isrg (56 o (3 lads o (3 QED owldgs (56 Th auhors wsh o ha h ssoa Edor h rfrs aul Sh ad Rahl Vs-Vsshrs for hr osruv os o forr drafs of hs ar Ja also has rof Sh E Fbrg ad rof r Kooa for hr suor as h D advsor durg hs rsarh Rfrs hlh JG ad Kllr WG (987 Lar wghg of sal survy daa Joural of Offal Sass 3( 4-53 ohra WG (977 Salg Thqus w Yor: Joh Wly & Sos I Fllg I (964 Rsos vara ad s sao Joural of h ra Sasal ssoao Fbrg SE ad Taur JM (987 Eral ad salg sruurs: arallls dvrgg ad g Iraoal Sasal Rvw 55( Fbrg SE ad Taur JM (988 Fro h sd ou ad h ousd : obg ral ad salg sruurs Th aada Joural of Sass 6( 35-5 Fbrg SE ad Taur JM (989 obg ogv ad sasal aroahs o survy dsg S Há J (960 Lg dsrbuos sl rado salg fro a f oulao Mahaal Isu of h Hugara ady of Ss Há J (97 o o a ar by D asu I Foudaos of Sasal Ifr (Eds V Godab ad D Sro Toroo: Hol Rhar ad Wso 36 Harly HO ad Rao JK (978 Esao of osalg vara oos sal survys I Survy Salg ad Masur (Eds K aboodr w Yor: ad rss Lha EL (975 oarars: Sasal Mhods asd o Ras w Yor: MGraw-Hll Mahalaobs (946 R rs sasal salg h Ida sasal su Joural of h Royal Sasal Soy Mogory D (00 Dsg ad alyss of Ers w Yor: Joh Wly & Sos I Morsso DF (990 Mulvara Sasal Mhods Sgaor: MGraw-Hll Särdal -E Swsso ad Wra JH (99 Modl sssd Survy Salg w Yor: Srgr Vrlag Shffé H (959 Th alyss of Vara w Yor: Joh Wly & Sos I Sarl SR (97 Lar Modls w Yor: Joh Wly & Sos I Sr J (989 Doa as rgrsso ad ulvara aalyss I alyss of ol Survys (Eds J Sr D Hol ad TMF Sh hhsr: Wly & Sos I Saaor (00 Saa Rfr Maual Rlas 70 ollg Sao Tas Va d ral J (00 Dsg ad alyss of Ers Ebddd ol Sal Survys hd Thss Rorda: Erasus Uvrsy of Rorda Va d ral J ad dr D (000 Vara sao for rs bddd ol salg shs rodgs of h So o Survy Rsarh Mhods ra Sasal ssoao Idaaols ugus Va d ral J ad dr D (004 Vara sao for rs bddd ol salg dsgs Uublshd rsarh ar r: H TMO Hrl: Sass hrlads Va d ral J ad Rss RH (998 Dsg ad aalyss of rs bddd sal survys Joural of Offal Sass 4( Va d ral J ad Va rl M (00 dsgbasd aalyss rodur for wo-ra rs bddd sal survys alao h Duh labor for survy Joural of Offal Sass 8( 7-3 Sass aada aalogu o -00-XIE

49 Survy Mhodology Ju Vol 3 o 4-5 Sass aada aalogu o -00-XIE Doa Esaors for h I ou Thqu Taahro Tsuhya bsra Th ou hqu whh s a dr qusog hqu was dvsd o sa h rooro of ol for who a ssv y holds ru Ths s ahvd by havg rsods ror h ubr of dsrv hrass fro a ls of svral hrass ha hy blv aly o hslvs Th ls for half h sal luds h y ad h ls for h ohr half dos o lud h y Th dffr a ubr of sld hrass s a saor of h rooro I hs arl w roos wo w hods rfrrd o as h ross-basd hod ad h doubl rossbasd hod by whh rooros subgrous or doas ar sad basd o h daa obad va h ou hqu I ordr o assss h rso of h roosd hods w odud sulao rs usg daa obad fro a survy of h Jaas aoal harar Th rsuls llusra ha h doubl ross-basd hod s uh or aura ha h radoal srafd hod ad s lss lly o rodu llogal sas Ky Words: Idr qusog hqus; I ou hqu; Doa saors; Survy of Jaas aoal harar Iroduo Idr Qusog Thqus Suos ha a oulao U s dvdd o wo suboulaos U (T ad U ( T whr U (T s a s of ls havg a arbu T ad U ( T s a ol of U (T O uros of soal survys s o sa Y ( Y whr Y 0 f U (T ohrws ad ( dos h rooro of us havg a arular valu of h varabl For al wh T s suorg h rs ab das h ab suor ra ad wh T s usg a ra llgal drug dos h rval ra of drug us I a dr qusog hqu rsarhrs as rsods Do you blog o U (T? ad drly oba h daor valu y as ys or o (ohra 977 ag 50 Wh vry rsod has a qual luso robably a sal a y srvs as o saor of O h ohr had so dr qusog hqus ludg h radozd rsos hqu (Warr 965 h oav hqu (Mllr 985 h ou hqu (Droour asar Hubbard arsly Vsshr ad Ezza 99 ad h hr-ard hqu (Droour Larso ad Shur 00 ar dvsd baus so rsods d o vad ssv qusos suh as hos org hghly rva ars soally uad or dva bhavors or llgal as Th ssal faur of dr hqus s ha sad of a dr obsrvao of Y aohr varabl X g( Y V whh s so sor of fuo of Y ad f ssary of ohr rado varabls V s obsrvd so ha rsods fl ha hr ru Y valus ar o rvald Whl hs faur s d o drv a ruhful aswr fro vasv rsods boh h qusog ad h sao rodurs ar rahr olad oard o h dr qusog hqu arly baus h fuo g ( sos luds so radozao rosss W shall oul wo dr hqus blow Th radozd rsos s h os oular aog h dr hqus ad varous odfaos hav b roosd (bul-ela Grbrg ad Horvz 967; Warr 97; haudhur ad Mur 988; Grbrg bul-ela Sos ad Horvz 969; Taahas ad Saasgawa 977 lhough h radozd rsos s o h o of hs arl w shall brfly oul Warr s orgal rodur hr for rfr baus hs hqu wll b sulad a lar so rar wo ys of qusoars I qusoar rsods ar asd Do you blog o U (T? ad qusoar rsods ar asd Do you blog o U? ( T L ( 05 b h rdrd robably Eah rsod sls qusoar or wh robabls or rsvly bu o o ohr ha h rsod ows whh qusoar s sld Taahro Tsuhya Th Isu of Sasal Mahas Ma-zabu Mao-u Toyo Jaa E-al: aa@sa

50 4 Tsuhya: Doa Esaors for h I ou Thqu 3 Suos X s a daor varabl whos valu s f h rsos s ys or 0 f h rsos s o Th saor of s gv by ˆ whr s a sal a of X S h rsarhrs hav o forao rgardg h y of qusoar sld by ah rsod or rsods ar d o gv ruhful aswrs ha hy would f asd dr qusos Th ou hqu whh s h sub of hs arl s o as oular ds s sly Th hqu s also ffv wh osg ssv qusos baus rsods ar asd o o aswr ssv qusos drly bu o rly ror h ubr of s ha hold ru wh h Th followg ar h rosss of h ou hqu: rar h y T whh s h rary fous of h sudy ad G ohr o-y s E K EG For al T s usg a ra llgal drug as od abov ad E g s so sor of ossv dsro suh as owg a byl rar wo ys of qusoars ad I qusoar rsods ar asd o aswr h ubr of s ha ar ru wh rs o hslvs aog G o-y s I qusoar rsods ar asd o aswr h ubr of s ha ar ru wh rs o hslvs ou of G s ludg h y T ( Tabl lss als of lss Our a s o sa h rooro of ol who us a ra llgal drug Th y s usg a ra llgal drug h qusoar ad h ohr four s ar o-y s E wh a rsos o h qusoar s 0 or 5 rsarhrs ao d as o whh s hold ru wh h rsod For al a rsod wll rly ha four s h qusoar ar ru bu w ao b sur ha h rsod uss h drug a all H s d ha or rsods usg a llgal drug wll ror ruhful aswrs suh a saro ha wh asd a dr quso 3 Dvd a oal sal o wo subgrous ad radoly of sz ad so ha ah qusoar s assgd o a orrsodg subgrou Tabl Eals of I Lss Qusoar Qusoar How ay of h followg hold ru How ay of h followg hold for you? ru for you? owg a byl owg a byl havg ravlld abroad havg ravlld abroad havg alld a abula havg alld a abula owg a sur vlla usg a ra llgal drug owg a sur vlla 4 Th saor of s gv by ˆ ˆ ˆ ( whr Ĉ ad Ĉ ar h sad as of ad rsvly Th usfao of ( s lad so Wh vry u h sal has a qual luso robably ˆ a b wr as G G ˆ (3 0 0 whr ad ar h ubr of rsods whos aswrs ar ad rsvly Morovr wh a aulary varabl Z s avalabl ad s dsrbuo ( Z z z h oulao s ow for al fro a sus ossrafao s of usd o adus h sal dsrbuo of Z o h oulao Tha s h ossrafd saor of s gv by ˆ S G 0 G 0 z v z z z z z z G 0 G 0 z v z z z z z z (4 whr z s h ubr of rsods for ah ad Z z v z G z z z 0 z z z ad z z ad v z ar dfd aalogous ways O raal r of h ou hqu s ha dos o dad ay radozao dvs whh ar rqurd for h radozd rsos hqu I s o h rsod bu a rsarhr who sls h qusoar o b aswrd H h ou hqu s asly ld va ay slf-adsrd or lho survys or labora oarso bw h radozd rsos ad h ou hqu s foud Hubbard asr ad Lsslr (989 Sass aada aalogu o -00-XIE

51 Survy Mhodology Ju Th qusoar s rodud o oba h dsrbuo of h ubr of o-y s Tha s rsods o h qusoar do o aswr h ssv quso Thrfor s ossbl o ras h rso of h saor usg h doubl-ls vrso of ou (Droour al 99 whh hags h rols bw h wo subgrous Howvr w l our argu hs arl o a sgl-ls vrso baus h so of saors o h doubl-ls vrso s sraghforward uros of hs rl Thus far w hav fousd o h arar Y ( Y of a oal oulao Howvr saors suboulaos or doas (Särdal Swsso ad Wra 99 ag 5 ar of rqurd hr a odoal rooro ( Y Z z or a o rooro ( Y Z z us b sad whr a oulao s dvdd o svral doas by h Z valu W rfr o h varabl Z as h doa varabl hs arl Th doa varabls of usd ar dograh hararss suh as gdr or ag For al govr ags would l o ow h rooro of ol who us a ra llgal drug a ah ag grou Ev hough h ossrafd saor ˆ S (4 uss h doa varabl Z s a s a sao of ( Y h r oulao Our a hs arl s o oba sara saos of ( Y Z z wh ah doa O sl sao hod s as follows: os-srafy h sal o sraa or doas basd o h Z valu I ah srau or doa saraly dr ( Y Z z usg ( or ( whr ( s a sal sa of ( 3 If ssary sa ( Y Z z by ullyg a ow doa rooro ( Z z or a sad doa rooro ( Z z Th abov hod s rfrrd o hroughou hs arl as a srafd hod baus sas ar obad saraly ah srau or doa lhough Rao (003 rfrs o h abov hod as a dr sa w hav avodd h us of h r dr ordr o avod ofuso wh h r dr qusog hqu advaag of h srafd hod s ha hs hod s alabl o ay dr qusog hqu ludg h radozd rsos ad ou hqus Th US Gral oug Off (999 ados h srafd hod o sa doas udr h hr-ard hqu Howvr o of h srous robls of h srafd hod s ha of rodus llogal sas sally gav sas h as of h radozd rsos ad h ou as lad lar hs arl Ths s aly baus h rduo of h sal sz ah srau rass h sadard rrors of h saors (Lsslr ad O Rlly 997 For al Droour al (99 ag 06 alulad sas saraly for h hr rs sraa ad obad gav rval ra sas of drug us I h as of h radozd rsos hr s ll ossbly ha doa saors ohr ha h srafd hod ar dvlod baus forao org h y of qusoar sld by dvdual rsods s uavalabl I oras h ou hqu h qusoar aswrd by ah rsod s ow Thrfor h rso of h doa saors s d o ras wh aulary forao s usd sfally ogy abls bw Z ad or I hs arl w roos w doa saors for h ou hqu whh ar rfrrd o as h rossbasd hod ad h doubl ross-basd hod I addo w wll llusra h fa ha h w saors ar or ff ha h radoal srafd hod by sulag h ou hqu usg daa obad fro h survy of h Jaas aoal harar org h sgfa arbus of h Jaas harar Doa Esaors for h I ou Thqu Srafd Mhod Hr w rforula h srafd hod L us assu ha h followg quaos hold ru for ah valu of ad z ssuo ( Z z ( Y 0 Z z ( Y Z z ( G Y 0 Z z 0 Ths assuos ly ha h dffr h dsrbuo bw ad dds solly o Y Quso ffs ludg ordr ffs ad o ffs (Shua ad rssr 98 ar o osdrd W hav h followg rsul basd o hs assuos Srafd Mhod ( Y Z z G 0 G ( 0 ( Z z Z z (5 (6 z z Sass aada aalogu o -00-XIE

52 44 Tsuhya: Doa Esaors for h I ou Thqu whr z ad z ar h doa as of Drvao G 0 G ( 0 G 0 G 0 G 0 ( ( { ( 0 G ( ( Z z Y 0 Z z Y 0 Z z 0 Y 0 Z z ( Y Z z G 0 G ( ( ( Z z ( Y Z z ad Y Z z Y Z z Y Z z} Trasosg h frs r o h lf-had sd ylds h srafd hod (5 Th saor ( Y Z z s obad by subsug doa as z ad z wh hr saors Ĉ z ad ˆ z ˆ ( ˆ Y Z z z (7 Wh h luso robabls ar qual for all us h sal h saor of ( Y Z z s wr as ( Y Z z (8 G z 0 z z G z 0 z whr z z z ad z ar dfd h so Th quaos ( ad (3 for h r oulao ar sal ass of (7 ad (8 O r of h srafd hod s ha h vara saor of ( Y Z z s asly obad by ˆ Vˆ ar ( ( Vˆ ar ( Vˆ ar ( ˆ Y Z z z (9 O h ohr had as od h rvous so h rduo of sal sz ah srau rass sad varas (9 Furhr h argal saor ( Y obad by usg (8 dos o orrsod o ha obad drly by (3 ulss z z for all z Tha s wh ( Z z s o ow s saor s gv by ( Z z ( /( ad z G 0 z z ( Y Z z ( Z z z z z G 0 G z 0 z ˆ G z 0 z z (0 Wh h doa rooro ( Z z z s avalabl h argal saor orrsods o h ossrafd saor (4 ( Y Z z ( Z z z z ˆ S z G z 0 z G z 0 z Ths rsuls da ha w should us a ossrafd saor ˆ S wh h doa saors f w us h srafd hod ross-basd Mhod I h srafd hod a oal sal s dvdd o sraa for h uros of dr sao of ( Y Z z whh auss sal sz rduo H h ross-basd hod roosd hs so h o rooro ( Y Z z s sad frs ordr o us h r sal ad h odoal rooro s subsquly obad by ( Y Z z ( Y Z z ( Z z ( Y Z z or ( Y Z z ( Z z Th r ross-basd hod s usd baus hs hod uss ross abulaos ( Z z as show (9 For h ross-basd hod w assu ha h followg quaos hold for ah valu of ssuo ( Y ( Y ( 0 Y ( Y 0 ( ( ( Y 0 ( Y 0 (3 Ths assuos also ly ha h dffr h dsrbuo bw ad dds oly o Y W hav h followg rsul basd o hs assuos ross-basd Mhod whr G ( Y Z z ( Z z Q (4 Q d 0 { ( d ( d } I addo w assu ha ( Z z Y ( Z z for vry > 0 Ths assuo would b vald o so dgr wh boh h y ad oy s dsrb h sa y of sgazg bhavor Sass aada aalogu o -00-XIE

53 Survy Mhodology Ju Drvao asd o h assuos w hav ( ( ( Y ( Y ( Th followg quao holds for ay Y 0 Y 0 ( Y 0 ( ( Y H subsug (6 (5 gvs ( ( Y { ( ( Y } Sug (7 ovr u o so g w oba g 0 ( 0 g g 0 ( g 0 { ( ( Y ( ( y rasosg h rs w df Q Q { ( d 0 ( ( Y Y d ( Y } g Y d} (5 (6 (7 (8 Hr h o rooro ( Y Z z s doosd as G 0 ( Y Z z ( Z z ( Y (9 Subsug h quao (8 ad h assuo ( (9 ylds h ross-basd hod Th o saor ( Y Z z s obad by subsug ah r of (4 for s saors Wh h sal s slf-wghg h saor s gv by whr G z ( d d Y Z z (0 d 0 z ad z Th odoal saor ( Y Z z s obad by dvdg ( Y Z z by h doa rooros ( Z z or hr saors ( Z z s od abov h a faur of h ross-basd hod s ha ( Y Z z s frs sad usg h z z r sal H h vara of ( Y Z z for h ross-basd hod s d o b sallr ha ha of ( Y Z z for h srafd hod Morovr gav valus wll sldo b obad h as of h ross-basd hod whl h gav valus wll b of obad h as of h srafd hod Furhror h argal saor ( Y obad by sug (0 s qual o h saor (3 ulss 0 for so : z ( Y Z z G G G 0 d 0 d d G G 0 G z z d d ˆ d 0 G d d d d ( Of ours wh h doa rooros ( Z z z ar ow w a us h o oba a ossrafd saor ( d of ( d Q of (4 ( d I hs as z ( Y Z z ods wh h ossrafd saor ˆ S O drawba of h ross-basd hod s ha h vara of ( Y Z z s alos ossbl o sa algbraally H so rsalg hods suh as h af or boosra would b ssary ddoally s s ossbl o dr h or ff hod bw h srafd hod ad h ross-basd hod sulao suds shall b odud a lar so z 3 Doubl ross-basd Mhod for rodg o h sulao sudy w suggs a odfd vrso of h ross-basd hod I quao (9 of h ross-basd hod w us ( Z z I h sa way wh ( Z z s usd w oba ( Y Z z G 0 G 0 ( Z z ( Z z z z dz ( Q Y ( H a doubl ross-basd hod s obad by obg (4 ad ( as follows: G w ( Z z ( Y Z z Q (3 0 w ( Z z Sass aada aalogu o -00-XIE

54 46 Tsuhya: Doa Esaors for h I ou Thqu whr w ad w ar h o-gav wghs for ah subgrou h su of whh s qual o o Th followg quao also holds for h doubl rossbasd hod of ay w ad w ulss 0 or 0 for so 3 Daa S z ( Y Z z ˆ 3 ural Ers (4 I ordr o oar h rso of h saors w odud sulao rs usg daa obad fro h survy of h Jaas aoal harar (Saaoo Tsuhya aaura Mada ad Fous 000 lhough h rsods wr sld va a srafd wo-sag salg fro Jaas agd 0 ad ovr w gl h salg dsg baus h olld sal of 339 s rad as h ru oulao hs r Tabl lss h rsuls of a quso org h sgfa arbus of h Jaas harar Rsods wr asd a fa-o-fa rvw o hoos as ay advs fro aog alravs as hy hough dsrbd h Jaas harar Tabl Sgfa rbus of Jaas harar 339 (Had ard Whh of h followg advs do you h dsrbs h harar of h Jaas ol? hoos as ay as you l Raoal 8% 6 Kd 4% Dlg 7% 7 Orgal 7% 3 Fr 3% 8 ol 50% 4 O fra 4% 9 hrful 8% 5 rss 5% 0 Idals 3% Th for of hs quso s dffr fro ha of h ou hqu I h ou hqu h rsod s asd o aswr h ubr of advs I oras hs survy h rsod s asd o rl as ay advs you fl ar arora I addo h s ar o vry ssv h h rsods should o hsa durg h slo Howvr s h ral ogy abl bw ah of h s ad aohr varabl Z s obad w a valua h rfora of saors hrough a sudo ou rodur W oo ah of h followg hr s as h y Y whr Y ls ha h was sld 7 Orgal ( s h las aog h s 8 ol ( s us 50% Dlg ( s h largs aog h s Thr obaos of o-y s ar usd as lsd Tabl 3 obao orss wo s wh low rooros whl obao orss wo s wh hgh rooros obao 3 s h as wh h au ubr of o-y s Tabl 3 Thr obaos of o-y Is o-y s obao (G : 9 hrful 3 Fr (8% (3% obao (G : 5 rss 6 Kd (5% (4% obao 3 (G 9: s ohr ha h y W usd hr gdr or ag as h doa varabl Z Gdr s hr al or fal ad h ag agors ar ad 70 ad ovr 3 Dr Qusog Vrsus I ou Thqu 3 Sulao Mhods Frs w oar h sadard rrors bw h dr qusog ad h ou hqus I hs r w ad o obao of 7 Orgal (y obao 3 (o-y s ad gdr (doa varabl Th ogy abl basd o h r sal of 339 s lsd Tabl 4 Tabl 4 ogy Tabl w 7 Orgal ad Gdr 7 Orgal Y Y 0 Toal Mal 46 ( (95 65 (000 Fal 5 ( ( (000 Toal 97 (7 4 ( (000 Th sulao was odud hrough h followg rodurs: S Suos h oal sal of 339 o b a oulao S Draw a subsal S of sz f whr f s a salg frao wh a sl rado salg whou rla S 3 s h sulad rsul of h dr qusog hod ou h rooro drly ( Y Z al ad ( Y Z fal S 4 Dvd h subsal S o wo grous S ad S of sz ad ha ar o ssarly of qual sz ou h ubr of sld oy s for ah rsod S lso ou h ubr of sld s ludg boh h y ad h o-y s S Sass aada aalogu o -00-XIE

55 Survy Mhodology Ju S 5 s h sulad rsul of h ou hqu ou ( Y Z al ( Y Z fal ad va h hr sao hods; srafd hod ross-basd hod ad doubl rossbasd hod I h doubl ross-basd hod w l w /( ad w /( S 6 W l f 0 s ad rfor ss o 5 for 000 raos alula h as E D ES E ad E W ad h sadard dvaos SE D SES SE ad SE W of ah sao hod o aroa h aos ad h sadard rrors of h saors whr h subsrs D S ad W da h dr qusog hod h srafd hod h ross-basd hod ad h doubl ross-basd hod rsvly I h sa way w l f 0 ad rfor ss o 5 for 000 raos ad so o u o ad ludg f 09 3 Sulao Rsuls Fgur shows h aroad aos ad sadard rrors of h saors Th horzoal as da salg frao f I boh h ass al ad fal h aroad aos of E D ar sabl a vry f valu whl E S E ad E W of h ou hqu fluua rrgularly Ths s baus radoss s rodud w udr h ou h salg has ad h dvso has whras radoss s rodud oly h salg has udr h dr qusog saro Ev f f h saor udr h ou hqu has a ra aou of vara du o h radoss a h dvso has s h rag of fluuao was glgbl oard o h agud of h sadard rrors whh ar rfrrd o blow w oludd ha h ubr of ro was suff Eaos (Mal Dr Qusog Srafd ross-basd Doubl ross-basd Sadard Errors (Mal Salg fraos Salg fraos Eaos (Fal Sadard Errors (Fal Salg fraos Salg fraos Fgur road Eaos ad Sadard Errors of Esaors Sass aada aalogu o XIE

56 48 Tsuhya: Doa Esaors for h I ou Thqu Th sadard rrors SE D of h dr qusog hod s osdrably sall oard o hos of h ou I h as of h ou sadard rrors do o ovrg o zro v f f s od abov hs s baus h radoss s also rodud h dvso has Th sadard rrors of h srafd hod ar obvously largr ha hos of h wo ross-basd hods Th ls dag h rsuls for h ross-basd hod ad h doubl ross-basd hod alos ovrla ad aar o hav o ousadg dffrs I ordr o valua h aou of varas or sadard rrors of saors l us osdr h followg ds ha ar aalogous o h dsg ff (Ksh 965 SEM DfM M SE whr M ad M da o of h four hods D S ad W lhough w hav od h dald rsuls roughly suarzd Df D rags fro 50 (wh f 0 o 700 (wh f 0 9 Tha s v f w us h ross-basd hod h sadard rrors of h ou fla arly sv- o wy-s-fold as oard o h dr qusog Howvr h vara rduo aad by usg h doubl ross-basd hod sad of h srafd hod rags fro Df W S 0 39 (al o 055 (fal I ohr words h sadard rrors of h doubl ross-basd hod ar rdud o abou 6 r of h srafd sa a h u ad 74 r a h au M 33 Srafd Vrsus ross-basd Mhod 33 Sulao Mhods I h rvous so h rso of h ross-basd ad h doubl ross-basd hod aard o b largr ha hos of h srafd hod W shall h h rso of hs hods for ohr obaos of h y h obao of o-y s ad h doa varabl Z by sulao rs I hs so w usd all sals as follows: S ou ( Y Z z for ah z basd o all daa of sz 339 S Dvd h oal sal ( 339 radoly o grou ad grou of sz ad whr S 3 ou h ubr of sld o-y s for ah rsod of grou ad ou h ubr of sld s ludg boh h y ad o-y s grou S 4 Esa ( Y Z z by h srafd hod h ross-basd hod ad h doubl ross-basd hod rsvly S 5 ou h h-squard dsa bw ( Y Z z ad ( Y Z z for ah hod z { ( Y Z z ( Y Z z} ( Y Z z S 6 Ra h abov rodur fro s hrough s 5 for 000 raos alula h as ad h sadard dvaos of for ah hod I addo w sulad h srafd hod udr h radozd rsos for rfrs va h followg rodur: S L b a rooro as dsrbd blow Dvd h oal sal ( 339 radoly o wo grous Grou s oosd of rsods ad grou s oosd of ( rsods S L z b h ubr of rsods who sld h y ad Z z grou L z b h ubr of rsods who dd o sl h y ad Z z grou L z b h ubr of rsods wh Z z ou z ( / ( z z Y Z z 339 S 3 alula loyg h sa quao as usd h ou hqu S 4 Ra h abov rodur fro s hrough s 3 for 000 raos alula h as ad h sadard dvaos of for ah hod W usd hr valus; 0 03 ad Sulao Rsuls Tabl 5 ad Tabl 6 ls h as ad h sadard dvaos of 000 s for h doa varabl Z of gdr ad ag rsvly sallr a of valu das ha h doa saors ar or rs I so ros llogal sas ( Y Z z whh dva fro h rag [0 ] wr obad Th olus of h abls dod by udr da h ubr of ros wh a las o of h sas ( Y Z z was udr 0 ad ovr das ha h sas wr ovr Idally h fgurs of h olus of llogal should b 0 z Sass aada aalogu o -00-XIE

57 Survy Mhodology Ju Tabl 5 Mas ad Sadard Dvaos of s ad ubr of Ts Illogal Esas wr Obad (Doa Varabl Z s Gdr 7 Orgal (7% 8 ol (50% Dlg (7% valu llogal valu llogal valu llogal a (sd udr ovr a (sd udr ovr a (sd udr ovr Srafd hod obao 38 ( ( (4 0 0 obao 89 ( ( ( 0 0 obao 3 34 ( ( (3 0 7 ross-basd hod obao 8 (4 0 4 ( (3 0 0 obao 45 ( ( (8 0 0 obao 3 63 ( ( (3 0 Doubl ross-basd hod obao 8 (4 0 3 (4 0 0 (3 0 0 obao 45 ( ( (8 0 0 obao 3 63 ( ( (3 0 0 Radozd rsos 0 ( (3 0 0 ( ( ( ( ( ( (3 0 3 o: valu s ulld by 0 3 Tabl 6 Mas ad Sadard Dvaos of s ad ubr of Ts Illogal Esas wr Obad (Doa Varabl Z s ag 7 Orgal (7% 8 ol (50% Dlg (7% valu llogal valu llogal valu llogal a (sd udr ovr a (sd udr ovr a (sd udr ovr Srafd hod obao 375 ( ( (6 0 0 obao 859 ( ( ( obao ( ( ( ross-basd hod obao 93 ( ( (6 0 0 obao 75 ( ( ( obao ( ( (7 0 0 Doubl ross-basd hod obao 70 ( ( (8 0 0 obao 53 ( ( (3 0 0 obao 3 56 ( ( (70 0 Radozd rsos 0 58 ( ( ( ( ( ( ( ( ( o: valu s ulld by 0 3 For vry obao of h y h o-y s ad h doa varabl Z h as of of h doubl ross-basd hod ar h salls ad h rossbasd hod s h sod salls by a arrow arg Wh of h y s low ( 7 Orgal h ubr of o-y s s larg (obao 3 ad h ubr of alravs of h doa varabl Z s larg (ag h auray of h srafd hod drass graly oard o ohr obaos Morovr wh of h y s low gav sas ar of obsrvd wh h srafd hod s usd For al wh obg 7 Orgal obao 3 ad ag h frquy of obsrvd gav sas s 96 ou of 000 raos Wh h doubl ross-basd hod s usd h gav sas ar lss lly o b obsrvd For radozd rsos wh h ubr of alravs of h doa varabl Z s sall (gdr h auray of h sas ss o b h sa as h rossbasd ad h doubl ross-basd hods Howvr h a s sowha largr ha ha of h ross-basd hod wh h doa varabl Z has ay oos (ag Sass aada aalogu o -00-XIE

58 50 Tsuhya: Doa Esaors for h I ou Thqu Th radozd rsos for whh oly h srafd hod s avalabl also suffrs fro gav sas arularly wh s sall ( 7 Orgal 4 oluso Th followg rsuls wr obad hrough sulao rs: Th ross-basd hod or h doubl ross-basd hod whh s roosd hs arl should b usd o sa doa arars wh h daa s obad va h ou hqu I h frs sulao h varas of ross-basd saors wr rdud o 39 r of h vara of h srafd sa a h u o 55 r a h au I h sulao suds h doubl ross-basd hod ad o dras rov rso as oard o h ross-basd hod Ev wh h doubl ross-basd hod s usd h sadard rrors of h doa saors ar uh largr ha hos of h dr qusog hqu Th ru Y ( Y of a quso o whh rsods vad gvg a ruhful aswr would b of sall I addo a dr qusog hqu s usd ordr o sur roo of rvay Th rsods fl ha hr rvay s surd wh ay o-y s ar ludd (Hubbard al 989 Th sulao suds show ha suh suaos h ross-basd hod or doubl ross-basd hod s or ff ha h radoal srafd hod Th doa saors obad by h radoal srafd hod ar grally oss wh h saor ˆ as show (0 ossrafd saor ˆ S by h doa varabl addrssd s ssal ordr o sur ossy lravly w hav o dvd h oal sal o wo subgrous so ha h dsrbuos of hr doa varabl ah adva O h orary h doa saors obad by h ross-basd ad h doubl ross-basd hods ar oss wh ˆ as show ( Howvr dos o a ha h ross-basd hod auoaally aduss h wo subgrous so ha h sal dsrbuos of h doa varabl ah bw h wo subgrous For h ross-basd hod ossrafao by h doa varabls or ohr dograh varabls s also adssbl bu o dssabl Ev wh h doubl ross-basd hod s usd gav doa sas ar sos obsrvd I s ossbl o avod gav sas by lg a gav sa q of Q (3 b zro Howvr suh a adus rodus a osv bas ( Y Z z Th daa of h survy of h Jaas aoal harar whh wr usd h sulao rs ar hr ssv or wr hy obad va h ou hqu I h fuur h rfora of h roosd hod should b assssd by alyg o daa obad va h ou hqu owldgs Th auhor s graful o wo aoyous rvwrs ad a asssa dor for hr hlful os o a rvous vrso of hs ar Rfrs bul-ela bdl-laf Grbrg G ad Horvz DG (967 ulrooros RR odl Joural of h ra Sasal ssoao haudhur ad Mur RM (988 Radozd Rsos: Thory ad Thqus w Yor: Marl Dr ohra WG (977 Salg Thqus 3 rd d w Yor: Joh Wly & Sos I Droour J asar R Hubbard ML arsly TL Vsshr W ad Ezza TM (99 Th ou hqu as a hod of dr qusog: rvw of s dvlo ad a as sudy alao I Masur Errors Survys (Eds r al w Yor: Joh Wly & Sos I Droour J Larso EM ad Shur FJ (00 Th hr ard hod: Esag ssv survy s-wh ra aoyy of rsos rodgs of h Soal Sass So of h ra Sasal ssoao ladra V: ra Sasal ssoao Grbrg G bul-ela bdl-laf Sos WR ad Horvz DG (969 Th urlad quso RR odl: Thoral frawor Joural of h ra Sasal ssoao Hubbard ML asr R ad Lsslr JT (989 Rsod raos o ou lss ad radozd rsos rodgs of h Survy Rsarh So of h ra Sasal ssoao Washgo D: ra Sasal ssoao Ksh L (965 Survy Salg w Yor: Joh Wly & Sos I Lsslr JT ad O Rlly JM (997 Mod of rvw ad rorg ssv ssus: Dsg ad lao of audo our-asssd slf-rvwg ID Rsarh Moograh Mllr JD (985 Th oav hqu: w hod of sag hro rval ID Rsarh Moograh Rao JK (003 Sall ra Esao w Jrsy: Joh Wly & Sos I Sass aada aalogu o -00-XIE

59 Survy Mhodology Ju Saaoo Y Tsuhya T aaura T Mada T ad Fous D (000 Sudy of h Jaas aoal harar: Th Th aowd Survy (998 Toyo: Th Isu of Sasal Mahas Rsarh Ror Gral Srs 85 Särdal -E Swsso ad Wra J (99 Modl sssd Survy Salg w Yor: Srgr-Vrlag Shua H ad rssr S (98 Qusos & swrs ud Survys w Yor: ad rss Taahas K ad Saasgawa H (977 radozd rsos hqu whou ag us of ay radozg dv als of h Isu of Sasal Mahas 9-8 US Gral oug Off (999 Survy Mhodology Iovav Thqu for Esag Ssv Is Washgo D: Gral oug Off Warr SL (965 Radozd rsos: survy hqu for lag vasv aswr bas Joural of h ra Sasal ssoao Warr SL (97 Th lar radozd rsos odl Joural of h ra Sasal ssoao Sass aada aalogu o -00-XIE

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61 Survy Mhodology Ju Vol 3 o Sass aada aalogu o -00-XIE Edg Sysa Uy Masur Errors Through Mur Modllg Maro D Zo Ugo Guarra ad Ora Luz bsra I Offal Sass daa dg ross lays a ora rol rs of lss daa auray ad survy oss Thqus rodud o dfy ad la rrors fro daa ar ssally rqurd o osdr all of hs ass sulaously og ohrs a frqu ad rvasv sysa rror aarg survys ollg ural daa s h uy asur rror I hghly affs lss daa auray ad oss of h dg ad uao has I hs ar w roos a robabls foralsao of h robl basd o f ur odls Ths sg allows us o dal wh h robl a ulvara o ad rovds also a ubr of usful dagoss for rorsg ass o b or dly vsgad hrough a lral rvw rorsg us s ora ordr o ras daa auray whl avodg was of du o h follow u of o-rally ral us Ky Words: Edg; Rado rror; Sysa rror; Slv dg; Modl-basd lusr aalyss Iroduo Els drg h qualy of a Edg ad Iuao (E&I ross ar varous ad hav b wdly dsussd lraur (Graqus 995 W dal wh a arular o-salg rror ha hghly affs wo a og qualy dsos: lss ad daa auray s far as auray s ord w ado h dfo suggsd h Eyloda of Sasal Ss (999: auray ors h agr bw sass ad arg hararss ubr of faors a aus auray alog h ovrall sasal survy ross Iauray a b rdud durg h E&I has whh a b vwd as a auray rov ool by whh rroous or hghly sus daa ar foud ad f ssary orrd (ud (Fdral o o Sasal Mhodology 990 Du o h oly of vsgad hoa ad h s of svral ys of o-salg rrors h E&I has a b a vry ol ad osug as (Graqus 996 I h salsd lraur a oo rror lassfao lads o df wo dffr rror yologs: sysa rror ad rado rror Th forr rlas o rrors whh go h sa dro ad lad o a bas sass whl h lar rfrs o rrors whh srad radoly aroud zro ad aff h vara of sas (Eyloda of Sasal Ss 999 Udrsadg aur of rrors s o oly usful ordr o dfy hr sour ad o assss hr ffs o sas bu also o ado h os arora hodology o dal wh h (D Zo ad Luz 00 Whl h Fllg Hol aroah (Fllg ad Hol 976 s a wll-sablshd aradg o dal wh rado rrors sysa rrors ar grally rad by as of ad ho soluos (s for sa Eurd 003 Vol har 5 Sysa rrors ar grally rad bfor dalg wh rado rrors arularly wh h lar ar ald hrough auoa sofwar l for sa h Gralsd Edg ad Iuao Sys (GEIS (Kovar Ma Mlla ad Whrdg 988 ad or rly D Waal (003 I h faly of sysa rrors o ha has a hgh a o fal sas ad ha frquly affs daa sasal survys asurg quaav hararss (g busss survys s h uy asur rror s a osa faor (g 00 or 000 Ths rror s du o h rroous ho by so rsods of h uy asur rorg h aou of so qusoar s s ral als of survys affd by hs y of rror w sld wo ISTT vsgaos: h 997 Iala Labour os Survy (LS ad h 999 Iala War Survy Sys (WSS Th LS s a rod sal survy ha olls forao o loy word hours wags ad salars ad labour os o abou 000 rrss wh or ha 0 loys I Fgur h logarh of Labour os (LOST ubr of Eloys (LEMLOY Word Hours (LWORKEDH ar rrsd a sar lo ar o ha h loy varabl a hs dg sag s rror fr baus of a rlary h wh rs o forao fro busss rgsrs (ra D Zo Luz ad Sbr 000 Th aalyss of Fgur shows ha Labour os s affd by wo ys of uy asur rror ( llo ad 000 faor whl Word Hours hbs oly h 000 faor rror Ths rrors aus h dffr lusrs Fgur o ha h lusrs h low lf orrs of ah sar lo rrs o-rroous daa Maro D Zo Ugo Guarra ad Ora Luz Iala aoal Sasal Isu Va sar albo Roa Ialy

62 54 D Zo Guarra ad Luz: Edg Sysa Uy Masur Errors Through Mur Modllg Fgur LOSTS LEMLOY LWORKEDH Mull sar lo bw oal labour os loys word hours (logarh sal Th WSS al wll b dsrbd dal subso 4 whr a alao of h hod roosd hs ar for dfyg ad rag h uy asur rror wll b rsd For h uy asur rror h ral o s h loalsao of s rror rahr ha hr ra I fa o a s lassfd as rroous h oal ra s uquly drd ad osss a drs ao rovrg h orgal valu hrough a vrs ao (g dvso by 000 uralsg h rror ff Th uy asur rror s grally ald hrough ad ho rodurs usg ssally grahal rrsaos of argal or bvara dsrbuos ad rao ds rao d s a rul sag ha h valu of a rao bw wo varabls us l wh a rdfd rval Th rval bouds ar grally drd hrough a ror owldg or va loraory daa aalyss ossbly usg rlabl aulary forao For hs y of rror rao ds ar ffv wh o of h wo varabls s rror fr Furhror rao ds allow ag o aou oly bvara rlaoshs bw varabls ad v usg rav grahal so (g sar lo ar o or ha a arws aalyss a b rford dsrgardg or ol raos bw varabls Fally w o ha adog arws aalyss ls ha varabls ar o b rad a r-dfd hrarhy hus rasg h oly of h rror loalsao rodur Wh radoal aroahs h rror loalsao robl s o oly ol bu also ad os osug T ad os ar aly affd by: h oly of dsgg ad lg auoa drs ad ho rodurs ad h rsours s aually dg obsrvaos havg low robabls of bg rror ad/or low a o arg sas (ovr-dg I hs ar w roos a robabls foralsao of h robl hrough f ur odls (MLahla ad asford 988; MLahla ad l 000 Ths odllg a rovd a rld sasal aroah allowg a sa of h odoal robably ha a obsrvao b affd by uy asur rror Th advaag of h roosd aroah s ha rrss a gral hod allowg a ulvara daa aalyss ad rovdg ls ha a b usd o os h bala bw h auoa ad rav oos of h dg rodur bw ad auray (Graqus ad Kovar 997 Ths wor s orgasd as follows I so h roosd odl s rodud oghr wh h EM algorh for h sas of h odl arars I so 3 dagoss for slv dg ar dsrbd I so 4 h rsuls of h alao of h roosd hod o boh sulad ad ral daa ar llusrad Fally so 5 oludg rars ad fuur rsarh ar ould Th Modl I s hard o gv a orhsv foralsao of rado ad sysa rrors I hs o w rovd a dfo ha hough o hausv luds ay oo suaos L X b h vor of h survy arg * varabls ad ( μ * h orrsodg a vor ad ovara ar L us suos ha h asur ross s affd by a rado rror has R havg * a o h ovara sruur of X bu lavg h a vor uhagd ad osquly l X b h orrsodg oaad varabl wh E (X * E ( X μ Var( X lso w assu ha X a ur b affd by a sysa rror has S ag oly o s d valu: μ S ϕ( μ for so fuo ϕ (g f a addv rror has s assud ϕ (μ μ osa s a osqu of h wo rror hass assud o b dd of o aohr obsrvd daa a b dsrbd by a rado vor Y whos dsrbuo odoal o X dds oly o h sysa rror has Our aroah o h ra of sysa rrors osss of buldg u a odl for Y fousg oly o h do of sysa rrors hus ag a rovrg h radoly oaad daa rrsd by h rado vor X Ths s h aroah grally adod dg rodurs whr sysa rrors ad rado rrors ar dal wh saraly ad hrarhally Sass aada aalogu o -00-XIE

63 Survy Mhodology Ju Th rvous dfo of sysa rror luds uy asur rror o daa hav b rasford logarh sal I fa uy asur rror grally as ullyg varabls by a osa faor H daa rror aar log-sal as raslad by a vor of osas ha dds o whh s ar rror ( rror ar whl h ovara sruur s h sa for ah rror ar Morovr as ar of fa busss survys varabls ar frquly osdrd log-oral Thus logarh sal h Gaussa sg a b adod Followg h foralsao so far rodud our goal bos o assg ah sgl obsrvao o a sf rror ar ha orrsods o loals s rror If w rr ah sgl rror ar as a lusr h rror loalsao robl s rasford a lusr aalyss robl ad w a lo rs fro h odlbasd lusr aalyss hory (Fraly ad Rafry 00 Mor dal l us suos w hav dd obsrvaos Y ( Y Yq orrsodg o h q dsoal vors X ( X X q wh df f ( q ; θ suh ha E ( X X q ( μ μ q μ ad Var( X X q asd o h assuo ha sysa rrors aff h rado vor X oly by rasforg s d valu q q μ o ϕ g (μ whr ϕ g ( : R R for g h ar a s of ow fuos h fuos ϕ g harars uvoally h ds lusrs (rror ars dffrg ah ohr oly o h loao arar For sa f h sysa rror ossbly affs all h varabls X s for s q h sa ar by rasforg hr d valus μ s aordg o μ s μ s whr s a ow osa h ubr of lusrs wll b h q h ubr of dffr obaos of rror ourr o h q varabls (ludg h as of o rror I hs as ah fuo ϕ g ad ah orrsodg lusr s assoad wh o of h q ossbl sub-ss of varabls affd by h rror; g h grou G hararsd by h a vor μ G ( μ μ μ 3 μ 4 μ q s a lusr of us wh rror affg oly h varabl X W rar ha w assu a oo ovara ar baus w a h hyohss ha h ossbl rado rror as h sa way o all h daa For h rror loalsao uros w follow a odlbasd aroah basd o f ur odls whr ah ur oo G g g h rrss a sgl rror ar Forally w assu ha Y ( Y Yq for ar d wr h f ( ; θ whr ad 0 Th g arars rrs h robably ha a obsrvao blogs o h h ur oo I ordr o lassfy a obsrvao y o of h h grous w ou h osror robably τ g ( y ; θ r( h obsrvao Gg y; θ ha s τ ( y ; θ g g f ( y ; θ g g h f ( y ; θ g h Th h obsrvao s assgd o h lusr G f τ ( y ; θ > τ ( y ; θ g h; g g Th rvous alloao rul s h oal soluo for h lassfao robl h ss ha ss h ovrall rror ra (drso 984 har 6 S la of h arars ( θ grally uow w us h au llhood sas ( θ ˆ ˆ h lassfao rul bos: τ ( y ; θˆ ˆ > τ ( y ; θˆ ˆ g h; g ( g W assu ha h f ( y ; θ s a ulvara oral dsy M ( μ ad ha ah fuo ϕ g ( as o h a vor μ as a raslao: ϕg ( μ μ g whr h g rrss h raslao vor for h a of h g lusr ad s suosd o b ow Ths sg as alrady od s suabl for dalg wh uy asur rror I ordr o ou h llhood sas w us h EM algorh as suggsd MLahla ad asford (988 vrhlss a addoal ffor s ssary o ada h algorh o our arular suao whr h a vors of h ur oos ar ld by a ow fuoal rlaosh Thus whl h oosrad as (MLahla ad asford 988 a dffr a vor has o b sad for ah ur oo our osrad suao oly o a vor ds o b sad Th rsulg odfd EM algorh osss of dfg so al guss for h (0 arars o b sad ˆ g for g h (0 ( μ ˆ ˆ (0 ad alyg ul ovrg h followg rursv sh: ou h osror robabls τg ( ( τ g ( y; θ udr h urr sas ˆ ( ( μˆ ˆ h ( s h d rfrrg o h yl τˆ ( g ˆ h ( g ˆ ( ( ( ' ( ( y μˆ ( y μˆ ( ( ( ' ( ( y μˆ ( y μˆ g ˆ ˆ g ( Sass aada aalogu o -00-XIE

64 56 D Zo Guarra ad Luz: Edg Sysa Uy Masur Errors Through Mur Modllg alula h w sas by h followg rursv quaos: ˆ μ ˆ ( ( h ˆ g h g ( ( g τˆ g / τˆ τˆ ( g ( g y / h g ˆ g ( g ( ( ' ( ( y μ ( y μ / ˆ ( g g g ( W rar ha μ ˆ sads for ˆμ g I raal alaos urs ou ha a rual rol s layd by h ho of sarg os as usual h EM algorhs (s ra lu ad Govar 003 To ovro hs robl w us a alsao sragy followg ra al (003 ossg of svral shor rus rs of ubr of raos of h algorh fro rado alsaos followd by a log ru of EM fro h soluo asg h obsrvd log-llhood I s worh o o ha du o h loao osras h arars o b sad ar ssbly fwr ha hos a usual ur robl ually h hghr s h ubr of varabls aalysd h bggr s hs dffr; for sa h as of hr varabls ad 8 lusrs w d o sa 6 arars sad of 37 Ths as s arularly ora wh w dal wh sall sals Morovr osras o lusr loaos a asr o dfy rar lusrs I fa bg h rlav dsas bw a vors fd h sao robl rdus o sa h loao of h ov olyhdro whos vrs ar h lusr rods I ohr words s h loao of o rod uvoally drs h osos of all h ohrs sall lusr arars ar or asly sad ha f hy wr o osrad S h rodud odllg s basd o h assuo ha obsrvaos ar orally dsrbud odl valdao s a ssu o a o aou Th robl of assssg oraly ur odls s wll dsrbd MLahla ad asford (988 I s ssally basd o h quas â g dsrbd h followg L y g for ˆ g b h obsrvaos assgd o h h g lusr for g h aordg o h sad odl L ˆ g b h valu alulad usg h sad arars followg h forula: ( ˆ / ˆ ; ˆ νg q D yg μ g ˆ g (3 ( ( ˆ ˆ ˆ ; ˆ ν q g g D yg μ g whr D( ; M s h Mahalaobs squard dsa basd o h r M ad ν h q W df â g g as h ara o h rgh of h ˆ g valu udr h F q ν dsrbuo (for dals s MLahla ad asford 988 har Udr h oraly assuo â g for ˆ g s aroaly uforly dsrbud o (0 Haws (98 suggss usg h drso Darlg sas for assssg h ufor dsrbuo of â g Th â g ar also usful o d oulrs ayal obsrvaos wh rs o h odl I MLahla ad asford (988 h lowr s â g h hghr s h robably of y g of bg ayal hus all obsrvaos wh a ˆ g < α whr α s a sfd hrshold a b osdrd as ayal Suggsd hrshold lvls rag fro α 0 05 o α 0005 ddg o whh oulyg obsrvaos (or or lss r valus ar o b sld 3 Dagoss for Slv Edg O h arars of h ur hav b sad w ar abl o lassfy daa o h dffr lusrs for ah obsrvao w a assss whhr s rror or o ad whh varabls ar rror Howvr dffr ys of ral obsrvaos a b dfd afr h odllg has: us lassfd a lusr bu havg a o-glgbl robably of blogg o aohr lusr ad obsrvaos ha ar oulrs wh rs o h odl I ordr o ras daa auray would b usful o a a doubl h o ral obsrvaos (hrough hr a lral rvw or h os dfful ass a follow-u O h ohr had ordr o rdu ossbl ovr-dg ad dg oss h aual rvw ad/or follow u should b orad o h os ral obsrvaos Th roosd ur odl drly rovds dagoss ha a b usd o hs a frs y of ral us s rrsd by ossbly slassfd obsrvaos I ordr o asur h dgr of blf h lass assgd o a obsrvao y w a osdr h orrsodg robably rsulg fro ( Obsrvaos for whh hs robably s o vry los o o hav a o-glgbl robably o blog o aohr lusr Ths obsrvaos ar hos h rgo whr h ur oos ovrla ah ohr I addo o h rvous y of ral us hr ar ohr obsrvaos ha ar far fro all h lusrs (all h ur oos oulrs wh rs o h odl lso hs obsrvaos rrs ral suaos I ordr o dfy hs d of oulr w rfr o h quas â dsrbd h rvous so lassfao robably ad ayaly d â g should b usd aordg o a slv/sgfa dg aroah (Laouh ad rhlo 99; Lawr ad MKz 000 o buld u arora sor fuos o Sass aada aalogu o -00-XIE

65 Survy Mhodology Ju rors ral us al of how o us hs dagoss o hs a s gv subso 4 4 Illusrav Eals I hs so so rs arrd ou ordr o vsga h ulars of h roosd hod ar rsd Frsly hrough a sulao sudy w aalys h rfora of h roosd odl wh ald o daa ha dar fro oraly Sodly hrough a alao o ral daa w dsrb how hs aroah a b ald Offal Sass ll h rs ar rford usg h R vro for sasal oug (h://wwwr-roorg/ 4 Sulad Eal: Darur fro oraly I hs r w dsrb h rsuls obad by alyg h ur aroah o h hr dffr oulaos dd h frs l of Fgur Th frs dsrbuo s a bvara oral (M h rrss h as wh h odl s orrly sfd Th sod o orrsods o a bvara dsrbuo (MT s h suao wh h darur fro oraly s ssally havg havr als Th las o s a bvara sw dsrbuo (ST (zzal ad aao 003 zzal Dal allo ad Koz 003 ad rrss a oulao dsrbud aordg o a asyr dsrbuo wh havy als Fro hs dsrbuos w buld a four oos ur odl by addg o ah u o of h four raslao vors (0 0 (0 log(000 (log( (log(000 log(000 wh 4 robabls ad rsvly Ths arars rrs h g rooros of h ur odl ad rfr rsvly o h robabls of o raslao h varabls raslao oly o of h wo varabls ad raslao boh varabls Fro ah ur w draw 00 sals of 000 obsrvaos I h sod l of Fgur w ror o of hs sals (M M MT M ST M orrsodg o h hr dffr oulaos M MT ST rsvly For ah sal w ou h ubr of orr lassfaos obad by usg h ur aroah dsrbd so Th a ubr of orr lassfaos ovr h 00 sals s rord Tabl s a b s Tabl h frquy of orr lassfaos drass wh h darur fro oraly Howvr ss aabl also h ral as ST whr h oulao s hararsd by boh asyry ad havy als M MT ST M M MT M ST M Fgur oour los of h hr bvara dsrbuos uloral (M sud (MT sw (ST ad sar lo of h orrsodg urs M M MT M ST M Sass aada aalogu o -00-XIE

66 58 D Zo Guarra ad Luz: Edg Sysa Uy Masur Errors Through Mur Modllg Tabl Frquy of orr lassfaos M MT ST % orrly lassfd s dsussd so 3 h ur aroah rovds ls (suh as h dgr of ayaly ad h lassfao robably ha a b usd ordr o rors us o b lrally rvwd Thrfor a ovrall assss of h rodur should osdr also h rsuls obad hrough a slv dg aroah basd o hs odl dagoss I ordr o aalys h hararss of ayaly d ad lassfao robably w a a sgl sal of 000 obsrvaos draw fro h hr oulaos so far rodud I Fgur 3 h hr sals M M(a MT M(a ST M(a ar rrsd furhror h slassfd us ar dd wh a ross h sa grah Th ubr of slassfd us s 9 for M M 0 for MT M ad 36 for ST M O hs sal w fous o h a of dffr hrshold lvls boh for ayaly (α ad lassfao robably (β For ah hrshold w ror Tabl ad Tabl 3 h ubr of us blow ha hrshold h ubr of ral obsrvaos ( y r lass ad aog h h ubr of slassfd us (y - Mslas r lass - Mslas s far as ayaly s ord w o ha wh h odl s orrly sfd h ora of h ayaly d rovrg slassfd us s glgbl whl h lassfao robabls ar or ffv O h ohr had h dgr of ayaly s ora wh h odl dars fro oraly I s lar ha h ubr of obsrvaos sld for a gv obao of hrsholds α ad β s o qual o h su of h frqus obad Tabl ad Tabl 3 Thus ordr o valua h o a of hs wo ds w hoos h wo followg hrsholds α ad β 0975 W ror Fgur 3 (sod l h us sld oly for h ayaly valu (squars oly for h lassfao robably (ragls ad for boh of h (rosss Fro hs fgurs w s how h a of ayaly s aly o oulrs dfao whl h lassfao robably wors o h ovrlag rgos I Tabl 4 h ubr of sld us ad ou of h h ubr of slassfd us ar show W o ha for oulao M M aar o obsrvao all h slassfd us ar sld For MT M w ar abl o sl 4 ou of h 0 slassfd us ad h os ral sal ST M w sl 4 ou of h 36 slassfd us M M (a MT M (a ST M (a M M (b MT M (b ST M (b Fgur 3 Mslassfd us (rosss M M(a MT M(a ST M(a ral us for ayaly (squar for lassfao robably (ragl ad for boh of h (ross M M(b MT M(b ST M(b Sass aada aalogu o -00-XIE

67 Survy Mhodology Ju Tabl ubr of ral Obsrvaos ad Mslassfd Us wh Rs o Thr Dffr Thrsholds for yaly M M MT M ST M α y y Mslas y y Mslas y y Mslas Tabl 3 ubr of ral Obsrvaos ad Mslassfd Us wh Rs o Thr Dffr Thrsholds for lassfao robably M M MT M ST M β r lass r lass Mslas r lass r lass Mslas r lass r lass Mslas Tabl 4 ubr of ral Obsrvaos ad Mslassfd Us wh Rs o yaly ad lassfao robably M M MT M ST M Thrsholds r Us Mslas r Us Mslas r Us Mslas α 0005 β lao o Ral Daa: Th 999 Iala War Survy Sys I hs so w dsrb a alao of h ur odl aroah o ral survy daa Th daa ar a fro h 999 Iala War Survy Sys (WSS Th WSS s a sus ha olls forao o war absrao suly ad usag for h 800 Iala uals W rsr our aalyss o h uals blogg o o of h daa doas dfd by alry (04 obsrvaos ad o h a varabls Toal Ivod War (TI ad Toal Suld War (TS oh hs varabls rfr o war volus ad h rsods ar rqusd o rovd h housads of ub rs Th sar lo o log-sal of r aa war vod (WI vrsus r aa war suld (WS (Fgur 4 shows h rs of four lusrs orrsodg o uy asur rror o boh or o of h arg varabls Ths s robably du o h sudrsadg of so rsods ha rssd war volus lrs or ub rs rahr ha housads of ub rs as rqusd s d h wo os oulad lusrs ar hos orrsodg o o-rroous us ad o us whr boh varabls ar rror vrhlss w a o h rs of wo rar lusrs orrsodg o obsrvaos whr h uy asur rror affs oly TI or oly TS rsvly I Tabl 5 a labl s assgd o ah grou assoad wh a sf rror ar For h sa of sly w rodu wo flags E TS ad E TI assug valu or 0 ddg o whhr h orrsodg varabls ar affd by h uy asur rror or o rsvly I ordr o dfy ad orr h uy asur rror w aly h rodur dsrbd sos ad 3 W lassfy ah obsrvao aordg o a sf rror ar w assg ah u o o of h lusrs G for 4 Th rsuls ar rord Tabl 6 For ah u h ayaly d s also alulad ad h hrshold α s hos ordr o flag ayal us ordg o hs hrshold 7 obsrvaos ar sld as ayal ard by rosss Fgur 7 O h valus â g ar oud aordg o Forula (3 a s assssg h oraly assuo a b rford ually followg MLahla ad asford (988 har h drso Darlg s o h ufory of â g o ah sgl sad lusr s rford Th valus ar blow 000 for h wo largs lusrs S h s s basd o asyoal aroaos w do o a o aou h rsuls o h ohr wo rar oulaos I Fgur 5 w ror h ral sal quals vrsus h oral quals of h varabls log(wi ad log(ws fousg oly o h subs of daa lassfd as orroous W o ha darur fro oraly s aly du o havy als asd o h rsuls obad so 4 whr h hod rford sasfaorly also o-gaussa sg w ar ofd abou h good rfora of h ur aroah o h survy daa Ths d bhavour s ofrd by h alao rsuls showd h followg Sass aada aalogu o -00-XIE

68 60 D Zo Guarra ad Luz: Edg Sysa Uy Masur Errors Through Mur Modllg Log(WI Log(WS Log(WS Fgur 4 Sar lo of log(ws ad log(wi Log(WI Sal Quals Sal Quals oral Quals oral Quals Fgur 5 oral qq lo of log(ws ad log(wi Tabl 5 Error ars ad Error Labls E Error ar TS 0 E TS 0 E TS E TI 0 E TI E TI 0 E TS E TI lusr labl G G G3 G4 Tabl 6 ubr of Us ssgd o Eah lusr lusr labl G G G3 G4 of us % I h rag ar of hs so s show how h osror robabls a b usd o rors us o b rvwd whh ar lly o rovd h gras dg bf ag o aou h oal a of h lral dg o h sas To hs a o ha a wrog lassfao of a obsrvao auss ha h fal valus of a las o varabl dffr fro h orrsodg ru valus by a ullav faor Ths dsras a srously aff h auray of h sas ladg o a srog bas I ordr o sl h oally rroous us ha os lly hav a srog a o h arg sas w follow h slv dg aroah L X X do h varabls TS TI rsvly For ah u u ad for ah varabl X l us df: Sass aada aalogu o -00-XIE

69 Survy Mhodology Ju X : daa fr of sysa rror; Y : obsrvd daa; X ~ : daa afr h ra of sysa rror basd o h lassfao hrough ur odl ( ~ ~ X Y or X Y / 000 ddg o h lusr h u u s assgd o L us suos ha h arg sas rfr o oulao oals T ( X X Furhr do by E ( ξ h ao ovr h dsrbuo of h rado varabl X odoal o h obsrvd daa Y ad h daa afr ~ orro X Th fro h qualy ~ ~ E ( X ξ X E ξ X X follows ha h quay o h rgh had sd a b vwd as a ur boud for h d bas of h oal sa for h ~ varabl X basd o h orrd valus X Th las osdrao suggss a hod for slg h os flual us wh rs o h sa T ( X : ordr o guara h rqusd lvl of auray ad o s oss du o aual h w df a loal sor ~ fuo S ( Eξ X X / Tˆ( X whr T ˆ( X s a rfr sa for T ( X for sa h sa fro a rvous survy or a robus sa I our as ordr o robusfy h rlary sa w frs lud fro h daa h ayal obsrvaos h ou h a valu o hs subs ad h ully by h oal ubr of us Th loal sor S asurs h a of h oal uy asur rror assoad o h u u o h arg sa T ( X Th us a b sord by hr sor S ad sarg fro h hghs valus h frs us a b sld ul h su of h rag S valus s lowr ha a rdfd hrshold If boh h varabls TS ad TI ar osdrd sulaously a global sor S for a b obad by suably obg h loal sor fuos S ossbl hos ar S ( S S or S a S Th lar fuo for sa surs ha h a of h oal uy asur rror assoad wh u o ah sa s o grar ha S I ordr o ou h sors S h odoal d valu E ~ ξ X X s o b sad for ah u u ad for ah varabl X for Ths a b asly do hrough h osror robabls For sa suos ha h u u has b assgd o h lusr G Ths as ha for hs u h obsrvd valu of TS ( Y has b osdrd orr whl h obsrvd valu of TI ( Y has b flaggd as affd by uy asur rror ( ulld by 000 Th orro osss of dvdg by 000 h obsrvd valu ~ ~ of TI ( X Y X Y /000 Th odoal d valu E ~ ξ X X a b oud as follows: ~ E X X Y Y r ( u G G E ξ ξ X ~ X Y Y Y (ˆ τ 3 (ˆ τ τˆ τˆ r ( u 4 Y Y r ( u Y Y Y r ( u G G G 3 G 4 4 G G whr τˆ s h sad robably ha u u g blogs o lusr G g I a slar ar h sor fuos a b alulad for all h us I ra our alao w sor h us by hr global sor S a S (asdg ordr Th w lud fro lral rvw all h frs obsrvaos suh ha hr uulav su of S s blow δ whr δ s a sfd olra lvl for h a o h sas du o rrors rag daa I Fgur 6 h bhavour of h uulav su of S S( S s show for h frs os ral 0 obsrvaos W rar ha for h sa of lary w hav o rord all h obsrvaos baus for os of h S ( s los o zro ausg a uradabl ur for hr dffr agud o ha a rsdual rlav rror lss ha δ 0 00 s d by slg oly h frs wo us (draw wh rosss I Fgur 7 all h us sld baus of hr ayaly (7 ad/or h rlav a o sas of hr oal rrors ( ar show: rosss orrsod o obsrvaos ha ar ral for ayaly squars da h ohr wo ys of ral us oarso wh h rsuls obad by h offal rodur s ad Ou of h 968 us o sld for lral rvw 9 obsrvaos ar rror fr or affd by uy asur rror oly For all of h h lassfao of h ur odl s orr Ou of h rag 57 us hararsd by ohr rror yologs 45 ar lassfd as o-affd by h uy asur rror whl as us wh h 000 rror boh h varabls Ths las slassfao a b lad by h rs of aohr sysa rror (s faors ha s o a o aou h odl usd for hs al 3 Sass aada aalogu o -00-XIE

70 6 D Zo Guarra ad Luz: Edg Sysa Uy Masur Errors Through Mur Modllg uul S( log (WI Obs Fgur 6 lo of h uulav sor S ( for h frs os ral 0 obsrvaos Fgur 7 Sar lo of log(ws vs log(wi rosss da ral us for ayaly squars ar ral us for h a of hr oal rror furhr oarso s abou h sa of h oals Udr h hyohss ha h valus sld for a lral rvw ar orrly rsord h rlav dffrs bw h ru oal valus aordg o h offal rodur T ( X ad h odl sa T ˆ( X as ( X ( Tˆ( X T ( X T ( X for ar ( X ad ( X 000 Ths valus ar o drly oarabl wh h olra lvl δ 000 fa hs hrshold rlas oly o a of h rag uy asur rrors whl X s also affd by ohr ( 6 Log(WS 8 0 d of rrors Thus for a or dr oarso w rla for hs us h wrog valus wh h ru os obag ( X ( X 0 Ths arularly hgh rfora of h odl s usfd by h low dgr of ovrlag of h lusrs as lar Fgur 7 5 Fal Rars ad Furhr Rsarh I hs ar w roos a f ur odl o dal wh a arular y of sysa rror ha frquly affs ural ouous survy daa: h uy asur rror s a osa faor Th roosd aroah has h advaags wh rs o h radoal os o forally sa h robl a ulvara o o b asly ld gralsd sofwar ad o aurally rovd usful dagoss for rorsg doubful us ossbly oag flual rrors Th lar harars s arularly ora wh h suao s ral wh dffr rror ars ovrla ah ohr or ohr words wh uy asur rrors ar aog lausbl obsrvaos I hs rusas a lral rvw s dd H s ora o os h slo of ral obsrvaos ordr o sav ad oss ll hs advaags ar h aural osqu of h roduo of a odl-basd hqu O h ohr had s lar ha h us of a odl-basd aroah ls robls rlad o odl assuos Howvr basd o h rs llusrad h ar ss ha also ass of darur fro h oraly assuo h roosd hqu rfors sasfaorly vrhlss s worh o o ha for r darur fro oraly g wh h dsrbuo s o uodal h hod s d o fal Ths a ha ral suaos wh ru daa oa dffr lusrs for sa dffrs ad wo o gh aus a bodal dsrbuo for h o slf I so ass h robl ould b ovro by srafyg daa wh rs o so lav varabls g s h rvous al alrav aroah o hs sf robl ould b basd o odllg ah lusr ur as a Gaussa ur hus obag a ur of ur odls (MLahla ad l 000; D Zo Guarra ad Ro 004 Fally a las or s abou h ubr of varabls ha a b rad sulaously ually h ubr of lusrs ad h h ubr of g arars a hav a oal growh wh rs o h ubr of varabls ag h arar sao a ral as Howvr s worhwhl og ha h ubr of arars rlad o h a vor ad ovara ar rass uh slowr du o h osras hararsg our odl Sass aada aalogu o -00-XIE

71 Survy Mhodology Ju owldgs W ar graful o h rfrs ad h ssoa Edor for hr hlful os Rfrs drso TW (984 roduo o Mulvara Sasal alyss Sod Edo w Yor: Joh Wly & Sos I zzal ad aao (003 Dsrbuos grad by rurbao of syry wh hass o a ulvara sw dsrbuo Joural of h Royal Sasal Soy ( zzal Dal allo T ad Koz S (003 Log-sw-oral ad log-sw dsrbuos as odls for faly o daa Joural of Io Dsrbuo 3- ra lu G ad Govar G (003 hoosg sarg valus for h EM algorh for gg h hghs llhood ulvara Gaussa ur odls ouaoal Sass & Daa alyss ra D Zo M Luz O ad Sbr (000 Th w grad daa dg rodur for h Iala Labour os survy: Masurg h ffs o daa of obd hqus rodgs of h Iraoal ofr o Esablsh Survys II uffalo 7- D Waal T (003 Solvg h rror loalzao robl by as of vr grao Survy Mhodology D Zo M Guarra U ad Ro R (004 ur of ur odls o d uy asur rror rodgs ouaoal Sass (Ed oh Jaror hysa Vrlag ragu ugus 3-8 D Zo M ad Luz O (00 obg hodologs a daa dg rodur: a r o h survy of ala Shs of grulural Frs Iala Joural of ld Sass Eyloda of Sasal Ss (999 w Yor: Joh Wly & Sos I Uda Eurd (003 Towards Effv Sasal Edg ad Iuao Srags Fdgs of h Eurd ro Forhog ow avalabl a h://wwwsyorau/urd/ Fdral o o Sasal Mhodology (990 Daa Edg Fdral Sasal gs Sasal oly Worg ar 8 Fllg I ad Hol D (976 sysa aroah o d ad uao Joural of h ra Sasal ssoao Fraly ad Rafry (00 Modl-asd lusrg dsra aalyss ad dsy sao Joural of h ra Sasal ssoao Graqus L (995 Irovg h radoal dg ross I usss Survy Mhods (Eds G o ad D dr Graqus L (996 Th w vw o dg Iraoal Sasal Rvw Graqus L ad Kovar J (997 Edg of survy daa: How uh s ough? I Survy Masur ad ross Qualy (Eds L Lybrg r M olls E d Luw Do Shwarz ad D Trw w Yor: Joh Wly & Sos I Haws DM (98 w s for ulvara oraly ad hoosdasy Thors Kovar JG Ma Mlla IH ad Whrdg (988 Ovrvw ad sragy for h gralzd d ad uao sys (udad Fbruary 99 Sass aada Mhodology rah Worg ar SMD E/F Laouh M ad rhlo JM (99 Us of a sor fuo o rors ad l roas busss survys Joural of Offal Sass Lawr D ad MKz R (000 Th gral alao of sgfa dg Joural of Offal Sass MLahla GJ ad asford KE (988 Mur Modls: Ifr ad laos o lusrg Marl Dr MLahla GJ ad l D (000 F Mur Modls w Yor: Joh Wly & Sos I Sass aada aalogu o -00-XIE

72

73 Survy Mhodology Ju Vol 3 o 65-7 Sass aada aalogu o -00-XIE Usg Mahd Subsus o Irov Iuaos for Gograhally Ld Daabass Wa Fug hu Ra M Yul Ela Zauo ad la M Zaslavsy bsra Wh adsrav rords ar gograhally ld o sus blo grous loal-ara hararss fro h sus a b usd as oual varabls whh ay b usful suls o varabls ha ar o drly obsrvabl fro h adsrav rords Of daabass oa rords ha hav suff addrss forao o r gograhal ls wh sus blo grous; h oual varabls for hs rords ar hrfor uobsrvd W roos a w hod ha uss forao fro ahd ass ad ulvara rgrsso odls o ra ull uaos for h uobsrvd varabls Our hod ourford alrav hods sulao valuaos usg sus daa ad was ald o h daas for a sudy o ra ars for oloral ar as Ky Words: U orsos; Mull uao; oual varabls; Mahd subsus; dsrav rords Iroduo I a sudy o ra ars for oloral ar as o ad duao ar dsrd varabls for osrug sasal odls of rlva sf rs Uforualy dvdual asurs for hs varabls ar o drly obsrvabl fro h ar rgsry daabass ha ar old fro hosal rords whh l ay adsrav daabass oa rarly forao rqurd for adsrav uross Isad a valus of hs varabls for sall gograhal aras (sus blo grous or ras ludg h sub s ara of rsd ar usd as rgrssors o sa o ad duao ffs alyss usg suh oual varabls ar oo dologal ad halh srvs rsarh (Krgr Wllas ad doss 997 ad of rodu rsuls broadly slar o hos basd o dvdual varabls If boh dvdual ad oual varabls wr avalabl gh b ossbl o sara h ffs of dvdual hararss ad os; a urly oual aalyss hs ffs ar ofoudd ohlss assoaos bw oual soooo hararss ad qualy of ar would suggs a quy robl rgardlss of whhr suh assoaos rarly rfl dvdual or ouy-lvl rlaoshs I h oloral ar ra sudy ah oual varabl for a gv a rord s assud o b h varabl s sus grou (or ra a valu obad by gograhally lg h rord s addrss o a sus blo grou (or ra sall bu subsaal rag of a rords (abou 33% or 696 rords hav suff addrss forao o r ls wh sus blo grous h ag h orrsodg oual varabls uobsrvabl Suh rords wll b alld ugoodabl rords whl rords ha a b ld o sus blo grous wll b rfrrd o as goodabl To gra ull uaos for h uobsrvd oual varabls w roos a sragy ha uss forao fro or ha o ahd as o hl buld arar/ oarar uao odls I arular forao fro h ahd ass aous for sall ara ffs our uao odls so ha hr s o d o lly odl suh ffs Rub ad Zauo (00 us h r ahd subsu sad of ahd as ad roos a arar uao odl usg oly o ahd subsu r rord Th aalyss rsuld fro hr odl wr oard o hos gv by ohr aaly hods a sv sulao sudy bu was o ald o ral daa W d Rub ad Zauo s hod by ( allowg us of forao fro or ha o ahd as r rord ad ( usg a ral rahr ha a arar dsrbuo of rsduals Ths rsarh was ovad by our d for ull uaos for h arally obsrvd varabls h sudy of ra ars for oloral ar as yaa Zaslavsy Fuhs Guadagol rh rss O oor Ws ll Wolf ad Wrgh (003 aalyzd a daas ha ludd uaos grad by our hod Wa Fug hu Dar of Sass Harvard Uvrsy O Oford Sr abrdg M 038 E-al: wfhu@osharvarddu; Ra M Yul Dar of osass ad Edology 408 rold Hous Shool of ubl Halh ad Halh Ss Uvrsy of Massahuss 75 orh lasa Sr hrs M E-al: yul@shoolhuassdu; Ela Zauo Th Wharo Shool Uvrsy of sylvaa 466 Jo M Husa Hall 3730 Walu Sr hladlha 904 E-al: zauo@wharoudu; la M Zaslavsy Dar of Halh ar oly Harvard Mdal Shool 80 Logwood vu oso M 05 E-al: zaslavsy@hdharvarddu

74 66 hu Yul Zauo ad Zaslavsy: Usg Mahd Subsus o Irov Iuaos rfrrg o Rub ad Zauo (00 ad a rlary vrso of hs ar ha aard a rodgs ublao (hu Yul Zauo ad Zaslavsy 00 Ths ar s h frs orhsv ublao of our hodology ad h frs ublshd ror ha dsrbs a alao of Rub ad Zauo s hod o ral daa Th orgazao for h rs of hs ar s as follows So suarzs Rub ad Zauo s hod ad gvs a gral dsro of our hod So 3 ouls h alao of our hod o h oloral ar sudy So 4 llusras a sulao sudy h rfora of our hod rlav o hr ohr ooly-usd orsos adus hods Iuao Mhodology Ths so wll bg wh a suary of Rub ad Zauo s hod followd by a gral dsro of our hod ha luds a dsusso o ou-of-sal vrsus wh-sal ahg h dals of h odlg ad ully-ug ass ad a aalyss of ffy as a fuo of h ubr of ahd ass usd Mahg Modlg ad Mully Iug Rub ad Zauo (00 roosd a hod alld ahg odlg ad ully ug (MMM ha uss ahd subsus o hl gra ull uaos for orsods sal survys whou rqurg ha subsus b rf rlas for h orsods Mahd subsus ar rsodg survy us hos o ah h orsods o o or or ahg ovaras varabls ha ar avalabl ror o h survy ad ar ov for ahg bu o ssarly for odlg s a rsul of ahg orsods ad hr subsus ay shar slar valus hr fld ovaras varabls ha ar oly lly obsrvd ad ar hrfor o avalabl for daa aalyss Modlg ovaras ar varabls ha a b ludd sasal odls o adus for obsrvd dffrs bw orsods ad hr subsus bu ha ay o b avalabl or usd for ahg Th ss of MMM s ha boh ahg ad odlg ovaras ar usd h o of ror ull uao (Ll ad Rub 987 ags ad rfrs hr osdr a sl al whr ag ad addrss ovaras ar avalabl for all us a oulao ror o salg Fdg subsus ahg orsods wh rs o boh ag ad addrss ay b dfful alrav s o ah oly o addrss (g hoosg a ghbor o b a subsu ad adus for sysa ag dffrs bw orsods ad ahd subsus hrough sasal odlg If ghborg housholds wr hos as ahd subsus for orsodg housholds h subsus ad orsods gh hav slar soooo os (g lvls of r ass o ubl rasorao v hough hs hararss gh hav o b rordd I hs al addrss s a ahg ovara ag s a odlg ovara ad h oual soooo hararss ar fld ovaras I suary MMM ( hooss ahd subsus for orsods ad so rsods basd o ahg ovaras ( uss odlg ovaras o f a odl sag h sysa dffrs rsoss bw ars of rsods ad subsus ( ully-us h uobsrvd valus usg h odl ( udr h assuo ha h sa rlaosh holds bw ars of orsods ad subsus ad (v dsards all ahd subsus afr uao Ou-of-Sal Vrsus Wh-Sal Mahg Mahd ass ay b obad fro ou-of-sal daa or wh-sal daa I h Rub ad Zauo aroah ahd subsus ar obad fro ou-of-sal daa afr h ssgss s dd Thr dsro haszs ha h ahd subsus us b dsardd afr uao s ludg suh addoal ass frs would odfy h sal dsg by addg ra ass h blos ha oa uobsrvd daa Mahd ass ar osdrd wh-sal daa f hy ar obad fro h daabas ha s avalabl bfor ug or v fdg ou whh rords h daabas hav uobsrvd varabls s far as h ovrall fral goals ar ord hs ahd ass ar o addoal ass bu ar ar of h orgal daa ollo ad hrfor wll b ludd sf aalyss ssug wh-sal ahg w ra h ugoodabl rords as orsods ad h goodabl rords as rsods For ah ugoodabl rord a gv ubr of ahd ass ar radoly hos fro a ool of goodabl rords wh h sa sall gograhal ara (g z od whh s a osal dlvry od usually rrsg a ara srvd by a sgl a US os off Slarly h sa ubr of ahd ass ar also hos for ah of h radoly sald goodabl rords (s Rub ad Zauo (00 for rodaos o h sz of suh a sal rlav o h oal ubr of ugoodabl rords a gv daas If or ahd ass wr dd ha hos ar avalabl h sa sall ara h slo ool would b dd o h ars gograhal aras ul h rqurd ubr of ahd ass was ahvd Sass aada aalogu o -00-XIE

75 Survy Mhodology Ju ll ahd ass h oloral ar sudy a fro h sa ar daabas I gral ahd ass d o b draw fro h sa oulao whh h orsods ad rsods orgad For al ahd ass for oloral ar rords a b obad fro a gral oulao of ar as ad a odl a h b fd o orr for sysa dffrs o ha wh ahd ass fro a or slar oulao srogr odls a b bul wh or ovaras I our al s w usd ohr as wh h sa ar y rlaoshs o ra ross ad ouo varabls ar lly o b oss 3 Modlg ad Mully-ug sl al of our hod s gv hr o ovy h bas da; ra or ol odls ay of b rqurd Suos h followg rlaosh holds h oulao y T β δ ε ( whr ds sall gograhal ara ds u wh ara ad y ad ar rsvly h rsos ad h hararss of h h u gograhal ara Ths odl luds a rgrsso rdo T β a sall-ara ff δ ad a u-sf rsdual ε W assu ha ε follows so dsrbuo F ε wh a zro ad vara σ o ha hs dvlo gralzs drly o ulvara y W d Rub ad Zauo s hod o allow or ha o ah h sa sall ara baus havg svral ahs sall aras s ossbl (of ov ad sv sus daa or larg adsrav daass Rub ad Zauo s assuo of a sgl ah s arora o survy daa ollo ha rqurs addoal fld wor for ah ah Th rgrsso offs quao ( ar sad usg ay ollo of obsrvaos wh wo or or rords r sall ara o f h rgrsso odl whh h δ ar rad as fd ffs Wh oly wo ass r ara β a sad b sad fro h wh-ara rgrsso T T ( β ( ε ε ( ( y y whr h sall ara ff dros ou Th rsduals fro hs rgrsso hav a syral dsrbuo wh vara σ ssug for h o ha w hav a draw fro h osror dsrbuo of β w arry ou h rs of hs aalyss odoal o ha draw ow suos ha w ar rsd ug for a w u (dd as 0 ara ad ha w hav obad K ahd ass for hs u Do h ouos of hs ahd ass by h vor y T ( y yk ad h orrsodg hararss by h ar X ( T K Wh a fla ror for δ h osror dsrbuo for δ y X β has a y T β (3 ad vara σ / K whr y K y / K ad K / K H h rdv dsrbuo for y y X β has a 0 0 y T T β (4 ( 0 ad vara ( / K σ whh s h su of h rdv vara udr h odl odoal o all arars ad h osror vara of δ Ths sas assu ha h a of h rsduals s a suff sas for δ Ths assuo s ru for h oral dsrbuo (or aural obsrvaos of ay oal faly dsrbuo; w assu s a las aroaly ru for F ε so ha w a bas frs o ha a o ha us of a fla ror lads o ovrdsrsd draws rlav o wha would b obad wh a ror ror fro a hrarhal odl bu s uh slr (sally aalyss wh h ulvara ouos uao for y 0 a b grad by frs drawg σ fro s osror dsrbuo sod drawg β odoal o h draw of σ hrd oug h rdv a quao (4 fro h draw of β ad fally addg a rsdual of vara ( / K σ o h rdv a I sl survys wh β sad by quao ( h osror dsrbuo of β (odoal o σ ad h daa udr a fla ror s aroaly ( β ˆ ( X T X σ whr h h row of X s ( T T I or ol dsgs h osror dsrbuo of β a b aroad usg h o sa ad salg vara alulad udr h assoad dsg Th rsdual a b obad hrough odlg or salg Modlg volvs sag σ usg h rsdual vara of quao ( ad drawg h rsdual udr uvara oraly (s Rub ad Zauo (00 for h sal as whr oly o ahd as was obad for ah rord or so ohr arar dsrbuo W rfr o suh a aroah as arar MMM (MMM alrav s o radoly sal a rgrsso rsdual fro ay ara whos rsduals gh b rgardd as hagabl wh hos fro ara (Rub 987 ags S also Lsslr ad Kalsb (99 so 84 Kalo ad Kasrzy (986 ad Kalo (983 S h vara of suh a rsdual s [( K / ] σ K w ully h radoly-sald rsdual by [( K / K ][ K /( K ] o oba h Sass aada aalogu o -00-XIE

76 68 hu Yul Zauo ad Zaslavsy: Usg Mahd Subsus o Irov Iuaos orr rdv vara W all hs aroah oarar MMM (MMM I suary our hod osss of hr bas ss: Draw ahd ass for h ugoodabl rords ad for so radoly sald goodabl rords; Us h sald goodabl rords ad hr ahd ass o f quao ( whr h δ ar rad as fd ffs ad sav h rsduals; 3 Ra h followg for (usually 5 o 0 s: (a Draw σ fro s osror dsrbuo h β odoal o h draw of σ ; (b For ah ugoodabl rord ra h su of h vor of rdv as obad fro quao (4 ad a vor of rsduals draw usg hr MMM or MMM as a ralzao of h uobsrvd vor of oual varabls 4 Effy Th ffy of a uao s rlad o h ubr of ahd ass usd L V K b h rdv vara of a uao odl whr K ahd ass r rord ar usd For h odl so 3 V ( / K σ K Df ffy as V σ K EK V ( / K σ K (5 for ay osv gr K Effy rass as h ubr of ahd ass r rord rass; for al E 067 E4 08 E0 09 ad E Thorally ah rord a hav as ay ahd ass as rd by avalabl rsours I ra h ubr of ahd ass usd of dds o h os of ahd ass ad h os of ouao volvd odl fg I our hod h os of ouao for ah addd ahd as r rord s glgbl I h oloral ar sudy whl h ahd ass wr fr h ably o do h uao basd o a ld ubr of ahd ass was rual baus ofdaly rsros rvd vsgaors fro usg h r daas odlg wh z ods (v a odd for aahd For llusrav uross w wll us wo ahd ass r rord subsqu aalyss 3 lao: Th oloral ar Sudy Th oloral ar daabas has a oal of a rords of whh aroaly 33% ar ugoodabl og hs abou half hav O bo addrsss (of a rural ara ad h rs ar syd addrsss or addrsss fro wly dvlod aras ha ar o addrss daabass I a sudy of faors rdg rovso of hohray for oloral ar as vsgaors blvd ha h followg hr sus blogrou as would b usful oual varabls: Y Y Y 3 da houshold o r wh o hgh shool dloa ad r blow ovry lvl Ths varabls wr obsrvd goodabl rords bu uobsrvd ugoodabl rords Th as was o gra ull uaos for h uobsrvd sus varabls usg h hods so Eah of h blo-grou as was rord h sus daa for s ra/h grous ad h sf aalyss usd oly h s of blo-grou as orrsodg o h ra/hy of ah a For uaos usd yaa al (003 w hrfor fd s sara odls o u all 8 (6 3 valus for ah ugoodabl a ad h sld h hr varabls r o ah a; o dsrbuos for dffr ra/h grous wr o ora baus ah uao oly usd valus for a sgl grou alrav would hav b o us ra as a ahg varabl bu hs would hav ford us o s so ahs a a uh grar dsa gograhally dlug h rdv valu of h gograhal ah For osory uross w assu hforh ha oly h blo-grou a orrsodg o h ra of ah rsod s avalabl bu o h as orrsodg o h ohr fv ras ha ar avalabl sulaously h sus daa Ths s or yal of daa ha would b olld drly fro h rsod whr h ra varabl slf (as a odlg varabl s qu rdv baus o daa for ol of dffr ras rfl dffrs o assoad wh ra 3 Mahg ad h Daas Th addrsss of ovr 90% of ugoodabl rords hav z ods Z od was hrfor hos as a ahg ovara sl dagos for s usfulss aars so 3 Th ural squ of z ods dos o always orrsod o ghborhood dsa rlaoshs For al abrdg Massahuss has a 038 os off ha also uss h 038 z od for albos ad arby oso hr s a 05 z od ha was arvd ou of h 05 ara Isad of usg h ural squ of z ods h dsas bw z ods wr oud basd o lauds ad loguds of hr a os offs udr h assuo ha wo z ods wr loss o ah ohr f hr a os offs wr loss o ah ohr Sass aada aalogu o -00-XIE

77 Survy Mhodology Ju Th oloral ar daabas has 696 ugoodabl rords Th sa ubr ( * 696 of goodabl rords was radoly sld fro h sa daabas For ah of hs 339 rords wo ahd goodabl ass wr radoly hos fro s ow z od or (f ssary ghborg z ods Ths rad a daas wh rords o ha * was a ov ho baus h daa wr fr I gral h ho of * ould aff boh h oal os ad h rso of h sas oh h radoly sld goodabl rords ad h ahd ass wr whsal daa ad h wr rad h aalyss for yaa al (003 W asd h ar rgsry for hs ass oly baus for ofdaly uross w ould o do h ahg ourslvs wh h daa (for h sa ass ha w had had Th odlg ovaras usd h uao odl wr h gh adsrav-rord varabls: ag s ra aral saus ar sag hohray ra ar y ad radohray ra ad agory of rag hosal s ra ollg of Surgos ardao as of 999 (OS99 Ths varabls ar obsrvd for all 076 rords ludd h uao odl (So of hs varabls ar rdors ad so ar ouos h sf odls of h a aalyss bu h dso s rrlva for uao Th sus a valus Y Y ad Y 3 ar obsrvd goodabl rords bu o ugoodabl rords Ths varabls wr rad as ouo varabls of h uao odl so 3 Th daa sruur s rrsd by Tabl Tabl Sruur of Daa Usd Iuao for h oloral ar Sudy Daa* Egh Modlg ovaras sus Varabls g S OS99 Y Y Y 3 Ugoodabl??? Frs Mah Sod Mah Goodabl Frs Mah Sod Mah * Thr wr 696 rords ah of h s ys of daa obsrvd? uobsrvd for w fd h odl h rag ouos y ad y 3 wr rasford usg h sald-log fuo: ( y a/( b a log ( y a/( b a wh a 0 5 ad b 00 5 so ha afr uaos h vrs rasforao wh roudg o h ars gr (6 would yld ud valus bw 0 ad 00 lusv (Shafr 999 Slarly a log-rasforao was ald o h o ouo y so ha h ud os would b ogav o ha h dsrbuos of h rasford varabls ar losr o oraly ha hy ar o h orgal sal (Shafr 997 To oao sl w rdf y y ad y 3 as hr rasford vrsos 3 rlary Dagoss sl dagos s for h usfulss of h ahg ovaras s o oar h adusd R for h rgrsso odls rdg h hr sus varabls wh oly h odlg ovaras h odls wh oly h ahg ovaras ad h odls wh boh I hs alao z od was h oly ahg ovara Thr wr 33 ds z ods (h 3 duy varabls h 8480 fully obsrvd rords (h goodabl rords ad all frs ad sod ahs Tabl shows h adusd R for odls wh oly h gh odlg ovaras odls wh oly z od ad odls wh boh odlg ovaras ad z od Th adusd R for odls wh boh odlg ovaras ad z od ar hghr ha h orrsodg os for odls wh oly o of h wo ovara ys Our uao rodur uss forao fro boh ahg ad odlg ovaras ad hus a b d o wor br ha rodurs usg oly h ahg or h odlg ovaras (as show by h sulao sudy so 4 lhough h orbuo of h odlg ovaras o R s rlavly ods hr luso s ora for rovg sysa bass ad rorly rrsg rlaoshs ha gh b ora h sf odls Tabl dusd R for lrav Rgrsso Modls Oly Oly Mahg Modlg ovara ovaras (Z od oh Modlg ad Mahg ovaras Mda houshold o (I r wh o hgh shool dloa (EDU r blow ovry lvl (OV Modl dgrs of frdo (a 6 (b Sal szs Rsdual dgrs of frdo (a Wh r (b Th odlg ovaras ar ag s ( lvls ra (6 lvls aral saus (6 lvls ar sag (6 lvls hohray ra ( lvls ar y ad radohray ra (3 lvls ad agory of rag hosal s ra ollg of Surgos ardao as of 999 (6 lvls To dr whhr a ulvara odl was dd w fd a ulvara-ouo rgrsso odl wh boh Sass aada aalogu o -00-XIE

78 70 hu Yul Zauo ad Zaslavsy: Usg Mahd Subsus o Irov Iuaos odlg ovaras ad z od Th sad orrlaos bw h rsduals wr: r 094 r ad r whr varabl s da houshold o varabl s r wh o hgh shool dloa ad varabl 3 s r blow ovry lvl Ths sas wr sgfaly dffr fro zro whh hrfor dad ha ulvara vrsos of h hods so 3 should b usd o gra uaos 33 Mull Iuao Rsuls ad oarsos Iuaos udr MMM wr usd h sudy of faors rdg rovso of hohray for oloral ar as (yaa al 003 Thr odl ludd hr daor varabls for rags of oual o oghr wh ohr varabls rrsg a ad hosal hararss Th ull uao aalyss shows ha h forao loss du o ssg forao s always lss ha 0% whh s uh sallr ha h frao of ugoodabl rords (33% s d h largs fraos of ssg forao aard for h o varabls Th sf rsuls yaa al (003 would o hav hagd draaally f h ol ass had b drod I hs y of rsarh howvr vry as s rous ad sv ad savg h 33% wh ssg daa was a orbuo o h sudy For oarso varas of arars udr h ol-as aalyss wr o h avrag 40% largr ha hos udr ull uao aalyss Suh rag dffrs ar los o h frao of ol ass dld for hs aalyss Wh h uaos grad by our hod wr ludd h sf aalyss h rso of h sa of h rural ff was draaally rovd (usg oly h ol ass ld o 46% ras vara du o h orao of ugoodabl rords rural aras (6% of rural rords ar ugoodabl bu oly 3% of orural rords ar ugoodabl 4 Sulao Sudy Ths sulao sudy oars rfora of our w hod wh hr ohr ooly-usd orsos adus hods Th oulao of hs sudy was h 696 fully obsrvd rls h 696 goodabl rords ad h orrsodg frs ad sod ahs (o row fro ah of h las hr horzoal blos Tabl or 5088 obsrvaos For sly w assud ha h rls wr fro ds z ods (lusrs h I 696 Eah lusr oad hr us ( u 3 ad h rord of ah u ossd of u (h ovaras ad y u (h sus varabls 4 Sulad Daa ad Rsos Mhas ssug ha h dsg was lusr salg wh sal sz 800 w drw rado sals of 800 lusrs For ah rado sal abou half of h 800 lusrs wr radoly sld o hav a ugoodabl rord whh h sus varabls wr uobsrvd wh h robably of ssgss ddg o a dvdual s ra ad o h a o of h lusr (z od W sulad ssgss udr a uloal log odl whr h ouos ar: ohg uobsrvd ( w 0 y uobsrvd w y uobsrvd ( w ad y 3 ( uobsrvd ( w 3 Sfally for ah I l z 0 0 ad z u a b I (u u s Wh (a o z od (7 whr u 3 Th r ( w u ( zu ( z for 3 u 0 u u 0 3 (8 Th rsuls of hs sulao sudy wr basd o daass grad by h has wh a b ad whh ad abou 7% of h us a rado sal ugoodabl wh robably of goodg osvly rlad o Wh ra ad hghr blolvl o Th as was o us h rado sal o sa y h a valus of h oulao (696 lusrs Th sulao odos dsrbd h rdg aragrahs wr dsgd o gv a srg s of h rodur ad alravs by aggrag h a of uobsrvd daa ad ag h ssgss srogly rlad o hararss boh of h dvdual ad of h ara W wr o ag o sula h a odos of h alao so 3 bu rahr o us a arfal oulao wh slar dsrbuos o hos h ral oulao o llusra h worgs of our hod ad s oors 4 Ifral Mhods ad Masurs of rfora rlary rsuls dad ha h rfora of MMM ad MMM s slar; MMM s howvr slr (sally aalyss wh ulvara ouos baus h hod dos o rqur l arar odlg of h rsdual vara Our sulaos oard rfora of MMM (usg wo ahd ass r rord wh hr ohr ooly-usd orsos adus hods: Sass aada aalogu o -00-XIE

79 Survy Mhodology Ju ol-as Mhod (M Th oulao as ar sad fro all goodabl us of a rado sal Subsu Sgl Iuao (SSI Ths s h radoal us of subsus Th uobsrvd sus varabls of ah ugoodabl u ar rlad by h valus of h sus varabls of a radoly sld u fro h sa lusr Th rsulg sal s rad as f hr had b o ugoodabl u; all 800 lusrs suh a sal ar usd for sag h oulao as 3 Mulvara oral Mull Iuao (MMI Ths hod uss oly o radoly sld u fro ah of h fully obsrvd lusrs a rado sal o f h ulvara oral lar rgrsso y T ~ ( βt 0 Σ wh a oforav ror o h arars Th odl s h usd o ra ss of ull uaos for h uobsrvd sus varabls usg a dr ulvara gralzao of h algorh gv by Rub (987 ag 67 o ha M uss hr ahg or odlg ovaras SSI uss oly h ahg ovara (z od MMI uss oly h odlg ovaras ad MMM uss boh h ahg ovara ad h odlg ovaras Th M ad SSI daa ar aalyzd by h usual ol-daa hod whh sas h oulao a fro h daa wh h arora saor for lusr salg fro a f oulao ludg h f oulao orro (ohra 977 hars 9 0 oh MMI ad MMM rodu ss of ol daa ah of whh s aalyzd by h sa ol-daa hod usd for h M ad SSI daa; h ss of o ad vara sas ar h obd usg h ull uao obao rul (Rub 987; Shafr 997 ags 08 0 For ah sulao { T} w do h o sas fro h four hods by y ( y SS( ym ( ad y ( ad h as of hs quas aross sulaos ar wr as y y SS ym ad y rfora valuao of h four orsos adus hods wll b basd o hr asurs: r rduo h avrag bas of a saor rlav o h avrag bas of h M saor Do h avrag bas of a saor by b E Th be y y T E whr E { SS M } W df h r rduo h avrag bas of a saor rlav o h avrag bas of h M saor as R( b E b b b b whr b E s a l of b E ad b s h orrsodg l b y dfo R ( b b s zro Esad ovrag of h oal 95% ofd rvals for y Irvals rodud by h M or SSI sas wr osrud udr arora dsrbuos For rvals assoad wh h MMI or MMM sas w followd h rodur ould Shafr (997 ags 09 0 ad rlad h dgrs of frdo v wh h udad vrso of arard ad Rub (999 3 Esad frao of ssg forao abou y For ah of MMI ad MMM w oud ˆλ a sa of h frao of ssg forao abou y (s arard ad Rub (999 for h os r rsso 43 Rsuls Th sulao rodur was ld 000 s ad 0 was usd for MMI ad MMM Th a valus of h sus varabls h oulao wr y ( T Th avrag bas of h M saor was b M ( T Ohr rsuls ar suarzd Tabl 3 MMM ahvd larg r rduos rlav avrag bas (950% o 995% SSI rdud bass or ha MMI baus h ahg ovara (z od was uh or forav ha h s of odlg ovaras (so 3 S h rsos has was ogorabl (h rsos robabls ddd arly o o h oor rfora of MMI whh dd o us h gograhal forao o hl rd o was d o ha MMI s basd ad h bas s larg ough so ha wh h sal sz osdrd hs ar h ofd rvals vr ovrd h hyohal oulao valus Udr MMI ad MMM h r of ssg forao was uh lss ha h avrag r of uobsrvd daa Th r of ssg forao was sallr udr MMM ha udr MMI Oly MMM rodud wll albrad rvals wh orr ovrag I suary MMM obs h bs faurs of h ohr wo hods los-o-oal ovrag ad lss ssg forao E Sass aada aalogu o -00-XIE

80 7 hu Yul Zauo ad Zaslavsy: Usg Mahd Subsus o Irov Iuaos Tabl 3 Sulao Rsuls (a : as Rduo ovrag ad Frao of Mssg Iforao Masur Ma Mhod MMM MMI SSI r bas I Rduo EDU R ( E M (b OV Esad I ovrag of h EDU % Is ( OV Esad I frao of ssg EDU ( d forao ˆλ OV (a asd o 000 rlaos ad 0 (b y dfo 00R ( bm bm 0 ( Rsuls for h M sas wr all zros (d Th avrag r of uobsrvd daa was aroaly 7% 5 oluso Ths wor ds Rub ad Zauo (00 wo rss Frs our hod allows or ha o ahd as r rord W show horally ha h ffy of a uao rass as h ubr of ahd ass r rord rass Wh h os of ahd ass s rlavly low our hod offrs a oo whr forao of or ha o ahd as r rord s usd o hl f uao odls a a glgbl ouaoal s Sod MMM dos o rqur l arar odlg of rsdual vara(s h slfyg h odlg as (sally for aalyss wh ulvara ouos Ths oarar aroah as fasbl o aly our hod o daass wh ol odl sruurs I a sulao sudy MMM sas ahvd subsaal bas rduos ad MMM rodud ofd rvals wh orr ovrag lhough w hav fousd o gograhally-basd ahg o ol uobsrvd gograhally-ld varabls h rodurs dsrbd hs ar a b gralzd o ohr ahg varabls For al o u lal varabls gh b or arora o ah o aohr a h sa hosal f lal hararss ad hras ar lly o b or srogly assoad wh h hosal ha wh h gograh loao of h a s rsd owldgs Ths rsarh was suord ar by h urau of h sus hrough a ora wh h aoal Oo Rsarh r ad Daars I ad by a gra fro h gy for Halhar Rsarh ad Qualy (HRQ ad h aoal ar Isu (HS09869 Th auhors ha Joh Z yaa for ladrsh of h Qualy of ar ar rsarh ro Mar ll ad Robr Wolf for rarao of daa ll Wrgh for hs suor o hs rsarh ad h assoad dor ad wo aoyous rfrs for hr hlful os Rfrs yaa JZ Zaslavsy M Fuhs S Guadagol E rh M rss RD O oor L Ws DW ll ME Wolf RE ad Wrgh WE (003 Us of aduva hohray ad radao hray for oloral ar a oulao-basd ohor Joural of lal Oology arard J ad Rub D (999 Sall-sal dgrs of frdo wh ull uao ora hu WF Yul RM Zauo E ad Zaslavsy M (00 Usg ahd subsus o rov uaos for gograhally ld daabass rodgs of h Survy Rsarh Mhods So ra Sasal ssoao ohra WG (977 Salg Thqus w Yor: Joh Wly & Sos I Kalo G (983 osag for Mssg Survy Daa Rsarh Ror Srs rbor MI: Isu for Soal Rsarh Kalo G ad Kasrzy D (986 Th ra of ssg survy daa Survy Mhodology -6 Krgr Wllas D ad doss (997 Masurg soal lass US ubl halh rsarh: os hodologs ad gudls ual Rvw of ubl Halh Lsslr JT ad Kalsb WD (99 osalg Errors Survys w Yor: Joh Wly & Sos I Ll RJ ad Rub D (987 Sasal alyss wh Mssg Daa w Yor: Joh Wly & Sos I Rub D (987 Mull Iuao for orsos Survys w Yor: Joh Wly & Sos I Rub D ad Zauo E (00 Usg ahd subsus o adus for ogorabl orsos hrough ull uaos I Survy orsos (Eds R Grovs R Ll ad J Elg w Yor: Joh Wly & Sos I Shafr JL (997 alyss of Iol Mulvara Daa Lodo: haa & Hall Shafr JL (999 ORM: Mull uao of ol ulvara daa udr a oral odl vrso Sofwar for Wdows 95/98/T avalabl a h://wwwsasudu/ ~ ls/ sofwahl Sass aada aalogu o -00-XIE

81 Survy Mhodology Ju Vol 3 o Sass aada aalogu o -00-XIE Hrarhal aysa ogorabl orsos Rgrsso Modls for Sall ras: lao o h HES Daa algob adra ad Ja Wo ho bsra W us hrarhal aysa odls o aalyz body ass d (MI daa of hldr ad adolss wh ogorabl orsos fro h Thrd aoal Halh ad uro Eaao Survy (HES III Our obv s o rd h f oulao a MI ad h rooro of rsods for doas ford by ag ra ad s (ovaras h rgrsso odls ah of hry fv larg ous aoug for h orsods Marov ha Mo arlo hods ar usd o f h odls (wo slo ad wo ar ur o h HES III MI daa Usg a dva asur ad a ross-valdao sudy w show ha h ogorabl slo odl s h bs aog h four odls W also show ha fr abou MI s o oo ssv o h odl ho rov s obad by ludg a sl rgrsso o h slo odl o rfl hags h rlaosh bw MI ad ag Ky Words: ross-valdao; Dva; Mrools-Hasgs salr; oral-logs rgrsso odl; Sl rgrsso odl Iroduo Th aoal Halh ad uro Eaao Survy (HES III s o of h survys usd by h aoal r for Halh Sass (HS o assss h halh of h US oulao O of h varabls hs survy s body ass d (MI ad h World Halh Orgazao has usd MI o df ovrwgh ad obsy Udr gorably saors fro h HES III daa ar basd baus hr ar ay orsods ad h a ssu w addrss hr s ha orsos should o b gord baus rsods ad orsods ay dffr Th uros of hs wor s o rd h f oulao a MI for hldr ad adolss ossrafd by ouy for ah doa ford by ag ra ad s ad o vsga wha adus ds o b ad for ogorabl orsos Our aroah s o f svral hrarhal aysa odls o aooda h orsos has Rly svral arls hav b wr abou ovrwgh ad obsy I oulg h frs aoal la of ao for ovrwgh ad obsy h Surgo Gral alld for swg hags shools rsauras worlas ad ous o hl oba h growg d of ras who ar ovrwgh or obs H sad ha h obsy ror Is o abou shs ad s o abou aaras W r alg abou halh s od by Squrs (00 Halh ar oss for ovrwgh ad obsy oal a sad $7 bllo aually Ovrwgh hldr of bo ovrwgh adulhood ad ovrwgh adulhood s a halh rs (Wrgh arr Lao ad raf 00 I a vry rsg arl usg HES daa Ogd Flgal arroll ad Johso (00 dsrb h os r aoal sas of h rval ad rds ovrwgh aog US hldr ad adolss asd o a ld aalyss hy olud Th rval of ovrwgh aog hldr h Ud Sas s oug o ras sally aog Ma- ra ad o-hsa bla adolss Svral dsordrs hav b ld o ovrwgh hldhood oal ras y dabs llus s rlad o h ras ovrwgh aog hldr (Fago-aaga 000; so ar ardovasular rs faor hgh holsrol lvls ad aboral gluos lvls (Dz 998 Thus would b hlful o sudy h MIs for hldr ad adolss usg hods ha a rovd aura adus for orsos ad br asur of rso Lg do ovaras ad y h rsos varabl Rub (987 ad Ll ad Rub (987 dsrb hr ys of ssg-daa has Ths ys dffr aordg o whhr h robably of rsos (a s dd of ad y (b dds o bu o o y ad ( dds o h y ad ossbly Th ssg daa ar ssg olly a rado (MR (a ssg a rado (MR (b ad o ay say ha h daa ar ssg o a rado (MR ( Modls for MR ad MR ssg-daa hass ar alld gorabl f h arars of h dd varabl ad h rsos ar ds (Rub 976 Modls for MR ssg-daa hass ar alld ogorabl algob adra Dar of Mahaal Ss Worsr olyh Isu 00 Isu Road Worsr M E-al: bala@wdu; Ja Wo ho aoal r for Halh Sass 33 Toldo Road Hyasvll MD 078 E-al: w7@dgov

82 74 adra ad ho: Hrarhal aysa ogorabl orsos Rgrsso Modls for Sall ras orsos odls a b lassfd vry broadly o slo ad ar ur odls (g s Ll ad Rub 987 L [ y ] ad [r ] do rsvly h dsy fuo of h rsos varabl y ad h rsos daor r wh obvous oaos for h o ad odoal dss Th h slo odl sfs ha [ y r] [ r y][ y] ad h ar ur odl sfs [ y r] [ y r][ r] Th slo aroah was dvlod o sudy sal slo robls (g Ha 976 ad Olso 980 Whl h wo odls hav h sa o dsy ra h oos [ r y] ad [ y ] for h slo odl ad [ y r] ad [r ] for h ar ur odl ar sfd Thus hs odls ay dffr Thus w us wo ogorabl orsos odls a slo odl ad a ar ur odl o aalyz h HES III daa Eah odl s usd h hrarhal aysa fra wor for our ogorabl orsos robl ad o sudy ssvy o odl ho h rsuls ar oard I h slo odl h rsos rosy s rlad o MI oly ad h h odl o MI has a lar odl o ag ra s ad h rao of ra ad s I h ar ur odl h rosy o rsod s rlad o ag ra ad s (o MI ad h odl o MI has wo losly rlad lar fors o ag ra s ad h rao of ra ad s Ths wo odls hold for h r oulao Th MI valus of h orsods ad h osald dvduals ar rdd fro ah odl W rfr h slo odl baus w a orora h sruur h HES III daa ad basd o sasal argus hs urs ou o b ru Grls R ad Zshag (98 dvlod a oral-logs rgrsso odl for ug ssg valus wh h robably of rsos dds uo h varabl bg ud Thy ald h odl o daa o wags ad salary h urr oulao Survy (S daa o wags Davd Ll Saul ad Trs (986 oard h S ho d hod ad h oral-logs rgrsso odl o wags ad salary fro a slar daa s ad hy foud vry ll dffr bw h wo hods W o ha h oral-logs rgrsso odl s a ogorabl orsos slo odl bu dos o aou for lusrg To aooda lusrg wh ous h HES III daa s aural o sar wh h oral-logs odl Our hrarhal aysa slo odl has a sal sruur I HES III h rosy o rsod rass wh ag (ra ad s lay a or rol ad doors blv ha obs dvduals d o o ur u for h hysal aao Thus gv h MI valus l Grls al (98 h rsos daors follow a logs rgrsso odl wh h logarh of h MI valus bg h ovara I ur h logarhs of h MI valus ar dsrbud aordg o a lar odl whh h ovaras ar ag ra ad s Ths s h os ora forao w orora o h slo odl I addo ul Grls al (98 our odl luds lusrg ffs o aou for hrogy aog ous hrough h rsos daors ad h MI valus Hr ah ouy has s ow s of arars ad hr s a oo dsrbuo ovr hs ss of arars Ths s also a ora ror forao w orora o our odl ad s o of h arav faurs of h hrarhal aysa hodology I h aysa aroah h a dffuly s forulag h rlaosh bw h rsods ad orsods Ths lar ssu a b aoodad wh h slo aroah hrough h oral-logs sruur W also osdr a hrarhal ays odl wh h ar ur aroah Th ar ur odl s a usful alrav o sudy ssvy o h assuo h slo odl To assss h assuo of ogorabl orsos w also osdr sal ass of h slo ad ar ur odls o oba wo gorabl odls W foud ha a ffh odl s rqurd whh w d our slo odl o a sl rgrsso odl o aooda h dya rlao bw MI ad ag adra Ha ad ho (00 dvlod a hodology o aalyz h MI daa by ag ra ad s wh MI s agorzd o hr rvals Ths s a uloal so of h orsos ogorabl aalyss of Sasy (99 for bary daa Ths hodology als grally o ay ubr of lls svral aras (ous our alao adra ad ho (00 ab osdr furhr sos of h wor of Sasy for bary daa ( daa fro h aoal Halh Irvw Survy ad h aoal r survy Hr w do o agorz h MI valus bu rahr w ra h hr ow rgh as ouous valus Th quas of rs ar h f oulao a MI ad h rooro of rsodg dvduals ah doa ford by ag ra s ad ouy Th rs of h ar s orgazd as follows I so w brfly dsrb h HES III daa I so 3 w dsuss h hrarhal aysa odls for gorabl ad ogorabl orsos W also dsrb h odl fg odl slo ad assss whh us rdv dva ad ross-valdao I so 4 w dsrb h aalyss of HES III MI daa So 5 has a dsro of a sl rgrsso odl ad oarsos Fally so 6 has oludg rars abou our aroah Sass aada aalogu o -00-XIE

83 Survy Mhodology Ju HES III Daa Th sal dsg s a srafd ulsag robably dsg whh s rrsav of h oal vla osuoalzd oulao ohs of ag or oldr h Ud Sas Th ubr of sald dvduals ah ag-ra-s grou s ow for ah ouy Th sal sz by ouy ag ra ad s ar rlavly sars Furhr dals of h HES III sal dsg ar avalabl (aoal r for Halh Sass Th HES III daa ollo osss of wo ars: h frs ar s h sal slo ad h rvw of h brs of a sald houshold for hr rsoal forao ad h sod ar s h aao of hos rvwd a h obl aao r (ME Th halh aao has forao o hysal aao ss ad asurs rford by has ad s ollo Th sal was sld fro housholds 8 ous aross h oal Ud Sas durg h rod fro Oobr 988 hrough Sbr 994 bu for ofdaly rasos h fal daa of hs sudy a fro oly h 35 largs ous (fro 4 sas wh oulao a las for sld ag agors by s ad ra I hs ar w aalyz ubl us daa fro hs 35 ous; h dograh varabls ar ag ra ad s ad h halh daor of our rs s body ass d (MI wgh logras dvdd by h squar of hgh rs (Kuzars arrol Flgal ad Troao 997 Th World Halh Orgazao (WHO osulao of Obsy 000 has dsgad a adul wh MI a las 30 as obs; ovrwgh rfrs o aduls wh MI h rag [5 30 For hldr 6 yars old ad adolss 7 9 yars old ovrwgh ad obsy ar ag-dd orsos ours h rvw ad aao ars of h survy Th rvw orsos arss fro sald rsos who dd o rsod for h rvw So of hos who wr alrady rvwd ad ludd h subsal for a halh aao ssd h aao a ho or a h ME hrby ssg all or ar of h aaos Hr w do o osdr h sall ubr of dvduals whos MI valus ad ovaras (ag ra ad s ar ssg ( u orsos For sly ad for all raal uross s rasoabl o lud all dvduals wh hr ovaras ( ol daa ad orsos rord our daa aalyss oh ad Duffy (00 o ou ha Halh survys ar a good al whr ss lausbl ha rosy o rsod ay b rlad o halh W o also ha for hldr ad adolss h obsrvd orsos ra s abou 4% aral raso for h orsos for youg hldr s ha h ars or oldr ohrs wr rly rov ad would o allow hr hldr o lav ho for a hysal aao W sudy h MI daa for four ag lasss ( yars Rallg ha hr ar 560 (35 4 doas h sal szs o h avrag ar vry sall r doa (g 647/560 4 Thus hr s a d o borrow srgh fro h doas lso h sal sz s sall rlav o h f oulao sz (g 00 (647/ % Th rdo robl ds uh ouao Th obsrvd daa da ha hr s a rasg rd of MI wh ag wh slghly rasg varably HES III daa ar adusd by ull sags of rao wghgs o b oss wh h oulao; s Mohadar ll ad Wasbrg (994 I hs rao-hod orsos adus s do by rao sao wh h sa adus lass ad h dsrbuos of h rsods ad orsods ar assud o b sa Thr s a d o osdr hods for hadlg ogorabl orsos ohr ha h rao-adus hod Hr w rs a aysa hod as a ossbl alrav for sudyg HES III orsos Shafr Ezza-R Johso Khar Ll ad Rub (996 ad a orhsv ull uao ro o h HES III daa for ay varabls Th uros was o u h orsos daa ordr o rovd svral daa ss for ubl us s o of h laos of h ro hy sad h rodur usd o ra ssgss orrsods o a urly gorabl has; h sulao rovds o forao o h a of ossbl dvaos fro gorabl orsos ohr lao s ha h rodur dd o lud gograhal lusrg Our uros s dffr; w do o rovd ud ubl-us daa Ul Shafr al (996 w lud lusrg a h ouy lvl alhough hr ay b a d o lud lusrg a h houshold lvl For h ol daa hr ar 6440 housholds Of hs housholds 5% orbud o rso o h sal 5% wo rsos ad 4% a las hr rsos W hav alulad h orrlao off for h MI valus basd o arg h brs wh housholds (s Rao 973 ag 99 I s 09 whh das ha as a frs aroao h lusrg wh housholds a b gord For our urr alao fr s rqurd for ah ag ra ad s doa wh ouy O sadard sall ara sao hod s o dfy ah sall ara by a arar ad h assu a oo sohas ross ovr h 560 arars u baus of h sarsss of h daa hs s o dsrabl Thus our odls ar osrud a ouy lvl ad a h sa ag ra ad s ar rrsd as ovaras Ifr s ad for Sass aada aalogu o -00-XIE

84 76 adra ad ho: Hrarhal aysa ogorabl orsos Rgrsso Modls for Sall ras ah doa ford by rossg ag ra ad s wh ouy hrough our rgrsso odls Ths s a y o our aalyss 3 Hrarhal aysa Mhodology I hs so w dsrb wo aysa odls for ogorabl orsos ad w ddu wo addoal gorabl odls as sal ass W dsrb h odl slo ad assss for h sld odl ( h slo odl Thr ar daa fro l 35 ous ad ah ouy has (ow dvduals W assu a robably sal of dvduals s a fro h h ouy L s do h s of sald us ad s h s of osald us L r for K l ad K b h rsos daor ( r for rsods ad r 0 for orsods for h h dvdual wh h h ouy h oulao lso l b h logarh of h MI valu W foud ha h logarh rasforao gvs a br rrsao ad w us hroughou o ha r ad ar all obsrvd h sal s bu hy ar uow s L r r ( r s h ubr of sald dvduals ha rsodd h h ouy For ov w rss h MI as K r r K s ad K s for ouy y o ha w o for wha follows s ha h r dvduals ar o ssarly rado rsods fro h dvduals radoly sald Ths s h orsos bas w d o addrss I s lar ha w d o rd h MI valu for (a h orsods s ad (b h dvduals s Thus for h f oulao of dvduals w d a aysa rdv fr for X r ad for K l ( s r r ( s r Lg / r r /( r ( s ad / w o ha X ( s ( s r ( s ( r ( s { g ( g } s ( f f ( ( s whr f / ad g r / o ha whl h f ( r ar fd by dsg h g ad s ar obsrvd lso ( s ( s lg ˆ r / ad ( r /( ˆ ( s ( s f ˆ ( f ˆ ( K l W dvlo our hrarhal aysa odls o rfor rdv fr for quas l ( ad ( ddg o h doa 3 og Modls Our odls hav wo ars o ar for h rsos has ad h ohr ar for h dsrbuo of MI Ths wo ars ar od o for a sgl odl udr ogorabl orsos or gorabl orsos Frs w dsrb h slo odl For ar of hs odl h rsos dds o h MI as follows β0 β r β ~ roull β0 β (3 ( β 0 d β θ 0 θ σ σ ρ ~ Voral( θ0 θ; σ σ ρ (0 (0 θ ~ ( θ Δ σ σ ~ Gaa( a / a / ad ρ ~ Ufor ( whr ror dss (5 ar all oly dd Th assuo (3 s ora baus rlas h rsos rosy o h MI valus; doors blv ha ovrwgh ad obs dvduals d o o o o h MEs for h aaos lusrg aog h ous s aoodad by (4 ad s hs assuo ha rs a borrowg of srgh aog h ous Th sod ar of h odl s abou h MI Th sgl os ora rdor of MI s ag wh ra ad s layg a rlavly or rol O ossbly s o a h MI valus o b (0 a θ ad (4 (5 (0 Δ ar o b sfd o ha h μ μ α0 α whr a dos ag ad σ 3 oral (0 σ 3 for K l ad K lso hr s a d o udrsad h rlaosh bw MI ad ag ra ad s W l z 0 for a r z for o-bla ad z 0 for bla z for al ad z 0 for fal z 3 z z for h rao bw ra ad s ad w l z ( z0 z z z3 Th for a rgrsso of MI o ag adusg for ra ad s lg α ( α0 α0 α03 α04 ad α ( α α α3 α4 w a α 0 z α v 0 ad α z α v o g μ z α v ( z α v a ~ d ( 0 whr v 0 ad v ar rado ffs rd a zro wh bvara oral dsrbuo show blow for ah odl Thus ar of h slo odl w assu ( z α v ( z α v a ad 0 σ 3 d ~ oral(0 σ 3 a (6 Sass aada aalogu o -00-XIE

85 Survy Mhodology Ju d ( v 0 v σ 4 σ 5 ρ ~ Voral(0 0; σ 4 σ5 ρ (7 ga lusrg aog h ous s aoodad by (7 ad s hs assuo ha rs a borrowg of srgh aog h ous For hs ar of h odl w us h ror α ~ oral( α σ 3 (0 σ Δ 4 ρ σ (0 ~ 5 d ad d ~ α Gaa( a / a / Ufor( ~ oral( α (0 3 Δ (0 3 ad (0 (0 whr a α ad Δ ar o b sfd o ha h ror dss (8 ar all oly dd Th ogorabl orsos ar ur odl s rsd d W hav ludd ra s ad hr rao h rsos ar of h odl alhough hs ur ou o b ussary Th dffr bw h rsods ad h orsods h ar ur odl s ha h rs h rgrsso vary wh ous for h rsods bu o for h orsods; ohr arars ar h sa I hs way w ar abl o r h ogorabl orsos odl o h gorabl orsos odl wh so varao; s adra ad ho (00 a for a slar da W d o do so baus h arars bo udfabl f subsaal dffr bw h rsods ad h orsods s assud h ogorabl orsos odl whou h sf owldg Whl w hav usd rado ffs o dsra bw h rsods ad h orsods h arars rovdg sysa dffr bw h rsods ad orsods odl of Rub (977 ar o dfabl o ha whl h ar ur odl (4 hr ar wo sfaos/ars for ( r 0 ad r bu h slo odl hr s a sgl sfao (0 (0 W show how o sfy arars l θ Δ (0 (0 α Δ d For a ror dffus ror w hoos a o b a valu l 000 O a also us a shrag ror o σ ad σ (s aaraa ad Kass 000; ad Dals 999 u hs s o ssary h hrarhal odl I s a arav rory of h hrarhal aysa odl ha rodus orrlao aog h varabls For al h slo odl (4 ad (7 rodu a orrlao aog h r ad h rsvly Ths s h lusrg ff wh h aras Suh a ff a b obad drly bu wll o b as sl as a hrarhal odl furhr bf of h hrarhal odl s ha as ar of raous varaos aog (8 h aras; hs s aly od o h lusr ff Y aohr bf s ha hr s robusss h odl sfaos a dr lvls byod h salg ross (g fr wh (5 ad (8 s farly robus o odra rurbaos of h sfaos of h hyrarars W hav foud hs rally hr ad lswhr W oba a gorabl orsos slo odl by sg β 0 for all ous wh arora adus h slo odl For a gorabl orsos ar ur odl w s ( z α v0 ( z α v a for boh valus of h r 3 Modl Fg I hs so w dsrb how o us h Mrools- Hasgs salr o f h odls W also us a dva asur o sl h bs odl aog our four odls Th w us a ross-valdao aalyss o assss h goodss of f of h sld odl ad baus h sa gral rl als o h four odls w dsrb odl fg for h slo odl oly Thus w ow ob h odl for h rsos has ad h odl for h MI valus o oba h o osror dsy of all h arars Th for r K K l ar uow; ha s hy ar ( s r la varabls W do hs la varabls by obs ad h obsrvd daa ar dod by Usg ays hor o ob h llhood fuo ad o ror dsrbuo w oba h o osror dsy whh aar fro h oralzao osa s ( s r ( s r ( σ α β v θ ρ ρ ad s gv ( d Th osror dsy ( s ol so w usd Marov ha Mo arlo (MM hods o draw sals fro Sfally w usd h Mrools- Hasgs salr (s hb ad Grbrg 995 for a dagogal dsusso W also usd h ra los ad auoorrlao dagoss rvwd by owls ad arl (996 o sudy ovrg ad w usd h suggso of Gla Robrs ad Gls (996 o oor h ug robably ah Mrools s our algorh I rforg h ouao rg h MI valus hl ahvg ovrg (s Glfad Sahu ad arl 995 Howvr hs s o qu a sraghforward as baus rg h logs rgrsso affs h MI ar of h odl as wll W obad a sal of 000 ras whh w usd for fr ad odl hg y usg h ra los w bur 000 ras ad o ullfy h ff of auoorrlaos w d vry h ra hrafr Ths rul was obad by ral ad rror whl ug h Mrools ss W aa h ug robabls (05 050; s Gla al (996 Sass aada aalogu o -00-XIE

86 78 adra ad ho: Hrarhal aysa ogorabl orsos Rgrsso Modls for Sall ras 33 Modl Slo ad Modl ssss W usd h u osror rdv loss aroah (Glfad ad Ghosh 998 o sl h bs odl aog h frs four Udr squard rror loss h u osror rdv loss s D G r obs r obs obs Var( G E( { } r obs r obs whr f ( f ( Ω ( Ω dω ad r ar h rdd valus ad Ω s h s of all arars Ths asur ds h o obad arlr (Laud ad Ibrah 995 ad w hav a 00 o ah hs arlr vrso o ha for h orsos alao hs asurs ar oud oly o h ol MI daa afr fg our orsos odls I Tabl w rs h dva asur ( D 00 ad s assoad oos goodss of f (G ad h aly ( for h four odls Usg h dva asur h slo odl s uh br Whl s roughly h sa G s uh sallr ag D 00 sallr for h slo odl Th dffr bw h wo ar ur odls ar or rooud ha h dffr bw h wo slo odls Howvr baus sadard rrors ar o avalabl s dfful o ll h srgh of h dffr Tabl oarso of h Igorabl ar Mur ad h Slo Modls Usg h Dva Masur Modl G D 00 SEI SE MI M o: D 00 G ( 00/(00 whr G s a goodss of f a aly ad D h dva; h ar ur (M odl ad h slo odl (SE ar boh ogorabl SEI s gorabl vrso of h slo odl MI s gorabl vrso of h ar ur odl w loo for dfs h slo odl W us a aysa ross-valdao aalyss o assss h goodss of f of h sld odl ( h slo odl W do so by usg dld rsduals o h rsods MI valus L ( ( r( do h vor of all obsrvaos h h ludg h ( obsrvao ( r Th h ( dld rsdual s gv by DRES { E( ( r( } STD( ( r( Ths valus ar obad by rforg a wghd ora salg o h Mrools-Hasgs ouu Th osror os ar obad fro f ( ( r( f ( Ω ( Ω ( r( dω For h ar ur odl f ( Ω f ( r 0 Ω ( r 0 Ω f ( r Ω ( r Ω ad for h slo odl f ( Ω ~ oral{( z α v0 ( z α v a σ3} W also osdrd usg h odoal osror orda (O whh s f ( ( r( valuad a h obsrvd Howvr hs O s lad o slar rsuls for dfyg rs W drw bo los (o show of DRES vrsus h four lvls of ra-s ad h hry fv ous ad hy showd ha h slo odl fs wll W drw bo los of DRES vrsus ag ad rsgly w foud a ar g lass 4 ss o f wll; h rdd MI valus ar sowha hgh for ag lass 5 9; ad ag lasss 0 4 ad 5 9 hav largr varably W loo a h bo los of DRES vrsus ag v furhr by sarag ou h bo los for 8 ( 9 yars old dvdual ags (s Fgur gs 9 fs wll bu hr s a robl wh ags 0 ( a dowward urvaur h das Th ohr hr odls show slar ars furhr rf of h slo odl so 5 fs hs robl 4 Esao ad rdo I hs so w rfor a aalyss o h HES III MI daa for hldr ad adolss ( 9 yars old W us h slo odl ad h as a as o sudy ssvy w oar rdo udr h ogorabl orsos slo odl wh ha of h ohr hr odls 4 Esao W hav sudd h rlao bw MI ad ag usg 95% rdbl rvals for h arars h slo odl Frs h rao of ra ad s s o ora bu as d hr s a ora rlao of MI o ag MI rass subsaally wh ag (95% rdbl rval for α s ( Th ra of ras for wh als s sallr (95% rdbl rval for α s ( ad h 95% rdbl rval for α 3 s ( Thus whl MI rass wh ag hr s rlavly lss ras for wh als ar fro Sass aada aalogu o -00-XIE

87 Survy Mhodology Ju h arar θ whh das srog ogorably h ohr arars ar ssally uora For al h 95% rdbl rvals for ρ ad ρ ar ( ad ( rsvly dag ha a slr odl a b usd ( ρ ρ 0 W a u h ssu of gorably furhr W drw bo los (o show of h osror dss of h β obad fro h ras fro h Mrools-Hasgs salr by ouy ll h bo los ar abov zro Ths suggss ha h orsos has for ah ouy s ogorabl I addo hr ar varyg dgrs of ogorably For al svral ous hav h das of h bo los ar 5 whl ohrs hav h ar 4 rdo I s dsrabl o rd h f oulao a MI valu ad h rooro of rsods h f oulao Th sald orsods MI valus ar obad hrough hr odoal osror dss ludd h Mrools-Hasgs salr Th osald MI valus ar o b rdd I s worhwhl og ha our odls ar ald o h logarh of MI wh ah dvdual havg hr/hs ovaras ad so h logarh of ah dvdual osald valu has o b rdd ad h rrasford o h orgal sal Howvr h ouao s rdud osdrably baus ag ra ad s for ah osald dvdual s o ow bu h ubr of dvduals ah ag-ra-s doa s ow h US oulao by ouy Th dsrbuos of h osald dvduals ar f ( r obs r obs obs obs f ( r Ω ( Ω r dω K l K For h ar ur odl w hav f ( r Ω f ( r Ω ( r Ω ad for h slo odl w hav f ( r Ω ( r Ω f ( Ω whr Ω do h s of all arars Thrfor f w a a sal of sz M fro h ( h osror dsrbuo { Ω : h K M} a saor for obs f ( r f ( rˆ obs M M f ( h r Ω (h Thus w a fll h ad r for ah Ω obad fro h MM algorh fro whh w g M ( h ( h ralzaos X h K M Ifr a ow b ad abou X ( ad ( ( h D R E S GE Fgur o los of h ross-valdao rsduals (DRES by ag for h slo odl Sass aada aalogu o -00-XIE

88 80 adra ad ho: Hrarhal aysa ogorabl orsos Rgrsso Modls for Sall ras W rs 95% rdbl rvals for h f oulao a (FM MI valu ad h f oulao rooro (F rsodg ordr o udg ssvy o h four odls o ha w rovd hs rvals for ah doa: ra by s for ah ag lass by ouy ad baus hy ar vry slar aross doas w hav rsd Tabl h avrag of h d os of h rdbl rvals ovr ouy for bla fals oly Th rvals for h FM aross h odls ar vry slar Howvr hos for h F ar vry dffr Th rvals for h ar ur odl ad s gorabl vrso ar slar for ag lass 4 Ths s d baus hs odls rss a lar rgrsso of h logarh of h odds of rsodg o ag Th rvals for h F udr h wo ar ur odls ar ssally h sa baus hy hav h sa rlao wh ag ra s ad hr rao Th rvals for h gorabl vrso of h slo odl ar all h sa ovr ag baus h rsos ar of hs odl boh ag ad MI ar gord W o ha h rvals for h slo odl hav fors slar o h ar ur odl ad s gorabl vrso s h rvals da h FM ad F ras wh ag 5 Sl Rgrsso Modl W ow addrss h ssu assoad wh h bo lo Fgur W hav a furhr loo a h obsrvd daa bo lo of obsrvd MI valus vrsus ag shows ha MI s roughly osa for ags 8 h rss roughly larly for ags 8 3 ad fally rss vry slowly for ags 4 9 Ths aarly ora faur s o ludd h four odls Thus hs so w a o lo hs faur usg a sl rgrsso odl W hav usd ar of h slo odl ad for ar w us a o-o rgrsso odl Grally lg 0 f 0 ad f > 0 w a ϕ 0 ϕ ( a 8 ϕ a 3 (9 whr h sr of our four odls ϕ I (9 w hav a z α dd v 0 σ 3 ~ oral(0 σ ad ovad by our arlr rsul (h v ar uorrlad rahr ha a rvara oral dsy o v v v v w hav a ( 3 dd v 3 σ ~ oral(0 σ 0 Th dsrbuo assuos o h hyr-arars ra uhagd W hav oud h dva asur for h sl odl; s Tabl for h ohr four odls For hs odl G 9 ad 07 oard wh G 8 ad 35 for h slo odl Tha s D 36 for h sl rgrsso odl ad D 53 for h slo odl Thus h sl rgrsso odl shows a rov ovr h orgal slo odl I Fgur w rs bo los of DRES vrsus ag Ths s a uh rovd lo ovr h o for h slo odl (s Fgur Obsrv ha h das fluua abou 0 wh vry ll varao Th bo los for ags ad 7 ar a ll lss varabl ha h ohrs W also f h quadra o-o odl whh w rla (9 by ϕ ϕ ϕ 0 ( a 8 {( a 3 } wh all ohr assuos rag uhagd Ths odl dd o show ay subsaal rov ovr h alrav odl sfd by (9 whh w ra whou furhr rf Tabl oarso of h Four Modls asd o h vrag Ovr ll ous of h Ed os of h 95% rdbl Irvals for h F oulao Ma MI (FM ad rooro (F Rsodg for la Fals ag Modl SEI FM ( ( (963 6 (40 59 F ( ( ( ( SE FM (555 6 ( (95 09 (74 39 F ( (07 08 ( ( MI FM ( ( ( (4 509 F ( ( ( ( M FM ( ( (96 45 ( F ( ( ( ( o: SEI s gorabl vrso of h slo odl MI s gorabl vrso of h ar ur odl M s ar ur odl ad SE s slo odl Sass aada aalogu o -00-XIE

89 Survy Mhodology Ju D R E S GE Fgur o los of h ross-valdao rsduals (DRES by ag for h sl rgrsso odl I Tabl 3 w oar h FM for h slo odls (rgrsso whou sls ad rgrsso wh sls ga w avrag h d os of h 95% rdbl rvals ovr all ous Th rvals ovrla suggsg slary bw h odl whou sls ad h o wh h Howvr hr ar so os Th largs dffr bw h rvals our for dvduals ag 5 9 yars old I gral h sl odl rovds hghr rso For al for ag 0 9 h rvals for h sl odl ar oad by hos for h odl whou h sls 6 olusos To aalyz MI daa fro HES III by ag ra ad s wh ah ouy (a w hav dd h orallogs rgrsso odl o a hrarhal aysa slo odl ad (b osrud a ar ur odl ad wo gorabl orsos odls o assss ssvy o fr dva asur shows ha aog h four odls h slo odl s h bs ad a ross-valdao aalyss shows ha hs odls f roughly qually wll Tabl 3 oarso of h Two Slo Modls (Rgrsso Whou Sls ad Rgrsso wh Sls usg h vrag Ovr all ours of h Ed os of h 95% rdbl Irvals for h F oulao Ma MI by g Ra ad S ag R S F o Sl (66 69 ( (96 4 (35 56 Sl ( (76 84 ( (95 38 M o Sl ( (66 69 ( ( Sl ( (73 8 (903 0 (084 6 OF o Sl ( ( (948 9 (6 539 Sl ( ( ( (6 338 OM o Sl ( ( (9 095 ( Sl ( ( ( (3 87 o: R S s ra-s: F s bla fal; M s bla al; OF s o-bla fal; ad OM s o-bla al Sass aada aalogu o -00-XIE

90 8 adra ad ho: Hrarhal aysa ogorabl orsos Rgrsso Modls for Sall ras ohr orbuo s h dfao of a oo dfy h slo odl h ar ur odl ad h wo gorabl odls asd o h obsrvd daa w hav foud ha hr s a dya rlaosh of MI wh ag Thus w hav furhr dd h slo odl o lud hr lar sls Th ross valdao aalyss shows ha hr s a rov ovr h slo odl ad fa h dva asur shows ha h lar sl rgrsso odl s h bs aog h fv odls Our sudy o obsy s o of h y orbuos hs wor Th lar sl rgrsso of MI o ag adusg for ra ad s gvs a br f ad rovd rso ha h slo odl whou sls I s o asy o osru a odl ha s sasfaory for all ass of h HES III daa sulaously W hav b abl o do so for hldr ad adolss MI rass subsaally wh ag; ra ad s orbug gavly o hs ras; hr s rlavly lss ras for wh als I gral h ffs of ra ad s ar rlavly or Thr s so varao aross h hry fv ous d Th ar Mur Modl For ar of h ar ur odl h rsos dds o ag ra ad s ad h rao of ra ad s hrough h logs rgrsso d ~ r β roull β0β aβzβ3z β4z3 β0β aβzβ3z β4z3 { /( } ( K l K ow lg β ( β0 β β β3 β4 o ha whl h vor β has 5 oos h orrsodg vor (4 has wo oos alogous o (4 w a d ad for h ror dsrbuo ad Δ β θ Δ ~ oral( θ Δ ( (0 (0 θ ~ oral( θ Δ (0 (0 (0 (0 ~ Wshar{( v Λ v } v > (3 (0 (0 (0 (0 whr θ Δ Λ ad v ar o b sfd ar of hs odl for MI ororas a dd o h rsos daors lg w w a σ ( z α rv w 0 d 3 ~ oral(0 σ 0 3 r 0 (4 Th dsrbuos o h ( v 0 v ar h sa as (7 Th ror dsrbuos ar aly hos ar of h slo odl ( s (6 ad (7 (0 W a v a valu ha das ar vaguss aas rory ad rs sably ouao W show how o sfy arars l (0 (0 (0 (0 (0 θ Δ Δ 3 Λ d α d Mrools-Hasgs lgorh for Fg h Slo Modl For h ogorabl orsos slo odl h o osror dsy s ( s r ( s r ( σ α β v θ ρ ρ l r ( { ( } β0 β z α aα v0 v a σ 3 β 0 β σ 3 l ( { ( } z α aα v0 v a σ 3 β 0 β r σ 3 l σσ ρ β θ β θ β θ β θ ρ (ρ σ σ σ σ v0 v0 v ρ v l (ρ σ σ σ σ σ 4σ5 ρ a a 5 (0 (0 (0 ( ( θθ Δ θθ σ σ (0 (0 (0 ( α Δ ( α α α ( L Ω do h s of arars β θ v α σ 3 ψ ψ ad ( s r whr ψ ( σ σ ρ ad ψ ( σ 4 σ5 ρ Grally l Ω a do all arars Ω a ; for al Ω β ( s r ( θ v α σ 3 ψ ψ so ha h odoal osror dsy (D of β s dod by ( r ( β Ω s β To rfor h Mrools-Hasgs algorh o ds h D for ah arar gv h ohrs ad ( s r Hr w gv a sh of h algorh Th D for ah of h arars θ v α ad σ 3 s asy o wr dow u w d Mrools ss for h D s of β ψ ψ ad ( s r Sass aada aalogu o -00-XIE

91 Survy Mhodology Ju odog o Ω β h arars β K βl ar dd wh whr ( β ( s r ( β ( σ ρ σ 0 β r ( β θ Δ ( β θ β0 β ρ σ σ σ Δ σ ad K l ad r K ar o b rdd; s blow W us a hqu basd o logs rgrsso o oba a ulvara Sud s roosal dsy whh ug s obad by varyg s dgr of frdo Th hod o draw fro h D s of ψ ( σ σ ρ ad ψ ( σ3 σ4 ρ s h sa Th D of ψ s ( ψ Ω ψ ( ρ l / a l b ( s r σ4 σ5 σ4 σ5 l ρ l l (ρ 4 5 σ v σ σ v v σ v W hav usd h Fshr s z rasforao (s Rub 966 o oba a roosal dsy assoad wh oral dsrbuo for log{ ρ /( ρ} ad gaa dsrbuos for σ 4 ad σ 5 Fally w osdr h Mrools s for drawg ( s r ( s r Ω ( s r W o ha hs D K l r K ar dd wh ( Ω ( s r β 0 β { } [ { ( 0 }] z α aα v v a σ3 W hav osrud a roosal dsy usg las squars hqus W o ha h roosal dsy oral ( z ( α aα v0 v a σ3 dd o rfor wll (s hb ad Grbrg 995 d Sfao of Hyrarars W dsuss how o sfy h hyrarars (0 (0 (0 (0 ( θ Δ ad ( α Γ assoad wh θ ad α h slo odl (0 (0 Frs osdr ( θ Δ For K l K f h logs rgrsso odl r d ~ roull β0 β β0β { ( } whr ar obad by rdo (s d Lg β ˆ K l do h las squars saors w assu ha d ˆ (0 ~ (0 (0 l β ~ oral ( θ Δ o g θ / l βˆ ad Δ ˆ~ (0 l l (ˆ β θ (0 (ˆ β θ (0 ( (0 ad w s Δ κ ˆ~ (0 Δ whr κ s o b sld (0 (0 w osdr how o sfy ( α Γ W f z ( α αa whr a s h ag of h h dvdual h h ouy K l K o g las squars saors α ˆ (ˆ α α ˆ ad s ovara ar ˆ (0 (0 (0 Γ W s α αˆ ad ˆ (0 Γ κ Γ whr ˆ (0 Γ s h orrsodg blo ar of ˆ (0 Γ ad κ s o b sfd W hav rd wh κ ( W usd κ 00 o rovd a ror dffus ror; a valu of κ 000 dd o hag our rdos Slarly w usd κ 00 Rfrs hb S ad Grbrg E (995 Udrsadg h roolshasgs algorh Th ra Sasa oh G ad Duffy J (00 r orsods o halh survys lss halhy ha rsods? Joural of Offal Sass owls M ad arl (996 Marov ha Mo arlo dagoss: oarav rvw Joural of h ra Sasal ssoao Dals MJ (999 ror for h vara hrarhal odls Th aada Joural of Sass Davd M Ll RJ Saul ME ad Trs RK (986 lrav hods for S o uao Joural of h ra Sasal ssoao Dz WH (998 Halh osqus of obsy youh: hldhood rdors of adul dsas dars Fago-aaga (000 Erg of y dabs llus hldr: Edologal vd Joural of dar Edorology Mabols Glfad ad Ghosh S (998 Modl ho: u osror rdv aroah ora 85 - Glfad Sahu S ad arl (995 Eff ararsaos for oral lar d odls ora Gla Robrs GO ad Gls WR (996 Eff Mrools ug ruls I aysa Sass (EdsJM rardo JO rgr Dawd ad FM Sh Oford UK: Oford Uvrsy rss Grls JS R WS ad Zshag KD (98 Iuao of ssg valus wh h robably of rsos dds o h varabl bg ud Joural of h ra Sasal ssoao Ha J (976 Th oo sruur of sasal odls of ruao sal slo ad ld dd varabls ad a sl saor for suh odls als of Eoo ad Soal Masur Sass aada aalogu o -00-XIE

92 84 adra ad ho: Hrarhal aysa ogorabl orsos Rgrsso Modls for Sall ras Kuzars RJ arrol MD Flgal KM ad Troao R (997 Varyg body ass d uoff os o dsrb ovrwgh rval aog US aduls: HES III (988 o 994 Obsy Rsarh Laud ad Ibrah J (995 rdv odl slo Joural of h Royal Sasal Soy Srs Ll RJ ad Rub D (987 Sasal alyss wh Mssg Daa w Yor: Joh Wly & Sos I Mohadar L ll ad Wasbrg J (994 aoal halh ad uro Eaao Survy III-oug for orsos bas Iral Ror aoal r for Halh Sass adra ad ho JW (00 a hrarhal aysa orsos odl for bary daa wh uray abou gorably Joural of h ra Sasal ssoao adra ad ho JW (00 b aysa aalyss of a rooro udr ogorabl orsos Sass Md 89- adra Ha G ad ho JW (00 hrarhal baysa ogorabl orsos odl for uloal daa fro sall aras Survy Mhodology aaraa R ad Kass RE (000 Rfr aysa hods for gralzd lar odls Joural of h ra Sasal ssoao aoal r for Halh Sass (99 Thrd aoal halh ad uro aao survy Val ad Halh Sass Srs 3 aoal r for Halh Sass (994 la ad orao of h hrd aoal halh ad uro aao survy Val ad Halh Sass Srs 3 Ogd L Flgal KM arroll MD ad Johso L (00 rval ad rds ovrwgh aog us hldr ad adolss Joural of h ra Mdal ssoao Olso RL (980 las squar orro for slvy bas Eoora Rao R (973 Lar Sasal Ifr ad Is laos w Yor: Joh Wly & Sos I Rub H (966 So w rsuls o h dsrbuo of h sal orrlao off Joural of h Royal Sasal soy Srs Rub D (976 Ifr ad ssg daa ora Rub D (977 Foralzg subv oos abou h ff of orsods sal survys Joural of h ra Sasal ssoao Rub D (987 Mull Iuao for orsos Survys w Yor: Joh Wly & Sos I Shafr JL Ezza-R TM Johso W Khar M Ll RJ ad Rub D (996 Th HES III ull uao ro Survy rsarh hods rodgs of h ra Sasal ssoao 8-37 Squrs S (00 aoal la urgs o oba obsy: Wghrlad llsss ll ras aually Surgo Gral says Th Washgo os Dbr 4 00 Sasy E (99 Hrarhal odls for h robabls of a survy lassfao ad orsos: al fro h aoal r Survy Joural of h ra Sasal ssoao Who osulao o Obsy (000 Obsy: rvg ad aagg h global d WHO Thal Ror Srs 894 Gva Swzrlad: World Halh Orgazao Wrgh M arr L Lao D ad raf W (00 Ilaos of hldhood obsy for adul halh: Fdgs fro housad fals ohor sudy rsh Mdal Joural Sass aada aalogu o -00-XIE

93 Survy Mhodology Ju Vol 3 o Sass aada aalogu o -00-XIE Towards ogav Rgrsso Wghs for Survy Sals Mgu ar ad Way Fullr bsra rodurs for osrug vors of ogav rgrsso wghs ar osdrd vor of rgrsso wghs whh al wghs ar h vrs of h aroa odoal luso robabls s rodud Through a sulao sudy h wghd rgrsso wghs quadra rograg wghs rag rao wghs wghs fro log rodur ad wghs of a llhood-y ar oard Ky Words: Rag rao; Mau llhood; Quadra rograg; Sl odoally Wghd (SW saor Iroduo I survy salg forao abou h oulao s of avalabl a h aalyss sag O hod of usg hs forao s hrough rgrsso sao Thr ar a ubr of ways o osru a rgrsso saor of h oulao a or oal O rgrsso saor of h a s y w y y ( β ~ ( whr w rg α ( φ φ ( - ( y ( y : α ( y ~ β φ α φ y Φ dag( φ φ s a osgular dagoal ar h s ar h slo robabls ad s h oulao a of ossbl ho of φ s α rvw of h us of suh forao rgrsso sao for sal survys s gv by Fullr (00 I s wll ow ha rgrsso wghs ha ar usd o df a rgrsso saor suh as ( a b vry larg or (ad a b gav If h rgrsso wghs ar o b usd o sa a f oulao oal a gral uros survy ss rasoabl ha o dvdual wgh should b lss ha o lso ss rasoabl o robusss grouds o avod vry larg wghs Thr ar svral ways o osru rgrsso wghs wh a rdud rag of valus Huag ad Fullr (978 dfd a rodur o odfy h w so ha hr ar o gav wghs ad o larg wghs Husa (969 suggsd quadra rograg as a rodur o la bouds o h wghs Quadra rograg ad a ubr of ohr rodurs buld o h fa ha h wghs a b dfd as valus ha oz so fuo Dvll ad Särdal (99 osdrd sv obv fuos ha a b usd o osru wghs Thy suggsd obv fuos ha a b usd o rodu wghs whh fall wh a gv rag Dvll Särdal ad Sauory (993 rodud h rogra LMR wr as a SS aro ha a b usd o alula wghs orrsodg o four dffr obv fuos wh aulary forao h survy osss of ow argal ous a frquy abl ohr odfao of rgrsso wghs s o rla so of h rsros usd osrug h saor Husa (969 osdrd odfyg wghs for a sl rado sal fro a oral dsrbuo H drvd h wghs ha z h a squar rror (MSE of h rsulg saor ardsly ad habrs (984 osdrd a saor basd o a obv fuo ad h dvso of h aulary varabl o wo oos Thy sudd h bhavor of h saor fro a odl rsv Rao ad Sgh (997 sudd a saor whh olras ar gv for h dffr bw h fal saor for ar of h aulary varabls vor ad h orrsodg ls of h oulao vor I hs ar w osdr dffr ys of rgrsso wghs ludg a rodur basd o Tllé s (998 odoal slo robabls Th aroa odoal Mgu ar Uvrsy of brasa 03 Mllr Hall Lol E US; Way Fullr Iowa Sa Uvrsy Sdor Hall s I US

94 86 ar ad Fullr: Towards ogav Rgrsso Wghs for Survy Sals luso robabls ar usd o ou rgrsso wghs ha ar osv for os sals Ths rgrsso wghs ar oard o rag rao wghs o quadra rograg wghs wghs fro log rodur ad o wghs basd o a llhood-y obv fuo Mau Llhood ad Rag Rao osdr a wo-way abl wh r rows ad olus Th oulao ll U oas ls; r ssu argal ous ar ow Th oulao hararss of rs ar h or quvally For a sl rado orla sal of sz Dg ad Sha (940 suggsd a rag rao rodur o g h soluo for h ll frqus S also Sha (94 If w assu h sal s a rado sal fro a uloal dsrbuo dfd by h oulao rs a wo way abl w a osru a saor usg h au llhood rodur Dvll ad Särdal (99 dfd a lass of albrao saors y al of h oulao a of y as yal w y (3 whr h w s z h obv fuo G( α sub o osras w w ad w (4 ad G( w α s a asur of dsa bw a al wgh α ad a fal wgh w Th rag rao ad au llhood saors of h oulao ll frao blog o h lass of albrao saors Th rag rao wghs for h oulao ll frao wh a sl rado sal a b obad by zg w sub o h osras (4 wh w log w (5 δ δ δ δ (6 ( r whr δ f h l blogs o h h row ad h δ 0 ohrws ad δ f l blogs o h h olu ad δ 0 ohrws Th rag rao saor for h oulao ll frao s h saor h (3 whr y f h l blogs o ll ad y 0 ohrws For h au llhood saor of h oulao frao wh a sl rado sal Dvll ad Särdal (99 suggsd zg w log w (7 sub o (4 wh dfd (6 h ad Sr (999 suggsd a sudo ral llhood saor Thy dfd h oulao llhood of y as log (8 w U whr w U s h dsy a obsrvao y Wh a sal of sz hy suggsd h sudo ral llhood saor of h for whr yel w y (9 w s ar obad by zg h fuo log (0 w udr h rsros (4 Th rsulg w ar qual o hos obad by zg (7 wh udr h rsros (4 Dvll ad Särdal (99 showd ha h rag rao ad au llhood saors ar aroaly qual o a rgrsso saor of h for ( ad h hav h sa lg dsrbuo as h rgrsso saor Wghs for h rag rao ad au llhood saors ar ogav f h soluos for h wghs s 3 Wghd Rgrsso Usg odoal robabls Tllé (998 suggsd h us of aroa odoal luso robabls odog o h Horvz-Thoso saors of aulary varabls o ou a saor for h oulao a of h sudy varabl Hs aroao a b dd o rodu rgrsso wghs ha ar ogav wh hgh robably ssu ha h vor of oulao as of aulary varabls s ow osdr h Horvz-Thoso saor of gv by HT ( Sass aada aalogu o -00-XIE

95 Survy Mhodology Ju whr ( ad s h uodoal luso robably Tllé (998 rodud h sl odoally wghd (SW saor y y ( HT whr s h odoal luso robably of h HT h l odog o HT To osru h SWsaor of y h odoal luso robably HT s rqurd If HT as h valu w hav { HT } HT (3 { } whr s h s of ds for h sal ls I ordr o ou h odoal luso robabls s ssary o ow h robably dsrbuo of HT uodoally ad odoally o h rs of ah u h sal E for so arular ass hs robably dsrbuo s vry ol For hs raso aroao of h odoal luso robably s osdrd Udr h assuo ha HT has a aroaly oral dsrbuo uodoally ad odoally o h rs of ah u h sal h odoal luso robably (3 a b aroad by ˆ HT / HT / ( {05 ( G G ( } (4 whr Var{ F} Var{ F } HT ( G ( ( HT HT HT G ( ( HT ( ( ( HT ( ( E{ HT F } ( ( s h s of ds aarg h sal ad F { y y } s h f oulao Tllé (998 gvs a rsso for ( for h gral as ssu h dsg ovara ars ad ( ar osv df ad assu h vor of aulary varabls s orally dsrbud Tllé (999 showd ha h SW-saor dfd ( wh h aroa odoal luso robabls of (4 sasfs y y ( β O ( (5 HT HT y O ( (6 rg whr y β rg yht y ( HT βˆ ˆ ˆ β ( X Φ X X Φ ˆ y y X ( y ( y y h h l of Φ s ( ( s h dsg vara of HT y s h dsg ovara of HT ad y HT ˆ s h Horvz-Thoso vara saor of HT ad ˆ y s h Horvz-Thoso saor of h ovara of HT ad y HT Gv a ol dsg a ubr of h quas (4 ar dfful o ou Howvr aroaos gvg h sa larg sal rors for h saor ar rlavly asy o ou W rla ad ( wh saors rla ( wh d df ˆ M ( y d y (7 ad assu ˆ Var{ ( M M } O( (8 y y d ( (9 O whr d s a fuo of h sal ad M y s a oulao quay Of M y s h oulao ovara ar y bu hs qualy s o rqurd ordr for h saor o b wll dfd I ay ass o a ou d as a ull of h af dva lso ay suaos a adqua valu for h saor ~ ( of ( s ( ˆ W wr our gralzao of (4 as ~ whr HT ˆ / ~ / ( ˆ ~ {05 ( G G ( } (0 ˆ ˆ G ( HT ( HT ~ ~ G ( ( HT ( ( HT d d L h saor ( osrud wh h ~ of (0 b y ~ ~ y HT HT ( aroa odoal luso robably wh a sl rado sal ad a sgl aulary varabl s Sass aada aalogu o -00-XIE

96 88 ar ad Fullr: Towards ogav Rgrsso Wghs for Survy Sals ~ σˆ ~ σ ( ( σˆ ( σ ~ d ( Th saor ( s aroaly qual o a rgrsso saor ad saor ( s also aroaly qual o h sa rgrsso saor Thor: L a squ of oulaos ad sals { F } sasfy whr ( y HT / ( y O ( (3 HT d [ ( ] ( ( s ( ( ( ( σˆ ( ~ σ ( ad s σ ˆ ( s ( ( I hs as d ( ad M y ov( HT yht Th SW-saor ( wh h aroa odoal luso robabls s o albrad ha s h saor ( for h a of h vor of aulary varabls s o h vor of oulao as I s rlavly asy o sadardz h robabls so ha hy su o o or su o h srau frao for srafd salg To osru a albrad saor for h gral as w suggs oug h rgrsso saor wh ~ ~ [ ] HT as al wghs Th suggsd HT saor s y y ( βˆ whr w wrg ( y w y α ( y 0 ( ˆ ˆ β β α z z α z y α z ( ~ ~ α HT HT ( ( α ( ( α ( ad ~ s h aroa odoal luso HT robably of (0 W assu h vor of aulary varabls oas o so ha h saor s loao vara ssu ha h squs of sad ovara ~ ars ˆ ad ( sasfy / ~ / D D [ ( ] [ ˆ ] / / D D O ( (4 whr D dos a dagoal ar havg h ls of h dagoal of ˆ o s dagoal L d b a fuo of h sal sasfyg (9 ad assu (8 holds ssu h squ of Horvz-Thoso vara saors sasfs Var { [ ( ˆ Vh z z HT z z ]} O( (5 whr z ( y ad z z s osv df ssu ~ E { } s boudd whr ~ HT s dfd (0 HT Th h SW saor y ~ of ( sasfs y ~ y y HT HT ( ( HT HT θ O ( ˆ θ O ( whr ˆ ˆ θ Mˆ y ad θ M y If Var{ } > 0 assu oas o as a l ssu M y y Th h wghd rgrsso saor of ( sasfs ˆ y y ( θ O ( wrg HT For roof s h ad To llusra h aur of h dffr ys of rgrsso wghs w sld a sl rado sal of sz 40 fro a oral oulao wh a zro ad vara o Th sal a s 064 ad h oulao a s zro Th wgh for h rgrsso saor s gv by ( wh α φ Th wghs for h rag rao ad MLE ar obad by zg h obv fuos (5 ad (7 rsvly udr h rsro (4 Wghs for h SW-wghd rgrsso saor ar gv ( Th wghs ar lod agas h sal valus Fgur Fv of h sl rgrsso wghs ar lss ha zro baus of h larg dsray bw h sal ad h oulao as ll wghs for h SWwghd rgrsso saor MLE ad rag rao ar ogav Fgur shows ha h bhavors of rag rao ad SW-wghd rgrsso wghs ar slar ad ha MLE has a rly larg wgh hs sal HT Sass aada aalogu o -00-XIE

97 Survy Mhodology Ju Tabl oas sld wghs for h salls valus valus los o h sal a valus los o h oulao a ad h largs valus For h valus farhs fro h oulao a MLE gvs h largs wghs For valus ar h sal a h ordary las squars wghs ar los o whl h ohr wghs ar lss ha Th MLE wghs ar los o for valus los o h oulao a whl h ohr wghs ar largr Tabl Sld Rgrsso Wghs for Illusrad Eal Wghs ulld by 40 Rg W Rg Rag MLE Sulao Sudy To oar h alrav hods of osrug rgrsso wghs w odud a sulao sudy oal of sl rado sals of sz 3 wr sld fro a χ dsrbuo wh wo dgrs of frdo Th arars bg sad ar hos of h f grag has L b h valu for h h sald l S sao rodurs wr osdrd Ordary las squars rgrsso (OLS Quadra rograg wh ur ad lowr bouds (Q 3 Wghd rgrsso wh SW wghs (SW rg 4 Mau llhood obv fuo (MLE 5 Rag obv fuo (Rag rg 6 Log rodur wh ur ad lowr bouds (Log Th wghs for h OLS saor wr alulad by ( wh α Th quadra rograg wghs z w sub o h osra 0 w for all ad sub o osras (4 Th quadra rograg rodur s quval o h ruad lar hod of as 7 of Dvll ad Särdal (99 Wghs for h SW wghd rgrsso wr alulad by zg α w sub o osras (4 whr α s dfd ( Th wghs for rag ad au llhood wr obad by zg h obv fuos (5 ad (7 rsvly udr h rsro (4 Wghs alulad by h log rodur z h fuo G( w sub o osras (4whr ( u w G w a ( w l( w ( u w l u Wgh Rgrsso W Rgrsso Rag MLE Fgur oarso of four ss of wghs Sass aada aalogu o -00-XIE

98 90 ar ad Fullr: Towards ogav Rgrsso Wghs for Survy Sals f 0 < w < u ad lswhr a u ( u ad u 08 o ha h soluo for h log rodur f ss sasfs h boud rsros 0 w for all Th log rodur was rodud as a as 6 Dvll ad Särdal (99 s h ur boud for h wgh 0065 was usd so ha 306 sals (aroaly 0% hav a las o rag rgrsso wgh grar ha 0065 I 99 sals aog o soluo for h quadra rograg ad log rodur s ossbl baus o fasbl o sasfs (4 ad h boud rsro For hos 99 sals h au of h OLS rgrsso wghs was usd as h ur boud for h quadra rograg ad log rodurs Tabl shows h avrag of h su of squars for h s wghs Th avrag wgh s / for vry saor Th las squars rodurs hav h salls su of squars of h wghs baus hs s h obv fuo for hos rodurs Th las squars rodurs also hav a slghly sallr rag h su of squars O r of h las squars sals hav a oralzd a of squars grar ha 40 whl o r of h a of squars for rag ar grar ha 44 Tabl Mo arlo vrag of h Su of Squars of h Wghs OLS Q SW MLE Rag Log Rg Rg vrag of w w ( Tabl 3 oas rors for h u of h wghs Mau llhood has h largs avrag u wgh whl h las squars rodurs hav a sallr avrag for h u wgh Th vara of h u wgh s largs for h ordary las squars rodurs o ha Q rs wghs ha qual h lowr boud of zro Tabl 3 Mo arlo Ma Vara ad Quals of h Mu Wgh Quals ( 3 rodur Ma ( 0 Vara ( OLS Q SW Rg MLE Rag Rg Log og h rodurs whou boud rsros o h wghs h ordary las squars rodur has sallr au wgh o avrag ad uh sallr vara for h au S Tabl 4 Th SW-wghd rgrsso has a sallr frao of vry larg wghs ha MLE or rag rao bu a hghr frao of larg wghs ha h ordary las squars rodur Th boudd Q ad Log rodurs hav sallr a ad vara for h au wgh ha h rodurs wh o ur boud rsros Tabl 4 Mo arlo Ma Vara ad Quals of h Mau Wgh Quals ( 3 rodur Ma ( 0 Vara ( OLS Q SW Rg MLE Rag Rg Log To valua h rfora of h rodurs wh h lar odl dos o hold w osdrd sao of h rls of h dsrbuo fuo of Tabl 5 oas h Mo arlo bas of h rl saors whr h abl rs ar [{ ( }] [ Eˆ{ ˆ} ] 00 ad s h rl For al h Mo arlo sad rlav bas h ordary las squars saor of h 00 rl s 775% Th ordary las squars saor has h largs bass sag h oulao rls aog h rodurs whou boud rsros Th MLE has h salls bas for all h h rls h ad 99 h whr h SW-wghd rgrsso saor has h salls bas For sals of sz 3 ay sals oa o h obsrvao grar ha h 99 rl Th Q ad Log rodurs hav largr bas ha ohr rodurs for h Log rodurs ar rlavly larg for h lowr rls h 75 rl Th bass of h Q ad Tabl 5 Mo arlo Sadardzd as rl Esaors rl rodur OLS Q SW Rg MLE Rag Rg Log Tabl 6 oas h rlav MSE of h rl saors whr h abl rs ar [{ ( }] ˆ{ ˆ [ E } ] 00 Thus h rlav a squar rror of h OLS saor of h 00 rl s 837% lhough h OLS saor Sass aada aalogu o -00-XIE

99 Survy Mhodology Ju of h 00 rl had h largs bas OLS has h salls a squar rror for h 00 rl aog h rodurs whou boud rsros Th Q OLS ad Log rodurs ar suror for h r rls whl h ohr rodurs rfor br for h ddl rls Tabl 6 Mo arlo Rlav MSE of rl Esaors rl rodur OLS Q SW Rg MLE Rag Rg Log I 56 of sals a las o of h OLS rgrsso wghs s gav I 7 of h sals a las o of h orgal SW rgrsso wghs was gav Th us of quadra rograg wh h OLS obv fuo (Q o rodu wghs grar ha or qual o zro ad lss ha 0065 rass h avrag su of squars by lss ha o r S Tabl 7 Usg quadra rograg o boud h SW rgrsso wghs (SW (QL by zro rass h avrag su of squars vry ll baus hr ar so fw wghs ha ar hagd Tabl 7 Mo arlo vrag of h Su of Squars of h Wghs for Sals wh a Las O gav OLS Wgh OLS SW SW Q Rg (QL Rag MLE Rg vrag of w w ( Tabl 8 gvs h Mo arlo MSE for h 56 sals wh gav ordary las squars wghs Th quadra rograg rodur s suror o ohr ogav wgh rodurs for h 00 rl ad s fror for h 099 rl Of h 56 sals 497 had a sal a grar ha h oulao a Rall ha h sudy oulao has a oal dsrbuo aus h wgh o h largs obsrvao s zro h 497 sals hr s a 00 r rror h quadra rograg saor of h 099 rl for os of h 497 sals wh a sal a grar ha h oulao a I salg fro a f oulao h boud o h wghs would b grar ha or qual o quadra rograg rodur for h 099 rl would b rdud Quadra rograg s suror o h ohr albrad rodurs for h 00 rl sals wh gav ad h MSE of h OLS wghs Rag rgrsso ad SW-wghd rgrsso ar suror o MLE for h 00 ad 005 rls Ths s baus MLE of has h largs au wgh Tabl 8 Mo arlo Rlav MSE of rl Esaors for Sals wh a Las O gav OLS Wgh rl rodur OLS Q SW (QL MLE Rag Rg I 306 of sals a las o of h rag rgrsso wghs s grar ha 0065 I 5 sals a las o of h OLS rgrsso wghs s grar ha 0065 ad 309 sals a las o of h SW rgrsso wghs s grar ha 0065 Th us of quadra rograg wh h OLS obv fuo o rodu wghs ( rass h avrag su of squars by 5 r Usg quadra rograg o boud h SW rgrsso wghs by 0000 ad 0065 rass h avrag su of squars 08 r S h olu for SW (Q of Tabl 9 Tabl 9 Mo arlo vrag of h Su of Squars of h Wghs for Sals wh a Las O Rag Rg Wgh Grar ha 0065 SW SW Rag OLS Q Rg (Q Rg Log MLE vrag of w w ( Tabl 0 gvs h Mo arlo rlav MSE for h 306 sals wh rag rgrsso wghs grar ha 0065 Th quadra rograg s suror o SW (Q ad Log for h ad 099 rl ad h Log rodur s suror o quadra rograg for ohr rls Tabl 0 Mo arlo Rlav MSE of rl Esaors for Sals wh a Las O Rag Rg Wgh Grar ha 0065 rl rodur SW SW Rag OLS Q Rg (Q Rg Log MLE Sass aada aalogu o -00-XIE

100 9 ar ad Fullr: Towards ogav Rgrsso Wghs for Survy Sals Dsusso W bga h rsarh wh h our ha sarg wh h SW wghs a rgrsso saor would rodu wghs ha wr alos always osv ad ha h wghs would hav dsrabl rors as asurd by h ably o sa h dsrbuo fuo of To so hs rsuls suor h ours Th u wghs of h SW rgrsso ar largr ha hos of OLS ad oarabl o hos for rag Quadra rograg a b usd o rov h gav wghs h fw sals wh gav wghs If o ur boud s osd h au wghs for h SW wghd rgrsso fall bw hos of las squars ad rag I s ow ha all of h rodurs our sulao sudy hav h sa ordr ad h sudy of gralzd rag rodurs do by Dvll al (993 da ha hr ar also ods dffrs sall sals o rodur s suror wh rs o all rra aus of h oor rfora for h r rls w rod agas h us of h MLE obv fuo Th quadra rograg ad Log rodur rodud wghs wh argally sallr sus of squars argally sallr au wghs ad argally sallr MSE for r rls ha h rag rgrsso Th MLE SW rgrsso ad rag rodurs gv argally largr u wghs ad argally sallr MSE for h ddl rls of h dsrbuo ha quadra rograg ad Log rodur Th rforas of quadra rograg ad Log rodurs sag h dsrbuo fuo of ar oarabl / rors Our sulao d roof Th rao of h dras of sad ovara ars (0 s ~ ( O ( ˆ (6 ~ by assuos (4 ad (5 Th dffr G Gˆ ( s ~ ( ˆ ( HT ( ( HT ~ ~ ( d d d HT y assuos (3 ad (4 ~ {05[( ( ˆ HT ( ( ( HT O ( ]} ( (7 Usg assuos (4 ad (9 h Taylor aso a d 0 gvs ~ ~ [ ( HT ( d 05 d ( d ] ~ ( HT ( d O ( ( ˆ d O ( (8 HT Thus by (6 (7 ad (8 [ ~ HT ] ( [ ( ˆ HT d ] O ( y assuos (8 (3 ad (5 ad usg h fa ha ~ E { } s boudd HT y ~ y y HT HT ( ( HT HT θˆ O θ O ( ( (9 If o s a l of or Var { } 0 ad f M y y h SW-saor for h oulao a of vor q sasfs ( ~ HT q ~ q ( O ( (30 baus h θ for s h dy ar y (30 ( Thus y wrg y ~ y y y y ~ ~ HT ( ( O ( ( HT ~ HT by (30 (3 ad (9 βˆ βˆ ( θˆ O ~ y ( ( y ( ~ ~ y y ~ ~ owldgs O ( ~ ( (3 βˆ Ths rsarh was arly suord by oorav gr 43-3EU bw Iowa Sa Uvrsy h USD aoal grulural Sass Srv ad h US urau of h sus ad by oorav gr bw h USD aural Rsours osrvao Srv ad Iowa Sa Uvrsy W ha h ssoa dor ad rfrs for os ha rovd h ar Sass aada aalogu o -00-XIE

101 Survy Mhodology Ju Rfrs ardsly ad habrs RL (984 Muluros sao fro ubalad sals ld Sass h J ad Sr RR (999 sudo ral llhood aroah o h ffv us of aulary forao ol survys Sasa Sa Dg WE ad Sha FF (940 O a las squars adus of a sald frquy abl wh h d argal oals ar ow als of Mahaal Sass Dvll J- ad Särdal -E (99 albrao saors survy salg Joural of h ra Sasal ssoao Dvll J- Särdal -E ad Sauory O (993 Gralzd rag rodurs survy salg Joural of h ra Sasal ssoao Fullr W (00 Rgrsso sao for survy sals Survy Mhodology Huag ET ad Fullr W (978 ogav rgrsso sao for sal survy daa rodgs of h Soal Sass So ra Sasal ssoao Husa M (969 osruo of Rgrsso Wghs for Esao Sal Survys Uublshd MS hss Iowa Sa Uvrsy s Iowa Rao JK ad Sgh (997 rdg shrag hod for rag rsrd wgh albrao survy salg rodgs of h so o survy rsarh hods ra Sasal ssoao Sha FF (94 alrav hod of adusg sal frquy abls wh d argal oals ar ow als of Mahaal Sass Tllé Y (998 Esao survys usg odoal luso robabls: Sl rado salg Iraoal Sasal Rvw Tllé Y (999 Esao survys usg odoal luso robabls: ol dsg Survy Mhodology Sass aada aalogu o -00-XIE

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103 Survy Mhodology Ju Vol 3 o Sass aada aalogu o -00-XIE Oal albrao Dsa Ladg o h Oal Rgrsso Esaor r Gösa drsso ad Dal Thorbur bsra Wh hr s aulary forao survy salg h dsg basd oal (rgrsso saor of a f oulao oal/a s ow o b (a las asyoally or Ef ha h orrsodg GREG saor W wll llusra hs by so sulaos wh srafd salg fro swd oulaos Th GREG saor was orgally osrud usg a asssg lar suroulao odl I ay also b s as a albrao saor; as a wghd lar saor whr h wghs oby h albrao quao ad wh ha rsro ar as los as ossbl o h orgal Horvz-Thoso wghs (aordg o a suabl dsa W show ha h oal saor a also b s as a albrao saor hs rs wh a quadra dsa asur losly rlad o h o grag h GREG saor Sl als wll also b gv rvalg ha hs w asur s o always asly obad Ky Words: Horvz-Thoso saor; Rgrsso saor; Survy salg hory oao ad ass osdr a f oulao U ossg of obs lablld wh assoad sudy valus y y ad J dsoal aulary (olu vors W wa o sa h oulao oal y U y by drawg a rado sal s of sz (fd or rado fro U wh frs ad sod ordr luso robabls ( s ( s Th sudy valus ad h aulary vors ar rordd for h sald obs ad bfor h sal s draw w assu ha a las U s ow Ths s h sadard su for a rgrsso saor I so w dsuss dffr rgrsso saors: h oo GREG saor (Särdal Swsso ad Wra 99 h oal saor (Moaar 987 drsso ra ad Wshall 995 ad albrao saors (Dvll ad Särdal 99 I s wll ow ha h GREG saor a b obad as a albrao saor I so 3 s show ha hs holds also for h oal saor bu wh a or olad dsa asur I h las wo sos hs ad h oal saor ar llusrad frs by horal als ad h by sulaos Fally so os abou ar oao hs ar: Grally h rasos of a ar s dod by T ad f s squar h vrs (gralsd vrs s wr ( W furhr l h olu vors y ( y s ad w 0 (/ s X b h J dsg ar of h aulary forao fro s ad fally I as a u dagoal ar of sz Rgrsso ad albrao Esaors ubasd sl saor of y s h Horvz- T Thoso saor ˆy s y / y w0 Howvr or ff saors ay b obad ulsg h aulary forao g h wll-ow odl asssd GREG saor s Särdal al (99 For al osrud fro h assuo of a hoosdas lar rgrsso suroulao odl h GREG saor s ˆ T T T T ˆ yr y w0 ( y Rr X ( X Rr X ( ( y T g ( whr R w I ˆ ad r 0 s / T T ( ( g ( ˆ X Rr X s ow h rsso ( for h GREG saor s rsg s w also hav ha T g (3 whh s alld h albrao quao Ths brgs us o a alrav ossbl drvao of h GREG saor aordg o Dvll ad Särdal (99 Suos ha w s a saor y T w of y wh a vor w of saldd wghs ( w s whh rss h orrsodg albrao quao whl also sg h dsa bw w ad w 0 aordg o h quadra dsa asur r Gösa drsso Mahaal Sass Dar of Mahas Lög Uvrsy SE Lög Swd; Dal Thorbur Dar of Sass Sohol Uvrsy SE-06 9 Sohol Swd

104 96 drsso ad Thorbur: Oal albrao Dsa Ladg o h Oal Rgrsso Esaor whr R ( w0 I Ths rsuls w w R T ( w w0 R ( w w0 ( X R X ( ˆ T T 0 whh as ha w g s hr R R r Turg o h oal saor osdr frs h vor T (ˆ ˆ y ad l y b h ovara (row vor of ˆ y ad ˆ ad h ovara ar of ˆ ow h u-vara s Moaar (987 ubasd lar saor ( ˆ y ad ˆ of y s h dffr saor (4 ( ˆ (5 ˆ y y S y ad ra ar uow w l h oal saor b ˆ y o y 0 ˆ ( y y T w ˆ T R y o ˆ X T ( ( X R ˆ o X T ( ˆ whr R o (( /( s I a asyo o whr ad ˆ y ad ˆ ay b vwd as oos of h asyo ovara ar of ˆT (ˆ y Udr h assuo of ossy of ˆ y ad ˆ whh holds udr vry ld odos s drsso al (995 h oal saor has h sa asyo vara as h dffr saor (5 I arular follows ha h oal saor s asyoally br ha h usual GREG saor s Rao (994 Moaar (000 ad drsso (00 s asyo vara s vr largr ad usually sallr I so 5 w aually rs so sl sulaos showg ha h oal saor a b uh or ff ha GREG Howvr o dos o ow ayhg abou h ffy for f sals s h ovara saor ay ovrg slowly Th ra of ovrg s llusrad so 5 o also ha so ass hr s asyoally v br saors whh ar o lar ow h fa ha h GREG saor s also a albrao saor usg T ( w w 0 Rr ( w w0 as h dsa asur ad oarg ( wh (6 lads o o blv ha rlag R r by R o (7 should ly ha w sad drv h oal rgrsso saor as a albrao saor Tha hs aually holds s show blow (6 (7 3 Th Ma Rsul I ordr o show s of a dsa asur orrsodg o h oal saor w wll frs sa ad rov a rsul h gral as La: Wh R dog a arbrary osv df ar T ( w w0 R( w w0 sub o h osra X w s sd by w w R X ( X R ( ˆ T T 0 roof: Irodug h J vor λ of Lagrag ullrs w g afr dffrao h quao sys X (8 T R ( w w0 X λ 0 (9 X W 0 (0 Mullyg (9 by XR usg (0 ad solvg for λ ylds wh X w ˆ : 0 T λ ( X R X (ˆ ( ug hs o (9 ad solvg for w fally lads o w w R X ( X R ( ˆ T T 0 Fro h la w hus hav h followg a rsul: Thor: Wh R o bg osv (s df ad usg h oal albrao dsa-asur whh w g by lg R Ro ( Ro (8 h albrao saor wll bo h oal rgrsso saor Rar: R o ay so ass b df (s blow Th oly hg w ow s ha s a ubasd saor of a ovara ar If s o osv s-df hr T also s valus suh ha X R o X s o osv s-df bu h robably of suh valus gos o zro as h oulao ad sal szs ras (ad f s osv df sr sao of a dsa wh a gav oo would lad o fly larg orros Ths robl of h oal saor has o our owldg o b od ou rvously Th sls way o fd a dsa whh gvs h oal saor as a albrao saor s o fd a ar R ds whh has h sa gvors as R o bu whr h gvalus ar rlad by hr absolu valus (Ths rsul a b show alog h sa ls as h roof of h la abov Th dsa a b s as h su of X Sass aada aalogu o -00-XIE

105 Survy Mhodology Ju h rodus of h gvalus ad h squard gvors ug h drvavs qual o zro as ha h rooso w foud h rs h a for osv gvalus ad h aa for gav gvalus y hagg all gav sgs h rs wll all b a 4 Eals osv df R o : Suos ha h obs U ar ddly draw wh luso robabls (osso salg; hus lyg a rado sal sz whr E[ ] U Du o h dd of drawgs R s dagoal ad sfally R o o I s osv s-df R o : Suos obs ar draw aordg o sl rado salg ah ob has luso robably / Th ls of R o ar : : ( Ths as ha R o s sgular wh ra Suos sad (as h followg sulao sudy ha U s arod o L sraa of szs L fro whh w draw dd sl rado sals of szs L Th ls of R o h ar : h : h h h h h h h h ( wh h lar as ad boh blog o srau h h L ad 0 ohrws Thrfor R o has ra h o osv s-df R o : L U oss of four ls ad s of wo ls Suos ha a sysa sal s a wh robably 094 ad a sl rado sal wh robably ad 00 I ha as h h 3/ R o ( 3/ wh robably 096 ad 96 R o (3 96 wh robably 004 Th sod ar has a gav gvalu Th robl dos o ssarly dsaar f s larg osdr sad a oulao ossg of / 4 sraa wh four ls ah Suos ha h abov salg rodur s usd ddly ah srau I ha as R o wll oss of a ar wh h abov ars alog h dagoal ad zros lswhr 5 oao ad Oul 5 Sulao Sudy I ordr o a ral oarsos bw h oal saor (OT ad h GREG saor (GREG ad also oar hs saors wh h Horvz- Thoso saor (HT w hav odud a sall sulao sudy I h rvous sos w od ha OT s s Lar syo Eff ad a albrao saor Ev hough has ay rors ay for rasoabl sal szs b ff Hr w wll so sulad suaos show ha h oal saor a b a subsaal rov oard o GREG also for odra sal szs wh h oulao s (dlbraly hos o b ufavourabl for GREG sl bu o-rval suao for whh OT s o qual o GREG arss for srafd sl rado salg arular wh h slos dffr bw h dffr sraa ad h usrafd oulao osdr hrfor a oulao of sz whh s arod o L sraa of szs L Fro ah srau h a sl rado sal s h of sz h s draw whr s s L s ad L For sly w furhr assu ha h aulary forao s o-dsoal ad global oly s ow bforhad For GREG w hav hos h hoosdas sl lar rgrsso odl s Särdal al (99 Th rsulg rssos for HT OT ad GREG rsvly ar ˆ ˆ y o ˆ y yr y s ( y ( y whr / aalogous ad s s ˆ ˆ o r ( ( s s L ( ys (/ h h y s h ( s Sass aada aalogu o -00-XIE

106 98 drsso ad Thorbur: Oal albrao Dsa Ladg o h Oal Rgrsso Esaor ˆ o h h h h L h h h h h L h ˆ r L h h h L h s h h h ( s s h ( s ( sh ( y h s sh ( ( y sh ys y I s asly s fro hs forula ha h oal rgrsso off s h a of h wh srau slos ad ha h GREG rgrsso off s h global slo Wh hr s a larg dffr bw hs slos h GREG orro bos bad W ar hr arularly rsd oarg h quals of hs saors wh h asssg (lar odl for GREG fals W hav hus grad ad y valus fro orrlad logorally dsrbud rado varabls X ad Y whr l X s orally dsrbud wh ao 0 ad vara σ ( (0 σ ad ly s ( 0 σ Th varas σ ad σ ad h orrlao bw l X ad ly a h b hos o oba rsfd valus of h varas σ of X ad σ y of Y ad hr orrlao ρ ( X Y Valus grad fro bvara oral dsrbuos wr obad by MTL (vrso 60 Twlv oulaos hav hs ar b rad ah of sz 0000 ludg four obaos of varas σ ad σ y (0 ad 00 ad hr valus of h orrlao ρ ( X Y (05 07 ad 09 For hs oulaos a vara of 0 ls a swss of 937 ad h vara 00 lads o swss 3859 ow bfor srafao h obs of ah oulao ar ordrd wh rs o asdg y valus Th ubr of sraa s L 5 hroughou wh szs ad Ths sraa ar osrud suh a way ha obs wh h salls y valus osu srau ad so forh Fro ah srafd oulao w hav draw sals of szs ad 500 whr for ah sal 5 Ths as ha w hav rad a aroa s (robably rooroal o sz dsg wh for al obs srau 5 havg h largs luso robably ( 5 / 5 Th ubr of sulad sals was K 5000 for ah of h 3 36 ass ad HT OT ad GREG wr h oud for ah sal sh I gral oo asurs of qualy for a saor ˆ of a oal fro a squ ˆ ˆ ar h sad L rlav bas ˆ ad h sad vara S K K (ˆ ˆ whr ˆ K (/ K ˆ S w ar aly ord wh oarsos of OT ad GREG w wll oly dslay rsuls of h rlav asurs of vara (or quvally sadard dvao S S y o y HT S ad S y r y HT fro whh w a oar h sad varas of OT ad GREG wh HT ad also dr whh of OT ad GREG hav h lows sad vara 5 Rsuls Frsly as rfr h absolu valu of h sad rlav bas of h ubasd HT dd o ay as d Th orrsodg au valus for OT ad 3 GREG wr 6 0 whh as ha w ay ora o h raos of sad varas ordr o valua rlav ffs of HT OT ad GREG s s fro Tabl OT s suror o boh HT ad GREG (wh o o: ρ( X Y 09 σ 0 σ y 00 ad 50 whr GREG has slghly lss sad vara For h lows orrlao hough h dras sad vara for OT oard wh HT s o subsaal GREG o h ohr had dos o o wll wh h ohrs ad hs aoaly s arularly auad for h largs sal sz 500 hagg ρ ( X Y o 07 as rov for boh OT ad GREG bu GREG s also ow for os ass fror o HT Fally for ρ( X Y 0 9 GREG sll dslays oor bhavor oard wh HT for 500 (wh h o of σ 00 ad σ y 0 I gral GREG s losg o OT for rasg valus of ρ ( X Y (h asssg lar odl bog lss ssfd whl OT o h ohr had s rasg s surory ovr GREG for rasg sal szs whh should o as o surrs s OT s asyoally wll ovad Sass aada aalogu o -00-XIE

107 Survy Mhodology Ju Tabl Rlav Esad Effs (Gv as rags of OT ( S y / S HT ad GREG ( S / o y y r S y HT o HT asd o 5000 Sulad Sals for Eah Sal Sz ρ( X Y 05 σ 0 σ 0 σ σ y 0 σ y 00 σ y 0 00 OT GREG OT GREG OT GREG OT GREG ρ( X Y ρ( X Y σ σ y Rfrs drsso G (00 Irovg sao qualy larg sal survys h D Thss Dar of Mahas halrs Uvrsy of Thology ad Göborg Uvrsy drsso G ra O ad Wshall J (995 ulary forao survy salg Thal Ror O 995:3 Dar of Mahas halrs Uvrsy of Thology ad Göborg Uvrsy Dvll J ad Särdal -E (99 albrao saors survy salg Joural of h ra Sasal ssoao Moaar GE (987 os-salg ff QR-rdo larg-sal survys Iraoal Sasal Rvw Moaar GE (000 odog o aulary varabl as f oulao fr usrala & w Zalad Joural of Sass Rao JK (994 Esag oals ad dsrbuo fuos usg aulary forao a h sao sag Joural of Offal Sass Särdal -E Swsso ad Wra J (99 Modl sssd Survy Salg w Yor: Srgr Vrlag Sass aada aalogu o -00-XIE

108

109 Survy Mhodology Ju Vol 3 o 0-04 Sass aada aalogu o -00-XIE roaos o * b h rdo of Dsg Effs Du o lusrg r Ly ad Sgfrd Gablr bsra Ksh s wll-ow rsso for h dsg ff du o lusrg s of usd o for sal dsg usg a aroao suh as b la of b If h dsg volvs hr wghg or varao lusr sal szs hs a b a oor aroao I hs arl w dsuss h ssvy of h aroao o darurs fro h l assuos ad roos a alrav aroao Ky Words: ol sal dsg; Iralusr orrlao off; Slo robabls; Wghg lrav Fuos of lusr Sz Ksh (965 usd a rsso for h dsg ff (vara flao faor du o sal lusrg dff ( b ρ whr b s h ubr of obsrvaos ah lusr (rary salg u ad ρ s h ralusr orrlao off Ths rsso s wllow s augh o ourss o salg hory ad s usd by survy raors dsgg ad valuag sals Th rsso holds wh hr s o varao lusr sal sz ad h dsg s qual-robably (slfwghg W a rss hs wo rra forally: b b ( whr do h lusrs ad w ( w whr I do h wghg lasss wh w h assoad dsg wghs Howvr os survys volv darurs fro ( ad ( I h gral as rovg rsros ( ad ( Gablr Hädr ad Lahr (999 showd ha udr a * arora odl dff ( b ρ whr b * I wb I w b b w b ad b s h ubr of obsrvaos wghg lass lusr b b (w hav hagd h oao fro ha of Gablr al (999 o rovd ossy ad w h s h wgh assoad wh h obsrvao lusr b Th quay b * a b alulad fro survy rodaa rovdd h dsg wgh ad lusr brsh s ow for ah obsrvao Howvr a h sal dsg sag s o lar how b * a b rdd Gablr al w (3 (999 rrd Ksh s b as a for of wghd avrag lusr sz: b w b b I w b b w I b w whr b s h ubr of obsrvaos lusr b I b Howvr (4 s o asr ha (3 o rd a h sal dsg sag slr rrao rhas ooly usd sal dsg s h uwghd a lusr sz: b b I s uh asr o rd b a h sal dsg sag * ha hr b w or b as rqurs owldg oly of h oal ubr of obsrvaos ad oal ubr of lusrs ad L * Rlaosh w b bw ad b Udr lrav ssuos w ov( b b w b b b I w w b b w w b b w (4 (5 r Ly Isu for Soal ad Eoo Rsarh Uvrsy of Ess Wvho ar olhsr Ess O4 3SQ Ud Kgdo E-al: ly@ssau; Sgfrd Gablr Zru für Ufrag Mhod ud alys (ZUM osfah Mah Gray E-al: gablr@zua-ahd

110 0 Ly ad Gablr: roaos o * b h rdo of Dsg Effs Du o lusrg Th Var( w b I b b b ( w ( w w w ov( b b w b b w * b (6 b Var( w b w If ( holds h (6 bos: w * b b (7 Var( w w * So ha rusa b b If addoally wghs ar qual wh lusrs vz: w * h b b If (8 holds bu o ( h * b b w (8 f ad oly f ov( b b w 0 * ov( b b w s b b b w Th ovara would b gav oly f sall lusr szs od wh larg avrag wghs wh h lusrs ad v vrsa I so 4 blow w obsrv ha hs dd o our ay oury o roud of h Euroa Soal Survy Furhror fro (3 ad (4 w hav: b * b w ( w b w b (9 If w addoally os h rsro ( h w * hav h obvous rsul b bw b b Th rsul (9 would aly o survys whr h oly varao slo robabls was du o dsrooroa salg bw doas ha dd o ross-u lusrs oo al would volv dsrooroa srafao by rgo wh SUs ossg of gograhal aras hrarhal o rgos raal rlaao of h rsro o h varao wghs s: b b b (0 I ohr words w allow varao wghs wh lusrs bu w osra h wghs o hav h sa rlav frquy dsrbuo ah lusr h as ad h varas of h wghs wh lusrs do o dd o h lusrs ow (3 slfs as follows: b * I b I w b w b I I b w b I I wb w b b w b ( I I o ha (( w b / w b / ( w whr w s h squard off of varao aross all obsrvaos of h wghs lso ( b / ( b / whr b s h squard off of varao aross all lusrs of h lusr sal szs Thus ( bos: * ( b ( b b b b say ( ( ( w So b wll udrsa b * f b > w ad v vrsa I arular f w w ad * b > 0 h b > b Th grar h varao b h grar h o whh * b wll udr-sa b ssuo (0 wll rarly hold aly bu hs rsul gh b usful suaos whr h dsrbuo of wghs s d o b slar aross lusrs al gh b addrss-basd sals whr o rso s sld r addrss If h dsrbuo of h ubr of rsos r addrss s aroaly osa aross SUs ( h oulao h h dsrbuo of wghs wll vary aross lusrs h sal oly du o salg varao ad dsrooroa orsos (h ff of hs ould of ours b subsaal f lusr sal szs ar sall If o rsro s osd o h varao wghs bu Var( w > 0 for a las o h fro (6 * b b ov( b bw f ad oly f ζ b Var( w If (0 holds h ζ b / w 3 Ilaos for Sal Dsg w (3 Ersso ( suggss ha b * ay b rdd by rdg h rlav aguds of b ad w Howvr hs rsul als o a sal suao whr Sass aada aalogu o -00-XIE

111 Survy Mhodology Ju ov( w whr b w b fro (0 0 b ( b b ( w w b w I ( b b b b b ( b b w b b w I b w b w b w ( b Wh hs ovara s d o b sall ay b * arora o rd b hus: bˆ * ˆ ˆ ( ˆ b b b (4 ( ˆ oh offs of varao a b sad fro owldg of h roosd sal dsg I h followg so w vsga ssvy of rdos obad hs way o assuo (0 usg ral daa fro dffr sal dsgs wh ov ( w > 0 b w 4 Eal: Euroa Soal Survy Th Euroa Soal Survy (ESS s a ross-aoal survy for whh gra ffors hav b ad o ahv aroa fuoal quval sal dsg bw arag aos (Ly Hädr Gablr ad Laaso 004 vrhlss hr s osdrabl vary h ys of dsg usd rarly du o varao h aur of avalabl fras ad loal obvs suh as a dsr for sub-aoal aalyss whh ay lad o dsrooroa srafao by doa W us hr daa fro h frs roud of h ESS for whh fldwor was arrd ou Of h arag aos 7 had a lusrd sal dsg Of hs wo had o y rovdd usabl sal daa a h of wrg I * Tabl w rs h sal valus of b b b w * * b b b b b orr( w b ad ζ for h rag 5 o ha h Ud Kgdo ad olad boh had a doa dsg wh h sal lusrd oly o doa aly Gra ra ( ludg orhr Irlad ad lss dsly-oulad aras ( all h largs 4 ows rsvly Fgurs rsd abl rla oly o h lusrd doa oury * b Tabl * * * Sal Valus of b b b w b b b b b orr( w b ad ζ for 5 Survys b b * * b b b b orr( w b b w usra T lgu E Swzrlad H zh Rubl Z Gray DE Sa ES Gra ra G Gr GR Hugary HU Irlad IE Israël IL Ialy IT orway O olad (rural L Slova SI ζ Sass aada aalogu o -00-XIE

112 04 Ly ad Gablr: roaos o * b h rdo of Dsg Effs Du o lusrg * Fro ( w would o obsrv b > b wh ˆw > ˆ b oo sal dsg for whh hs qualy a b aad s o whr a h sld lusr sal sz s osa so varao b wll b ld o ha ausd by dffral o-rsos; ad b h sals ar qual-robably sals of addrsss wh subsqu rado slo of o rso r addrss ladg o varao dsg wghs rflg h varao houshold sz Thr ar s aos wh sal dsgs of hs y (T H ES G GR IL I s dd h as ha for all of hs aos ζ < ad * b > b Furhror for 5 of hs 6 aos (T H ES G GR h 5 w gh (0 o b a rasoabl aroao as h oly varao wghs s ha du o slo wh a houshold/addrss For hs w gh bṱ o rfor br ha b Idd * * 5 * b b < b b for 4 of h 5 ad ( h b b / 5 * h b b 048 Th o ao whr bṱ would o rovd a rov s Sa ad hs s o b d as b s sall Sall lusr sal szs lav h rlavly or susbl o h ffs of orsos ad also salg vara whh wll lad o volao of (0 I Isral hr was a furhr sour of varao dsg wghs as hr was dsrooroa srafao by gograhal aras Ths oo auss volao of (0 so w would o bṱ ssarly o rovd a rov * o b as a rdor of b Of h aos whr b < w hr s oly o (Z for * whh b < b ad ζ > Ths s also h ao wh h salls valu of b Wh lusr sal szs ar arularly sall dff wll b sall ad h ho bw * saors of b ay b lss ora Thr ar fv aos whr sal us wr dvduals sld wh qual robabls (wh lusrs fro oulao rgsrs (E DE HU L SI I hs as (8 (ad hrfor (0 holds srly so w hav * b < b For hr of hs aos (E HU SI h sal s qual-robably so w obsrv b b * I s lar ha bṱ s suror o b for qual-robably sals For Gray ad olad hr s so varao dsg wghs bw lusrs (bu o wh Ths varao s * * ods olad ad b b < b b bu h sa s o ru Gray whr h -Eas Gray was sald a a osdrably hghr ra ha h -Ws Gray Th orwga sal dsg was h oly o ha rsuld osdrabl varao lusr sal szs a * h slo sag Th draa a of hs o b b a larly b s ga hs s a suao whh bṱ s * lly o b rfrabl o b as a rdor of b Th dsgs Irlad ad Ialy boh volvd slg addrsss fro h loral rgsrs wh robably rooroal o ubr of lors ad h slg o rsd a rado fro ah sld addrss Suh dsgs ar o qual-robably bu ar lly o rsul osdrably lss varao dsg wghs ha h addrss-basd sal dsgs dsussd arlr (Ly ad sa 005 I boh hs ass ˆw < ˆ b h dffr bg grar h as of Ialy whr so lusr sal szs ( h largs uals wr osdrably largr ha h ohrs ( Irlad all wr qual a h slo sag sd fro h zh Rubl hs ar h oly wo aos wh ζ > 5 oluso To ad rdo of h dsg ff du o lusrg w blv ha bṱ s lly o b a br ho ha bˆ as a rdor of b * suaos whr a rasoably b d ha (0 wll aroaly hold Ths luds bu s o rsrd o h followg oo ys of sal dsg: Equal-robably dsgs whr lusr sal szs vary by dsg; Equal-robably dsgs whr lusrs do o vary by dsg bu ar lly o vary du o orsos; ddrss-basd sals whr o rso s sld a ah addrss hr s o ohr sgfa sour of varao slo robabls ad lusr szs do o vary by dsg owldg Ths rsarh was arrd ou whl h frs auhor was Gus rofssor a h r for Survy Rsarh ad Mhodology (ZUM Mah Gray Rfrs Gablr S Hädr S ad Lahr (999 odl basd usfao of Ksh s forula for dsg ffs for wghg ad lusrg Survy Mhodology Ksh L (965 Survy Salg w Yor: Joh Wly & Sos I Ly Hädr S Gablr S ad Laaso S (004 Mhods for hvg Equval of Sals ross-aoal Survys ISER Worg ar valabl a h://wwwsrss au/ubs/woras/df/004-09df Ly ad sa M (005 Irovg h qualy of sal dsg for soal survys Ialy: Lssos fro h Euroa Soal Survy Forhog Sass aada aalogu o -00-XIE

113 Survy Mhodology Ju Vol 3 o Sass aada aalogu o -00-XIE o o h Sas Udr h sd Error Rgrsso Modl Ja L Mza ad Lahr bsra sd rror rgrsso odls ar frquly usd sall-ara sao ad rlad robls Sadard rgrsso odl slo rro wh ald o sd rror rgrsso odls ay rsul ff odl slo hods W llusra hs o by ag h rfora of h sas hrough a Mo arlo sulao sudy Th ffy of h sas ay howvr b rfd by a suabl rasforao of h daa Ky Words: sass; sr rror rgrsso odl; Mo arlo sulao Iroduo Ths ar as h laos of a sadard rgrsso odl slo rro h sas for sd rror rgrsso odls Th sas (Mallows 973 s dfd by RSS ( σˆ whr RSS s h rsdual su of squars ad s h ubr of arars for odl s h ubr of obsrvaos ad ˆσ s a sa of σ If h odl s orr h valu of should b slar o or sallr ha Th odl slo rro s ssv o oulrs ad darurs fro h oral d assuo o h rrors Th sas hrfor ao b drly ald o h sd rror rgrsso odl s hr h rror sruur s o d W roos a rasforao ha aduss for ralusr orrlao ad allows us of h sadard odl slo rro Th hod rsd hs ar a b ald o sl ovaras h aalyss of ol survy daa ad sall-ara odls For al our hqu ould b usd o sl ovaras h sd rror rgrsso odl usd by as Harr ad Fullr (988 o sa h ara lad ( hars wh or or soybas for wlv Iowa ous Thy usd h followg odl: y β v ( for u K ouy K whr s h sal sz for sall ara ad h oal sal sz s Th ouy ffs v ar dsrbud as (0 σ v dd of h rado rrors whh ar dsrbud as (0 σ Th ara ( hars u of ouy s dod by y ad ( K s a vor of h valus of h ovaras K for u ouy Th vor β ( β0 β K β s a vor of uow arars Th sd rror rgrsso odl a b rssd ar for as y X β ε (3 whr y ( y K y ( ε ( ε ε y y K y K ε ( ε K ε ε v Furhr X ( X K X whr X s a ( ar wh rows for ~ (0 K ε σ V whr σ σ v σ V has blo-dagoal for V wh V ( ρ I ρ J whr ρ σ / σ v s h oo srasrau orrlao I s h dy ar ad J s h u ar S h sd rror odl dos o hav d rrors sadard rgrsso rodurs do o aly Th sulao sudy so 3 rvals ha h rro dos o rfor wll udr h sd rror rgrsso odl Th rasforaos osdrd h so ar usd o rasfor h sd rror rgrsso odl o a sadard rgrsso odl wh d rrors Wh hs rasford obsrvaos h rro rfors uh br dusg for Ira-ara orrlaos s od h rvous so ovoal odl slo hods l h rro ar o arora s h srasrau orrlaos ar gord Wu Hol ad Hols (988 ad Rao Suradhar ad Yu (993 sudd h ff of ovoal hods for h sd rror rgrsso odl a dffr o osdr h sd rror rgrsso odl ad l σ σv σ ad ρ b h oo ra-ara orrlao ρ σv / σ s Fullr ad as (973 ad Rao al Ja L Mza Uvrsy of brasa Mdal r brasa Mdal r Oaha E E-al: za@udu; Lahr Uvrsy of Marylad a ollg ar 8 L Fra Hall ollg ar MD E-al: lahr@survyuddu

114 06 Mza ad Lahr: o o h Sas Udr h sd Error Rgrsso Modl (993 rasfor h sd rror rgrsso odl o a sadard rgrsso odl wh d rrors L ρ α ( ρ y * * / (4 y α y (5 α (6 whr y y / ad / Th rasford odl h bos * * * y β (7 for K K ad * ar ddly dsrbud as (0 σ ow h sadard odl slo rro ay b ald o h rasford daa I ra ρ s usually uow ad us b sad fro h daa Rao al (993 usd Hdrso s (953 hod o oba ubasd quadra saors σ ˆ v ad σ ˆ of h vara oos σ v ad σ O h saors hav b obad ρ σv /( σv σ ay b sad by σˆ v ρ ˆ a 0 (8 σˆ v σˆ To oba h saors of h vara oos l { u } b h rsduals fro h ordary las squars rgrsso of { y y } o { K } whou h r r whr l l / for l K L r } b h rsduals fro h ordary { las squars rgrsso of y o { 0 K } wh h r r Th saors of σ v ad σ ar gv by σ ˆ ( λ (9 σˆ v * r ( σˆ (0 * r ( X X ( whr λ 0 f h odl has o r r ad λ ohrws W roos o aly sadard odl slo rro o hs rasford obsrvaos y * * ad 3 Sulao Sudy sulao sudy was odud o a h bhavor of h odl slo rro ad h roosd rasforaos for h sd rror rgrsso odl Th followg odl was osdrd: y β0 0 β β β3 3 β4 4 v ( for K0 { K 5} K ad 40 Th v ar dsrbud as (0 σ v dd of whh ar dsrbud as (0 Th daa l ar a fro a al gv by Gus ad Maso (980 ad ludd Shao (993 (Tabl Th valu of 0 s for all K 0 K Tabl Daa for sd Error Sulao Sass aada aalogu o -00-XIE

115 Survy Mhodology Ju So of h β ay b zro ad hus varous obaos of varabls wr hos fro ( o b h rdors usd o gra daa og fro a sd rror rgrsso odl Thr ar 3 ossbl odls Eah odl wll b dod by a subs of (0 3 4 ha oas h ds of h varabls l h odl Daa wr grad usg 000 sulaos for svral valus of σ v o sa h robably of slg ah odl usg h rro Th valu of σ was a o b for all sulaos Th rsuls of h sulao ar gv Tabl Th valus of σ osdrd wr 0 v 5 0 ad 6 ad h valus of β wr a o b ( ( ( ad ( as Shao (993 Modls wr agorzd as oal agory II (orr bu o oal or agory I (orr Th rro dd o rfor wll for larg valus of σ v For h odl β ( wh σ v h sad slo robabls wr: oal odl 054; orr odl 046; orr odl 0 I oras wh σ v 6 h sad slo robabls wr: oal odl 043; orr odl 035; orr odl 0 Th rro also dd o rfor wll for largr odls wh larg valus of σ v Th rro howvr Tabl robabls of Modl Slo for Trasforao β ( Modl agory σ v 0 σ v σ v σ v 5 σ v 0 σ v Oal II II II II II II II I I I I I I β ( Modl agory σ v 0 σ v σ v σ v 5 σ v 0 σ v Oal II II II I I I I β ( Modl agory σ v 0 σ v σ v σ v 5 σ v 0 σ v Oal II I I I I I β ( Modl agory σ v 0 σ v σ v σ v 5 σ v 0 σ v Oal I I I I I I I Sass aada aalogu o -00-XIE

116 08 Mza ad Lahr: o o h Sas Udr h sd Error Rgrsso Modl dd vry wll for larg odls wh sall valus of σ v For h full odl β ( wh σ v h sad slo robabls wr: oal odl 098; orr odl 00; orr odl 0 I oras wh σ v 6 h sad slo robabls wr: oal odl 0; orr odl 089 o ha hs saro hr ar o orr odls ohr ha h oal odl I suary wh h rro s ald o daa followg h sd rror rgrsso odl: For ay arular odl h sad robably of slg h oal odl drass as σ v rass For ay arular odl h sad robably of slg a orr odl rass as σ v rass 3 s h ubr of varabls ludd h odl rass ad σ v rass h sad robably of slg h oal odl drass 4 s h ubr of varabls ludd h odl rass ad σ v rass h sad robably of slg a orr odl rass Th daa wr h usd o sa h robably of slg ah odl usg h rro udr h rasforao for ρ ow Th rsuls of h sulao ar gv Tabl 3 For h odl β ( wh σ v 0 (sadard rgrsso odl h sad slo robabls wr: oal odl 06; orr odl 038; orr odl 0 (Tabl Slarly udr h rasforao for ρ ow wh σ v 6 h sad slo robabls wr: oal odl 060; orr odl 040; orr odl 0 (Tabl 3 For h full odl β ( h sad robably of slg h oal odl was for boh h sadard rgrsso odl (Tabl σ v 0 ad udr h rasforao for ρ ow for all valus of σ v osdrd (Tabl 3 I ra ρ s uow ad us b sad fro h daa Th rasforao for ρ uow s hrfor or hlful for raors Th rsuls for h rasforao wh ρ uow ar dslayd Tabl 4 Wh ρ was sad hr was oly a sall dras h sad robably of slg h oal odl or a orr odl Th largs dras h sad robably of slg h oal odl was 003 for h odl wh β ( ad σ v 0 6 for ρ ow (Tabl 3 oard o 058 for ρ uow (Tabl 4 Tabl 3 robabls of Modl Slo fr Trasforao ρ Kow β ( Modl agory σ v σ v σ v 5 σ v 0 σ v Oal II II II II II II II β ( Modl agory σ v σ v σ v 5 σ v 0 σ v Oal II II II β ( Modl agory σ v σ v σ v 5 σ v 0 σ v Oal II β ( Modl agory σ v σ v σ v 5 σ v 0 σ v Oal Sass aada aalogu o -00-XIE

117 Survy Mhodology Ju Tabl 4 robabls of Modl Slo fr Trasforao ρ Uow β ( Modl agory σ v σ v σ v 5 σ v 0 σ v Oal II II II II II II II β ( Modl agory σ v σ v σ v 5 σ v 0 σ v Oal II II II β ( Modl agory σ v σ v σ v 5 σ v 0 σ v Oal II β ( Modl agory σ v σ v σ v 5 σ v 0 σ v Oal asd o our sulao rsuls wh h rro s ald o daa followg h sd rror rgrsso odl: Udr boh rasforaos ( ρ ow ad ρ uow h sad robably of slg a orr odl was 0 Udr h rasforao for ρ ow h robably of slg h oal odl was slar o ha of h sadard rgrsso odl 3 Wh ρ was sad hr was oly a sall dras h sad robably of slg h oal odl or a orr odl 4 Udr boh rasforaos ( ρ ow ad ρ sad h rro rford wll v for largr odls wh larg valus of σ 5 Th rfora of h rro for h sd rror rgrsso odl rsbls ha of h rro for h sadard rgrsso odl I suary h rro dos o rfor wll udr h sd rror rgrsso odl wh σ v s larg Wh h rasforao for ρ uow (or ρ ow s ald h odl h bos a sadard rgrsso odl ad h sas rfors aordgly v owldgs Th rsarh was suord ar by a gra fro h Gallu Orgazao Rfrs as GE Harr RM ad Fullr W (988 rroroos odl for rdo of ouy ro aras usg survy ad sall daa Joural of h ra Sasal ssoao Fullr W ad as GE (973 Trasforaos for sao of lar odls wh sd rror sruurs Joural of h ra Sasal ssoao Gus GF ad Maso RL (980 Rgrsso alyss ad Is lao w Yor: Marl Dr Hdrso R (953 Esao of vara ad vara oos ors Mallows L (973 So os o Thors Rao JK Suradhar ad Yu K (993 Gralzd las squars F s rgrsso aalyss wh wo-sag lusr sals Joural of h ra Sasal ssoao Shao J (993 Lar odl slo by ross-valdao Joural of h ra Sasal ssoao Wu FJ Hol D ad Hols DJ (988 Th ff of wo-sag salg o h F Sas Joural of h ra Sasal ssoao Sass aada aalogu o -00-XIE

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119 JOURL OF OFFIIL STTISTIS Iraoal Rvw ublshd by Sass Swd JOS s a sholarly quarrly ha salzs sasal hodology ad alaos Survy hodology ad ohr ssus r o h roduo of sass a aoal offs ad ohr sasal orgazaos ar haszd ll ausrs ar rgorously rvwd by dd rfrs ad brs of h Edoral oard os Volu 0 o Th Twlfh Morrs Has Lur Sl Rsos Vara: Th ad ow aul r 47 Dsusso Robr M Grovs 44 Kh Rus445 Ls-basd Wb Survys: Qualy Tlss ad orsos h Ss of h arao Flow Moa ras Kaa Lozar Mafrda Slva ffgad ad Vasa Vhovar 45 Th Ia of odg Error o T Us Survys Esas ar Surgs467 O h Dsrbuo of Rado Effs a oulao-basd Mul-sag lusr Sal Survy Ob Uouu Mar Gullford ad Susa h 48 Esag Margal ohor Wor Lf Eas fro ross-soal Survy Daa Maru M ur hrsohr R Haho ad r Davs 495 Mssg h Mar? Iuao as h urr oulao Survy s Sa Io ad Halh Isura ovrag Esas Mhal Davr Ly lw ors rshadsy ad or rold 59 Dos Vo Mar? Irav Vo Rsos (IVR Er M our Elaor Sgr ad Rogr Touragau55 I Ohr Jourals57

120 Volu 0 o Rvsos o Offal Daa o US G: Mulvara ssss of Dffr Vags Krry D arso ad SM Hrav573 Dsusso Ds Trw603 r va d V ad Gorg va Luw607 Do M Egggo65 Rob Lyh ad rag Rhardso 63 Rodr Krry D arso ad SM Hrav63 Th s roah o Doa Esao rluds orrowg Srgh Vor Esvao ad arl-er Särdal645 ros of Dsably: Th Eff of Slf- ad roy Rsos Sugh L ay Mahowz ad Rogr Touragau 67 Maag Ra ad Ehy Trd Ls US Govr Survys Elzabh Grbrg Jo oh ad Da Sdor687 ofd Irvals for rooros Esad fro ol Sal Dsgs lsar Gray Sh Hasl ad Goffry Kuzh705 Edoral ollaboraors 75 Id o Volu Volu o 005 Ifr for h oulao Toal fro robably-rooroal-o-sz Sals asd o rdos fro a alzd Sl oarar Modl Hu Zhg ad Rodr J Ll Th uray of Esaors of ubr of Sgaors o a o asd o a Sal Dua I Hddrly ad Sh J Hasl Two-sag oarar Sal Survy roah for Tsg h ssoao of Dgr of Ruraly wh Halh Srvs Ulzao Joh S rssr ly E Mhll Jas M owrs Thoas rury ad Wlbr M Gslr 39 Irovg oarably of Esg Daa by Rsos ovrso Sf va uur Soh Eyrs la Ta ad Mar Hoa-Ro53 Th aur of orsos a Mdad Survy: auss ad osqus ara M Gallaghr Floyd Jaso Fowlr Jr ad V L Srgfllow73 Tlho Ir ad ar Daa ollo Mods for h sus 000 Shor For Sd J Shdr Davd aor Lawr Malahoff arlos rra aul Sgl Khaa-Luu guy ad Jfr Guaro Taro89 Th roduvy of h Thr-s Ts-rvw (TSTI oard o a Er Rvw of a Slf-adsrd Qusoar o lohol osuo Harr Jas ad Toy Ha03 Udrg h E-usss Frawor Dfg E-usss os ad lassfyg E-usss Idaors Xadr J d Graaf ad Rob H Muurlg I Ohr Jourals37 ll qurs abou subssos ad subsros should b drd o os@sbs

121 Th aada Joural of Sass OTETS Volu 33 o Marh/ars La Rvu aad d Sasqu TLE DES MTIÈRES Douglas WIES Edor s ror/raor du rédaur hf Gra Y YI & Mary E THOMSO Margal ad assoao rgrsso odls for logudal bary daa wh dro-ous: a llhood-basd aroah3 Ds OSQ Esao suroal d la dsé ar roo Joh RU Thrry DUHESE & Jas E STFFORD Loal llhood dsy sao for rval sord daa 39 Zhgag ZHG Luqua SU Xgqu ZHO & Jaguo SU Rgrsso aalyss of rval-ord falur daa wh lar rasforao odls 6 la G VDL Robr GETLEM & Xuhg LIU osrad sao ad llhood rvals for sord daa 7 Jaguo SU & Lqua SU Sarar lar rasforao odls for urr saus daa 85 ladr X RVLHO & Mar TER Modlg olar srs wh loal urs of gralzd lar odls97 Mayr LVO & aul ILIO Gral sors sass o ras h aalyss of ubalad dsgs 5 Sudhr R UL & Xg JIG Tsg h hoogy of svral wo-arar oulaos 3 owldg of rfrs srvs/rrs au brs ds urys45 Forhog ars/rls à araîr 46 Volu 33 (005: Subsro ras/fras d abo 47

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123 GUIDELIES FOR MUSRITS for havg a ausr yd for subsso las a a r ssu of Survy Mhodology (Vol 9 o ad oward as a gud ad o arularly h os blow rls us b subd ah-radabl for rfrably Word ar oy ay b rqurd for forulas ad fgurs Layou Mausrs should b yd o wh bod ar of sadard sz (8½ h o sd oly rly doubl sad wh args of a las ½ hs o all sds Th ausrs should b dvdd o ubrd sos wh suabl vrbal ls 3 Th a ad addrss of ah auhor should b gv as a fooo o h frs ag of h ausr 4 owldgs should aar a h d of h 5 y ad should b lad afr h aowldgs bu bfor h ls of rfrs bsra Th ausr should bg wh a absra ossg of o aragrah followd by hr o s y words vod ahaal rssos h absra 3 Syl 3 vod fooos abbrvaos ad aroys 3 Mahaal sybols wll b alzd ulss sfd ohrws for fuoal sybols suh as ( ad log( 33 Shor forula should b lf h bu vryhg h should f sgl sag Log ad ora quaos should b sarad fro h ad ubrd osuvly wh arab urals o h rgh f hy ar o b rfrrd o lar 34 Wr fraos h usg a soldus 35 Dsgush bw abguous harars (g w ; o O 0; l 36 Ials ar usd for hass Ida als by udrlg o h ausr 4 Fgurs ad Tabls 4 ll fgurs ad abls should b ubrd osuvly wh arab urals wh ls whh ar as arly slf laaory as ossbl a h boo for fgurs ad a h o for abls 4 Thy should b u o sara ags wh a dao of hr arora la h (orally hy should aar ar whr hy ar frs rfrrd o 5 Rfrs 5 Rfrs h should b d wh auhors as ad h da of ublao If ar of a rfr s d da afr h rfr g ohra (977 ag 64 5 Th ls of rfrs a h d of h ausr should b arragd alhabally ad for h sa auhor hroologally Dsgush ublaos of h sa auhor h sa yar by aahg a b o h yar of ublao Joural ls should o b abbrvad Follow h sa fora usd r ssus