Cro-ecional and longiudinal eighing in a roaional houehold panel: applicaion o EU-SILC Viay Verma, Gianni Bei, Giulio Ghellini Working Paper n. 67, December 006
CROSS-SECTIONAL AND LONGITUDINAL WEIGHTING IN A ROTATIONAL HOUSEHOLD PANEL: APPLICATIONS TO EU-SILC Viay Verma, Gianni Bei, Giulio Ghellini ABSTRACT Thi paper provide a comprehenive decripion of an inegraed yem of cro-ecional and longiudinal eighing for roaional houehold panel urvey. To be concree and deailed, i develop he eighing procedure ih reference o he EU-SILC inegraed deign. EU- SILC (Saiic on Income and Living Condiion) cover daa and daa ource of variou ype: cro-ecional and longiudinal; houehold and peronal; economic and ocial; and from regier and inervie urvey. The andard inegraed deign involve a roaional panel in hich a ne panel i inroduced each year o replace one quarer of he exiing ample; peron enumeraed in each ne panel are folloed-up in he urvey for four year (Verma and Bei, 006). A common roaional ample of hi ype yield each year a cro-ecional ample a ell a longiudinal ample of variou duraion. Thee ample daa have o be eighed o make hem more repreenaive of he arge populaion hey repreen. The paper begin ih a ummary of he main feaure of EU-SILC and an overvie of he inegraed eighing yem for he differen ype of daa coming ou of he roaional panel annually. I decribe a ep-byep procedure for conrucion of iniial eigh o be applied o each ne ample a i i inroduced ino he urvey. An innovaive feaure of he eighing procedure i he concep of bae eigh (Verma and Clemenceau, 996). Saring from he iniial eigh of each individual in he original ample, he peron bae eigh i conruced for each ubequen year o compenae for panel ariion. The final obecive i of coure o conruc cro-ecional eigh and longiudinal eigh for ue in daa analyi. Procedure are decribed for conrucing hee o ype of eigh from he ame bae eigh. Thi make he hole yem of eigh inernally conien and inegraed. Key ord: eighing, houehold panel, roaional deign, cro-ecional eigh, longiudinal eigh, EU-SILC. V. Verma, e-mail: verma@unii.i (correponding auhor); G. Bei e-mail: bei@unii.i, G. Ghellini, e-mail: ghellini@unii.i. Deparmen of Quaniaive Mehod, Univeriy of Siena, P.za S. Franceco, 7, 500, Siena, Ialy.
. The EU-SILC frameork.. Inroducion: conex and conen of he paper The preen paper provide a comprehenive decripion of an inegraed yem of croecional and longiudinal eighing for roaional houehold panel urvey, pecifically ih reference o he EU-SILC inegraed deign. A i ell-knon by hi ime, EU-SILC i he maor ne ource of comparaive aiic on income and living condiion in Member Sae of he European Union and ome neighbouring counrie. I ha been developed a a flexible ye comparable inrumen for he follo-up and monioring of povery and ocial excluion a he EU and naional level. I cover daa and daa ource of variou ype: cro-ecional and longiudinal; houehold-level and peron-level; economic and ocial; from regier and inervie urvey; from ne and exiing naional ource. In previou paper and repor (Verma, 00; Verma and Bei, 006) e have elucidaed he rucure and main characeriic of EU-SILC urvey, and he variou echnical conideraion involved in he deign and implemenaion of ample for EU-SILC. Depie he diveriy of arrangemen permied under EU-SILC, he andard inegraed deign recommended by Euroa ha been adoped by a big maoriy of he paricipaing counrie. Thi inegraed deign involve a roaional panel in hich a ne ample of houehold and peron i inroduced each year o replace a par (normally one quarer) of he exiing ample. Peron enumeraed in each ne ample are folloed-up in he urvey for four (or more) year. A common roaional ample of hi ype yield each year a cro-ecional ample a ell a longiudinal ample of variou duraion. In mo iuaion, hee ample daa have o be eighed o make hem more repreenaive of he arge populaion of he urvey. The complex rucure of he ample mean ha he correponding eighing procedure can alo be quie complex. The eighing procedure decribed here i in fac baed on deailed recommendaion originally developed by one of he preen auhor (Verma, 006). Thee recommendaion have been adoped by Euroa and are being implemened in EU-SILC naional urvey. The preen paper aim o provide a more yemaic and clearer decripion of he eighing procedure, alo inroducing ome refinemen o a o enhance he coniency and compleene of original recommendaion. The re of Secion ummarie he main feaure of EU-SILC, uch a i cope and conen, daa rucure, longiudinal follo-up (racing) rule, and in paricular he inegraed roaional panel deign adoped by mo counrie. The obecive i o provide he neceary background for decribing he recommended eighing procedure. Furher deail may be found in variou EU-SILC regulaion publihed in he Official Journal of he European Communiy, he many echnical repor produced by Euroa, and alo in he reference already cied above. Secion provide an overvie of he inegraed eighing procedure. I clarifie he differen ype of eigh required for he differen ype of daa coming ou of EU-SILC annually. Wih a -year roaional deign, once eablihed, one cro-ecional daae and hree longiudinal daae, repecively of, and year duraion are generaed each year. We explain he concep of iniial and bae eigh, on he bai of hich he required croecional and longiudinal eigh can be conruced a an inegraed hole. Secion deal ih he conrucion of iniial eigh, by hich e mean eigh o be applied o each ne ample a i i inroduced ino he urvey. A ep-by-ep procedure i decribed, aring from deign eigh, folloed by adumen for non-repone and calibraion o exernal conrol, and finally rimming and caling a required o obain he iniial eigh. Of coure, hee procedure are applicable o any urvey and are no pecific o a roaional panel. Hoever, in a panel urvey i i paricularly imporan o conruc good iniial eigh for each ne ample a i i inroduced, ince hee deermine he qualiy of he longiudinal eigh, a ell a he cro-ecional eigh, o be applied in ubequen year he ample remain in he urvey.
An innovaive feaure of he eighing procedure i he concep of bae eigh, developed originally in he conex of European Communiy Houehold Panel (Verma and Clemenceau, 996). Saring from he iniial eigh of each individual in he original ample, he peron bae eigh i conruced - for each ubequen year he peron remain in he urvey - ih he obecive of compenaing for panel ariion. The procedure for conrucing bae eigh i decribed in Secion. Secion 5 and 6 decribe he procedure for conrucing, repecively, longiudinal eigh and cro-ecional eigh. Thee o ype of eigh can in fac boh be obained in a raighforard ay from he ame bae eigh. Thi make he hole procedure inernally conien and inegraed. Finally, in Secion 7 e commen on ome imporan pracical apec in he implemenaion of he eighing procedure... Scope and conen of EU-SILC A noed, EU-SILC aim o be a flexible ye comparable inrumen covering daa and daa ource of variou ype. In erm of he ubanive conen, four ype of daa are involved: (i) variable meaured a he houehold level; (ii) informaion on houehold ize and compoiion and baic characeriic of houehold member; (iii) income and oher more complex variable meaured a he peronal level, bu aggregaed o conruc houehold-level variable (hich may hen be acribe o each member for analyi); and (iv) more complex non-income or ocial variable colleced and analyed a he peronal level. For e (i)-(iii) variable, a ample of houehold including all houehold member i required. Among hee, e (i) and (ii) are normally colleced from a ingle, appropriaely deignaed reponden in each ample houehold. Alernaively, ome or all of hee daa may be compiled from regier or oher adminiraive ource. Se (iii) variable - concerning mainly, bu no excluively, he deailed collecion of houehold and peronal income - mu be colleced direcly a he peronal level, covering all peron in each ample houehold. In many counrie, hee income and relaed variable are colleced hrough peronal inervie ih all adul aged 6+ in each ample houehold. Thi collecion i normally combined ih ha for e (iv) variable, ince he laer mu alo be colleced direcly a he peronal level. Thee are he o-called urvey counrie. By conra, in ome counrie, e (iii) variable are compiled from regier and oher adminiraive ource, hu avoiding he need o inervie all member (adul aged 6+) in each ample houehold. Thee are he o-called regier counrie. Se (iv) variable are normally colleced hrough direc peronal inervie in all counrie. Thee are oo complex or peronal in naure o be colleced by proxy, nor are hey available from regier or oher adminiraive ource. For he urvey counrie, hi collecion i normally combined ih ha for e (iii) variable a noed above, boh being baed on a ample of complee houehold, i.e. covering all peron in each ample houehold. Hoever, from he ubanive requiremen of EU-SILC, i i no eenial in conra o e (iii) variable ha e (iv) variable be colleced for all peron in each ample houehold, ince hee variable need no o be aggregaed o he houehold level. I i herefore ufficien o do hi collecion on a repreenaive ample of peron. Thi opion i normally folloed in regier counrie, ince for hee counrie inervieing all houehold member for e (iii) i no involved. In counrie hich chooe o do o, he ampling proce involve he elecion of peron (uually one adul member aged 6+ per houehold) eiher direcly or, opionally, hrough a ample of houehold.
.. Daa rucure Hence differen ype of uni of analyi are involved in EU-SILC for hich ample eigh have o be defined: (i) privae houehold; (ii) all peron reiding in ample houehold; (iii) all houehold member aged 6+; and opionally (iv) one eleced adul per ample houehold. One may alo be inereed in pecial group, uch a children. Anoher dimenion i ha boh cro-ecional and longiudinal daa are required. The cro-ecional componen cover informaion peraining o he curren and a recen period uch a he preceding calendar year. I aim a providing eimae of cro-ecional level and of ne change from one period (year) o anoher. The longiudinal componen cover informaion compiled or colleced hrough repeaed enumeraion of individual uni, and hen linked over ime a he micro-level. I aim a meauring gro (micro-level) change and elucidaing he dynamic procee of ocial excluion and povery. Boh cro-ecional and longiudinal microdaa e are updaed on an annual bai. In EU-SILC a period of four year i aken a he minimum duraion for longiudinal follo-up a micro level. Combining he variou ype of uni and he ime dimenion, he ne daa e dieminaed each year coni of he folloing: cro-ecional daa peraining o he mo recen reference year for houehold and peron; daa peraining o hree differen longiudinal period, covering, and year preceding he urvey, only for peron... The inegraed deign Verma and Bei (006) illurae a ypology of poible daa ource rucure in EU- SILC. A ingle inegraed ource covering all componen cro-ecional and longiudinal, income and ocial - i by far he mo common one adoped by counrie up o no. Throughou, e ill decribe he eighing procedure ih reference o hi inegraed deign. The baic idea i a follo. A any one ime, he ample i made up of, ay, hor-erm ubample or panel. Each year one ne panel i added o ay in he urvey for year, and hen dropped o be replaced by anoher ne panel. Mover from he original ample are folloed-up o heir ne locaion for up o he ime heir panel remain in he urvey. Each panel provide a longiudinal ample of he choen duraion. The uni preen a a given ime from all he panel are appropriaely pu ogeher o coniue he cro-ecional ample. Clearly, an imporan advanage of hi cheme i ha boh cro-ecional and longiudinal daa are obained from he ame common e of uni. Thi overlap i highly economical, and alo maximie inernal coniency beeen longiudinal and cro-ecional aiic produced from he urvey. The roaional cheme i illuraed in Figure. I alo pecifie he noaion e ill ue. In he above diagram, i a ypical panel ample inroduced in year (-); hi ample (more ricly, he ample derived from i according o cerain follo-up rule) i enumeraed over four year (-) o. Longiudinal ample of o year duraion are conruced by puing ogeher differen panel of hi ype, a ill be dicued laer (Secion 5). The full cro-ecional ample a year i compoed of four panel +, o, a hon in Figure. Folloing he EU-SILC erminology, e ill refer o hee differen ype of uni and o he aociaed daa file a follo: H ( houehold ), R ( regier covering all member), P ( peronal covering all adul aged 6+), S ( eleced reponden ), and Q (children or oher pecial group). According o Commiion Regulaion (EC) No 98/00 a regard he Sampling and Tracing Rule roaional deign refer o he ample elecion baed on a number of ubample or replicaion, each of hem imilar in ize and deign and repreenaive of he hole populaion. From one year o he nex, ome replicaion are reained, hile oher are dropped and replaced by ne replicaion.
Figure. The panel and cro-ecional ample Panel: year eleced Panel: duraion a - () - () Panel - or () - () () Cro-ecion Survey ear - - -.5. Sample follo-up (racing) rule Follo-up rule are required in a houehold panel o preerve i repreenaive naure over ime. In he cae of EU-SILC, he relevan Commiion Regulaion (European Communiy, 00) pecifie hee formally a follo. (a) Iniial ample: refer o he ample of houehold or peron a he ime i i eleced for incluion in EU-SILC. (b) Sample peron: mean all or a ube of he member of he houehold in he iniial ample ho are over a cerain age. (c) Age limi ued o define ample peron: In counrie ih a four-year panel uing a ample of addree or houehold, all houehold member aged and over in he iniial ample hall be ample peron. In counrie ih a four-year panel uing a ample of peron, hi hall mean he elecion of a lea one uch peron per houehold.... (e) Sample houehold: mean a houehold conaining a lea one ample peron. A ample houehold hall be included in EU-SILC for he collecion or compilaion of deailed informaion here i conain a lea one ample peron aged 6 or more.... (g) Co-reiden (non-ample peron): all curren reiden of a ample houehold oher han hoe defined above a ample peron.... (i) Age: refer o he age a he end of he income reference period. Ideally, all peron, irrepecive of age, in iniial houehold hould be folloed-up over he panel duraion. The age limi of ha been inroduced in EU-SILC regulaion merely for pracical reaon. The impac of hi limiaion i generally no imporan becaue e can expec 5
very fe children under o move o a ne addre alone, ihou being accompanied by one or more adul in heir original houehold a he ime of elecion. Hence for he preen dicuion, e ill conider a ample peron all individual in he iniial houehold, irrepecive of age, and aume ha all hee are uppoed o be folloed-up o heir ne addre if hey move. The fe cae here he lighly rericive rule adoped in EU-SILC do no require a follo-up can imply be reaed a non-reponden. The above applie o he normal iuaion in urvey counrie here all adul in he houehold are uppoed o be folloed-up. Addiional problem can arie in regier counrie here only one adul per houehold i eleced for follo-up. We commen on hi in he concluding Secion 7... Overvie of he ample eighing procedure.. The imporance of eighing ample daa A noed by Kih (99), hy, hen and ho o eigh are among he fundamenal and mo common queion in eimaion and analyi uing ample urvey daa. The aner o hee queion may depend on he conex, he daa ource and he ype of daa and analyi involved. Someime here are harp argumen a o heher or no i i appropriae or neceary o eigh a all. In he cae of an inenive and complex urvey of limied ize, uch a a houehold panel like EU-SILC, e believe ha he aner o he queion i quie clear: in mo iuaion i i boh neceary and ueful o eigh he ample daa o compenae for imperfecion of he achieved ample. Firly, eighing i inroduced o compenae for difference in ampling probabiliie. Such eighing i eenial if hoe difference are large. Anoher imporan reaon making eighing neceary i he high rae of non-repone and ariion over ime in panel urvey. Non-repone and ariion i ofen no only large bu alo elecive, uch a being higher for houehold a he exreme end of he income diribuion. Furher improvemen in he repreenaivene of he ample can be made hrough i calibraion again more reliable exernal informaion uch a age-ex compoiion and geographical diribuion of he populaion, and he diribuion of houehold by ype and ize. Such calibraion can reduce biae in he ample due o non-repone, non-coverage and oher diorion, and alo reduce variance. In he EU conex a lea, a grea deal of exernal informaion i available in mo counrie for calibraion of he ample. In houehold panel urvey, o addiional facor make he eighing procedure complex: one, he urvey deal ih uni of differen ype (houehold, all member, adul); and o, boh cro-ecional and longiudinal componen are involved, each ih i on eighing requiremen. In all iuaion, he legiimae obecive of eighing he ample daa i o reduce he reuling mean-quare-error of he eimae from he urvey. In pecial iuaion (uch a opimal allocaion and calibraion) eigh are inroduced o reduce variance. Hoever, in mo iuaion he inroducion of unequal eigh end o inflae variance, and he purpoe of eighing i o reduce biae in he eimaion. Compromie i ofen required o balance hee effec and conrol he mean-quare-error. Even a mall number of exreme value, in paricular a he upper end of he eigh diribuion, can inflae he variance ignificanly. In recommending he raher complex eighing procedure for houehold panel in hi paper, e mu emphaie he imporance of checking for exreme value or large variaion being inroduced in he eigh. Alernaive procedure have been uggeed o limi he range of eigh value encounered, uch a hrinkage of eigh (Spencer and Cohen, 99). In our experience, he rimming of exreme value i ofen he imple. 6
.. Iniial and follo-up eigh in a houehold panel There are o broad apec of he eighing procedure in a houehold panel: iniial eighing a he ime of inroducion of he panel uni ino he urvey; and modificaion of he ample and of he iniial eigh in he folloing period. Iniial eigh Irrepecive of he deail of he deign, any panel inroduced ino he urvey begin ih a ample of houehold, and hence alo of peron ho are member of hoe houehold. We aume ha by deign, hee ample are probabiliy ample. We erm eigh aigned o he achieved ample a i fir appear in he urvey a he iniial eigh. Thee ill be dicued in more deail in Secion. The procedure for conrucing he iniial eigh are in fac he ame a hoe ued for all ype of urvey, including purely cro-ecional urvey. The developmen of iniial eigh i generally performed in age: hree or four age may be involved, poibly ome of hem involving muliple ep. Some ueful reference in he lieraure include Kih (99), Kalon and Kaprzyk (986), Lile (986), and, for deailed applicaion o ECHP, Verma and Clemenceau (996). Follo-up ample and eighing The iniial ample provide he e of individual, called ample peron, ho are folloed-up over duraion of he panel. The ample need o be modified o reflec change in he arge populaion over ime. A lea hree ype of adumen are involved. The fir concern change in he arge populaion in privae houehold: individual leaving he populaion due o deah or ou-migraion, and ne peron oining he populaion hrough birh or in-migraion. Unle upplemenary ample of ne enran ino he populaion are added, he panel canno reflec in-migraion fully. The econd arie from non-repone and oher loe in he ample. The eigh of uni remaining in he ample need adumen in order o reduce he impac of non-repone on ample repreenaivene. The hird ource of change in he ample i he enrance of non-ample peron ino he houehold included in he ample. Many houehold panel urvey, including EU-SILC, collec a grea deal of informaion on hee non-ample member or cohabian, hile hey are living ih ome ample peron, in order o meaure he circumance (uch a income) of he hole houehold. I i deirable (efficien) o exploi he informaion a he individual level colleced for hee cohabian. Appropriae eighing cheme are required for heir incorporaion ino he ample, hich of coure mu coninue o reflec he correponding arge populaion. The bai of hee procedure i provided by he eigh hare mehod expounded by Ern (989). Some oher ueful reference in he lieraure include Lavallée (995), Kalon and Brick (995), Lavallée and Caron (00), Deville and Lavallée (006), and, in he pecific conex of ECHP, Verma and Clemenceau (996)... Srucure of he eighing procedure; noaion In hi ecion, e provide an overvie of he propoed eighing procedure. Anoher imporan obecive i o inroduce he noaion e ue hroughou. Conider he roaional rucure repreened in Figure. A a given ime, he oal ample i made up of a number of panel. The folloing noaion ill be ued for panel-pecific eigh (): here he idenifier of he eigh are a follo (U,X) refer o he year he panel a eleced; alernaively, i may be a more convenien o idenify he panel by i curren age (T). T, refer o he panel age in general. 7
U X idenifie differen ype of uni: H (houehold); R (all houehold member); P (all member aged 6+); S (here relevan, he eleced reponden); and Q (children or oher populaion ubample of inere). idenifie he ype of eigh a ave (D, N, F, I, ee belo). Thereafer e deal ih bae eigh X B. i a paricular uni (houehold or peron). I i underood ha () belong o (U) ample idenified in he ame ay a :. When cerain idenifier are nor needed, hey are dropped for impliciy. For inance, mo commonly e deal ih bae eigh (X B) of individual peron (U R), for any unpecified uni (), o ha he eigh can be idenified a and he correponding ample a. When he only needed reference i o, e ill employ he implified and commonly ued noaion and, repecively for he eigh and he ample. A longiudinal ample,, i defined a he e of individual () ho have been enumeraed in he urvey hroughou he period o incluive:... ; () hen convenien, e ue implified noaion correponding o, namely. Iniial and bae eigh A decribed in Secion, he final ave eigh are conruced involving a ep-byep procedure defining: D, deign eigh, in invere proporion o he uni elecion probabiliy; N, he above eigh modified o reflec non-repone a ave ; F, he reuling eigh calibraed o fi cerain pecified conrol diribuion; I, rimming and caling of he above, giving he iniial ave eigh. For individual remaining in he ample during ubequen period >, e define a equence of bae eigh (B), hich ake ino accoun ariion of he panel. To ar ih, he bae eigh i defined o be idenical o he ave iniial eigh: (U,B) (U,I). () Cro-ecional and longiudinal eigh for he full ample The panel-pecific eigh () are inermediae quaniie. Thee are pu ogeher o conruc eigh (v) for he full ample compried of differen panel. Weigh v are of differen ype (C, L, L, L; ee Figure ) and repreen he acual eigh variable ued in analyi. We indicae hee a: (U) X v. Firly, for cro-ecional eigh (X C), for reference year, e have: (U) C v, defined for he full cro-ecional ample, i.e. all uni in he urvey a year : S. C 8
Figure. The annual cro-ecional and hree longiudinal ample - () - () S L - () S L. () S L S C Survey ear - - - Panel: duraion a Panel: year eleced I can be een ha each year, reul for hree ne longiudinal ample of differen duraion, and year become available. We idenify he correponding eigh, repecively, X L, L and L. The coniuen ample, S, o hich hee apply are: L ) ( ) ( ) ( ) ( ) ( S, () L ) ( ) ( ) ( S, () L ) ( S. (5) The quaniy ha been defined in (). Noe ha generally here i a large overlap in erm of uni and daa among he longiudinal ample and, in an inegraed roaional deign, alo ih he cro-ecional ample. Neverhele, each ample ) S S, S, S, ( L L L C S, ih correponding X (C, L, L, L), ha i on diinc e of eigh. Furhermore, in general, he e of eigh differ by he ype of uni U (H, R, P, S, Q). 9
. Iniial eigh.. A ep-by-ep procedure We begin from he conrucion of iniial eigh given o houehold and peron a hey fir ener he urvey. Throughou, e conider one panel a a ime. Thi eighing procedure i of coure he ame a ha in any comparable cro-ecional urvey, bu e aim a bringing ou ome imporan heoreical and pracical poin and make ome recommendaion. In developing he eigh, he be poible ue ha o be made of he informaion available, boh inernal o he ample and from exernal ource. Thi include informaion on: (i) coverage and elecion probabiliie; (ii) characeriic and circumance of non-reponding uni; (iii) he rucure and characeriic of he arge populaion. Such informaion can be ued in a yemaic manner o apply eigh in a ep-by-ep procedure. We may idenify he folloing four ep: Deign eigh. Each houehold and peron in he ample i eighed in invere proporion o i probabiliy of elecion. Non-repone eigh. Thee are inroduced o reduce he impac of non-repone on he rucure and characeriic of he achieved ample. Thee eigh are derived on he bai of iem of informaion hich are available for boh reponding and non-reponding uni. Calibraion eigh. Thi refer o he adumen of he diribuion of he eighed ample according o variou characeriic o agree ih more reliable informaion on hoe diribuion available from ource exernal o he urvey. In a houehold urvey, diribuion boh in erm of houehold and peron may be involved. Trimming and caling. Thi refer o adumen made o avoid exreme value in he diribuion of eigh. The obecive i o avoid large increae in variance hich reul from he preence of exreme eigh, even hough uch adumen may inroduce ome bia. For many purpoe, only he relaive value of eigh are relevan, and heir overall caling i immaerial. Hoever, an appropriae caling of hee quaniie i uually neceary for clariy and convenience. Some baic feaure of he eighing procedure decribed belo may be noed: The eigh are applied in a equence. Tha i, a any ep afer he fir, he eigh are compued from ample value already eighed according o he reul of all preceding ep. Thu eighing for non-repone i deermined from he ample reul eighed by he deign eigh. Thi implifie he compuaion, and ho more clearly he conribuion of each ep in aduing he eigh. In a houehold panel urvey, ypically he daa are ued imulaneouly for analyi a he houehold and he peronal level. I i deirable, herefore, o ue a eighing procedure hich enure coniency beeen analye involving he o ype of uni. The recommended procedure i inegraive eighing a ave, hich enure a uniform eigh for all member of a houehold, he ame a he eigh of he houehold. The pecific variable involved a each ep and he ource of he daa ued may vary from one urvey o anoher. Neverhele, cerain variable can be expeced o be imporan in mo circumance, uch a geographic locaion of he houehold, houehold ize and compoiion, and diribuion of he populaion by age, ex and oher baic characeriic. I i poible in principle o combine more han one ep ino a ingle procedure. Hoever, i i deirable ha each ep i eparaely implemened, here poible. 0
The final eigh of a uni i he produc of he eighing facor deermined a each ep. The reuling eigh a each ep may be appropriaely caled, uch a o average.0 per ample uni... Deign eigh Deign eigh of a uni i inverely proporional o i probabiliy of elecion ino he ample, hough alloance can omeime be made for knon excluion or under-coverage of par of he udy populaion. In a panel urvey, he deign eigh are defined only a ave, hen he uni i eleced ino he ample. The uni, or derivaion from i, a ubequen ave may be conidered ubec o indirec ampling (Deville and Lavallée, 006), bu in he preen cae he concep of bae eigh decribed in he nex ecion provide a clearer and impler alernaive. There are eenially o ay of elecing he ample for a houehold panel. The fir i o elec houehold - or addree, delling or oher rucure hich conain houehold - direcly from appropriae li. The procedure direcly give he probabiliy of elecion of he houehold (P h ). In he noaion inroduced in Secion., he houehold deign eigh i: ( H,D) h k Ph, here k i an arbirary caling facor o be choen. In o far a all peron in he houehold are auomaically aken ino he ample once he houehold i eleced, he member elecion probabiliie and hence eigh are idenical o hoe of heir houehold. The above equaliy applie alo o any ubpopulaion in he houehold, uch a peron aged 6+ (P), or children (Q): ( P,D) ( Q,D ) ( R,D) ( H,D) h h h h. (6) In iuaion here one adul in he houehold i eleced a he reponden for a peronal inervie, e have he elecion probabiliy and eigh of eleced reponden (S) a: ( S,D) ( H,D) P h Ph n h ; h h. n h, (7) here n h i he number of houehold member eligible o be a eleced reponden. The oher ay of obaining a ample of houehold i o fir elec a ample of individual meeing cerain pecified crieria, and hen conruc a houehold around each uch eleced individual. A houehold i eleced hrough i aociaion ih one or more uch individual. Normally, he laer are eleced from a li of adul. In o far a each eligible houehold conain a lea one uch peron in he li, he houehold receive a non-zero probabiliy of elecion. The populaion of houehold no conaining uch a peron ill no be covered in he urvey. The probabiliy of elecion of a houehold (P h ) relae o ha of he individual (P ) hrough hich i could have been eleced a: P. Concerning eigh e have: h P h ( S,D) k P, ( H,D) k. h P h The peron eigh (R) of houehold member are idenical o hi houehold eigh, a in equaion (6). Uually, peron eligible for elecion ihin a houehold all have he ame probabiliy of elecion, o ha: P n hp, giving: h
.. Non-repone adumen ( H,D) ( S, D). (8). n h In a panel, he large lo of he ample due o non-repone generally occur a he fir ave hen he houehold i inroduced ino he urvey. Good, efficien procedure o re-eigh he reponding cae i, herefore, a criical requiremen a ave. Hoever, he poibiliie are ofen conrained by lack of informaion: non-repone adumen ha o be baed on characeriic hich are knon for boh reponding and non-reponding houehold. Here he concern i ih non-repone a he age of he houehold inervie, hich obain informaion a he houehold level and enumerae he populaion in he houehold. The procedure involve eimaing repone rae or propeniie o repone a funcion of characeriic available for boh reponding and non-reponding houehold, including characeriic of he area here he houehold i locaed. Thi i alo rue hen a ample of eleced reponden ha been ued, excep ha peronal characeriic of he eleced individual are alo ueful a deerminan. There are o commonly ued procedure for non-repone eighing. Weighing ihin clae The fir i o modify he deign eigh by a facor inverely proporional o he repone rae ihin each eighing cla: (H,N) (H,D) R K K., (9) R here R K i he repone rae in eighing cla K, and R heir average (hi i u a conan inroduced for convenience). The repone rae hould be compued ih daa eighed by he deign eigh: (H,D) R K Kr K (H,D) here he e K r repreen he reponding uni in he cla, and K he eleced uni in he ame cla. By cla e mean an appropriaely deermined grouping of uni. I i common o ue ampling raa or oher geographical pariion a eighing clae. Numerou, very mall eighing clae can reul in large variaion in R K value, and hould be avoided. On he oher and, if only a fe broad clae are ued, lile variaion in he repone rae acro he ample may be capured making he hole re-eighing proce ineffecive. On pracical ground, clae of average ize 00-00 uni may be recommended. Weighing according o repone propeniie An alernaive i o ue a regreion-baed approach. When many auxiliary variable are available, hi approach i preferable o he previou one. Uing an appropriae model uch a logi regreion, repone propeniie can be eimaed a a funcion of auxiliary variable (X) hich are available for boh reponding and non-reponding cae: R h Pr( rh X h ), here r h i a (0,) repone indicaor, equal o if houehold h ha been uccefully enumeraed; X h i an appropriae e of auxiliary variable relaed o he houehold repone propeniy, and R h i ha propeniy prediced uing regreion., K
The eighing of each reponding uni i adued by he invere of he eimaed repone propeniy, in he ame ay a by he invere of repone rae in he previou mehod (Lile, 986). A very imporan poin hen uing he regreion approach i o enure ha eigh aigned are confined o be ihin reaonable limi. The regreion can predic zero or even negaive value, hich of coure mu be reeced. The problem i more general han ha: exreme value hould no be permied. I i for hi reaon ha i i very imporan o check he diribuion of he reuling eigh adumen, and apply rimming or imilar procedure o remove exreme value. Thi i dicued furher in Secion.5 belo. Non-repone affec he enumeraion of houehold and of all houehold member in exacly he ame ay. Hence he non-repone adumen o eigh reain he baic equaliy in equaion (6). Some pracical apec Generally i i ueful o apply he adumen in o ep: (i) for non-conac (of houehold and/or of eleced individual); and (ii) for non-repone, once a conac ih he houehold or he peron concerned ha been made. For boh ep, epecially for (i), area-level characeriic provide a main par of he auxiliary variable explaining non-repone. Thi i becaue hey are more eaily available for boh reponding and non-reponding uni. In dealing ih he effec of non-repone, i i of crucial imporance o correcly diinguih beeen non-eligible and non-reponding uni. In fac, eleced uni hich urn ou o be non-eligible or non-exien mu be excluded and no couned a non-reponden. Someime, impuaion ha o be made for uni ih unknon eligibiliy-repone au, i.e. hen i i no clear heher hey are non-eligible or non-reponden. For hi purpoe i i ueful o diinguih he folloing caegorie:. Houehold ha are ou-of-cope: all individual in hee houehold are, of coure, alo ou-of-cope.. Houehold ha are uccefully conaced and enumeraed. Thee conain peron ha are:.a in cope;.b ou-of-cope;.c peron for hom e do no kno heher or no hey are in-cope.. Houehold ha are knon o be in-cope, bu are non-reponden. Thee houehold may conain peron ho are acually ou-of-cope, bu hi informaion i no available.. Houehold ha are no conaced, and he eligibiliy au of he hole houehold i no knon. In order o impue a definie au for an individual in (.c) or (), e may aume ha he propeniy o be in-cope for hee peron can be deermined on he bai of he combined group (.a+.b), conrolling for appropriae auxiliary variable. A logi regreion model ih appropriae conrol variable may be ued. Hoever, a impler approach for inance aigning individual in (.c) and () an eligibiliy au ih probabiliy equal o he proporion in ha au in group (.a+.b), ould uffice if he incidence of miing informaion i mall. Peron in group () are more likely o be ou-of-cope han group () or () alone. I eem reaonable o aume ha he au for group () can be impued on he bai of group ()-() combined. A regreion or a imple approach on he ame line a above may be ued. Some urvey allo ubiuion of non-reponding uni ih ne uni (depie he general undeirabiliy of hi pracice). In uch cae, non-reponding original uni for hich ucceful ubiuion have been made are o be conidered a reponding uni in he compuaion of repone rae for he purpoe of deermining non-repone eigh.
.. Calibraion o exernal daa ource Calibraion i carried ou in an aemp o enure ha eighed ample um of pecified conrol variable or caegorie equal o he knon populaion oal for hoe variable. In o far a he fir ave of a panel like EU-SILC i ubec o high rae of non-repone and poibly alo o random and yemaic diorion of he ample, e conider calibraion o be paricularly imporan in he fir ave. Once he iniial ample ha been o adued, recalibraion a ubequen ave may be done more elecively. A robu and convenien mehod of aduing he eighed ample diribuion o a number of exernal conrol imulaneouly i he claical ieraive proporional fiing or raking (Deming, 9). Uing pecial algorihm uch a hoe implemened in he INSEE program CALMAR, upper and loer bound can be impoed on he eigh adumen during calibraion. (The limi, hoever, canno be made oo narro a he ieraive procedure involved become lo in converging, and may fail o converge alogeher beyond a cerain limi.) Deville and Särndal (99) develop a family of calibraion eimaor of hich he andard general regreion eimaor (GREG) i a fir approximaion. A problem ih GREG and imilar procedure i ha hey can yield negaive eigh, hich of coure doe no make ene. In our experience he claical raking procedure, ih imple rimming of any eigh value ouide deirable limi, coninue o provide a pracical and accepable approach in many iuaion. (Concerning rimming, ee Secion.5 belo). Boh houehold and peron-level conrol variable are ueful in calibraion. Ueful variable end o be imilar o hoe ued for non-repone adumen, auming availabiliy: geographical locaion, enure au, houehold ype and ize, age-ex compoiion of he populaion, ec. In ome iuaion, addiional variable may be available. Hoever, he crucial requiremen in calibraion i o enure ha he exernal conrol variable are ricly comparable o he correponding urvey variable, he diribuion of hich i being adued. I i deirable ha a ave, all peron in he ame houehold receive he ame eigh, o ha he eigh given o each member i he ame a he eigh of he houehold, a in equaion (6). Such uniform ihin-houehold eighing can be reained, even hen he exernal conrol in he calibraion are a boh he houehold and he peronal level, by pecial echnique knon a inegraive calibraion. 5.5. Trimming and caling Trimming I i imporan o enure ha no ep in he eighing procedure reul in exreme value of he eigh. More preciely, ha i required i o enure ha large variaion in he eigh value i no inroduced a a reul of he adumen. Thi i becaue ha variaion inflae variance of he eimae from he urvey (Kih, 99). In fac, conrol of exreme value and large variaion in eigh i deirable a each age of aduing he eigh - afer nonrepone adumen, and hen again afer calibraion. A common approach, a indicaed earlier, i o rim exreme value. 6 Hoever, here i no rigorou procedure for general ue for deermining he limi for rimming. While more ophiicaed approache are poible, i i deirable o have a imple and pracical approach. Such an approach may be quie adequae for he purpoe, a lea in iuaion here he main problem i caued by a limied number of exreme value aigned during he adumen proce. 5 The procedure i decribed in, for inance, CALMAR documenaion from INSEE (documen no. F90, November 99). See alo a brief decripion in Verma and Clemenceau (996), Secion 5. 6 For a more echnical dicuion of he iue, ee Poer (988, 990).
Afer calculaion of non-repone eigh, e have recommended and ued he folloing imple procedure: any compued non-repone eigh ouide he folloing limi are recoded o he boundary of hee limi: ( H,N) ( H,D) h h ( ) ( ) L H,N H,D, (0) L (H,D) (H,N) here, are repecively he mean value of houehold deign and non-repone eigh, and L i ome appropriae upper bound for he adumen in eigh. L could be a reaonable value for hi parameer. 7 Afer calibraion, e can follo he ame form of check and correcion for exreme value: L ( H,F) ( H,D) h h ( ) ( ) L H,F H,D, () here each quaniy i divided by i mean, o a o appropriaely cale he eigh value being compared. Noe ha in boh (0) and (), he limi impoed are in erm of he raio of he adued o he original deign eigh, i.e. he facor by hich he deign eigh are being modified. Any rimming or imilar adumen can be applied idenically o houehold and peron level eigh, reaining he equaliy (6) for he rimmed eigh, for inance: (R,F) (H,F) h h. Scaling A ill be noed in Secion 5 and 6, he final longiudinal and cro-ecional eigh acually ued in daa analyi may be caled uch ha heir um i proporional o he ize of he arge populaion. Such caling allo daa from differen counrie and urvey o be pu ogeher for combined analyi ihou furher adumen o he eigh (Verma, 999). Hoever, a he preen age of he eighing procedure, e are conidering one ou of a number of panel hich coniue he oal ample a any given ime. Thee panel are o be ubequenly pu ogeher o coniue he full ample. Unlike he previou cae, hi i no an aggregaion over differen populaion, bu of ample repreening he ame populaion. In uch aggregaion, i i appropriae ha each ample conribue inverely proporional o i variance, i.e., approximaely in direc proporion o i ample ize. Hence he eigh hould be caled uch ha heir um i proporional o he ample ize of he panel concerned hich i obained mo imply by caling he eigh o average.0 per uni. Such caling allo daa from differen panel o be pu ogeher o conruc he oal ample ihou furher adumen o he eigh. Finally, e noe ha i i deirable o reain equaliy of he ype in equaion (6) alo for he final recaled eigh for houehold and peron. To be precie, e need o chooe heher o deermine he required caling facor ih reference o he houehold or he peron level ample. The laer i more appropriae in o far a he individual peron i he more commonly ued uni of analyi, a i he cae for inance in he analyi of income diribuion and povery. Hence e define he required re-caling facor a: n R F n, R R (R,F) here n R i he number of individual enumeraed in houehold of he panel ample a ave. The recaled iniial eigh are: 7 Since rimming aler he mean value of he eigh, he above adumen may be applied ieraively, ih he mean re-deermined afer each cycle. A very mall number of cycle hould uffice normally. 5
(R,I) (R,F) (H,I) (H,F).FR, h h. FR, o ha he folloing equaliy i mainained: (R,I) (H,I) h h. () I i no neceary o define hee quaniie for oher ubpopulaion (P, Q, S) a hi age, bu hee can be aken imply a: (P,I) (Q,I) (R,I), () (R,I) (S,I) (S,D). (R,D), (5) ha i, for all he differen ype of uni, he ame modificaion (he fir facor in he la equaion) i applied o he original deign eigh.. Bae eigh.. Longiudinal populaion and longiudinal ample In he folloing e conider a panel eleced freh a ime from populaion P, and hen enumeraed for a oal of T (ay ), ave, o T. In hi ecion e are primarily concerned ih bae eigh (B) of he oal populaion of peron (R) and for convenience ill ue he folloing implified noaion unle required oherie (ee Secion.): (R,B),, here, he longiudinal ample of peron from ime o. We define he bae eigh a ave a being idenical o he iniial eigh defined in he previou ecion: (R,B) (R,I). From Secion, hee eigh have been deermined a ave uch ha ample ih eigh repreen populaion P, hich e rie a (, ) P. Bae eigh are defined for peron bu no for houehold. According o he folloing procedure, member of he ame houehold may have differen eigh afer ave. By longiudinal populaion in he inerval and i mean all peron ho have remained in he arge populaion hroughou he period o, incluive. Le P be he longiudinal populaion in he inerval o. I comprie peron ho ere in he arge ( L) populaion a ave, and have remained in he populaion up o and including ime. P differ from P by peron (ay OUT ) ho have lef he populaion beeen year and : ( L) P P OUT. Thi may for inance be due o deah, migraion ou of he counry or ( L) movemen o an iniuion. Similarly, P differ from P by peron ho have lef beeen ime and ( OUT ) or beeen ime and ( OUT ): ( L) P OUT P (OUT OUT ). In general, P ( L) T P P + T OUT. The longiudinal populaion ( L) P differ from he acual (cro-ecional) populaion P a, a he former doe no include peron ho are born or have migraed ino he arge populaion ince ime, and have remained in ha populaion ince ha ime. 6
Longiudinal ample ) (L i defined a individual ho have been member of an enumeraed houehold hroughou he period o incluive. (The peron i no necearily a member of he ame houehold hroughou hi period). ( L) differ from by peron in he original ample ho lef he populaion beeen year and ( ou ), and by peron ill in he populaion (x ) hoe houehold a enumeraed a bu no a : ( L) (ou + x ). We aume ha ( ou, ) i a repreenaive ample of OUT ; conequenly: ( L) (L ( + x ), P OUT. (6) [ ] ( ) ) P.. The evoluion of bae eigh aring ih ave We aume ha all peron enumeraed a ave are eligible for follo-up o he nex ave. Thoe no uccefully folloed-up are conidered non-reponden (unle re-claified a ou-of-cope a he laer ime). 8 The obecive i o deermine ne bae eigh,, a, uch ha: ( L) (L x, P OUT P ) [( ) ] ( ) +, i ranformed ih he ne eigh o: ( L) (, ) ( P OUT ) P. (7) In order o deermine bae eigh from knon, e ue he folloing procedure. ( L) Conider he e ( ou ) of peron enumeraed a (-) ho are ill in-cope a. For each peron () in hi e, e can define a binary variable: ( L) r if he peron i in, i.e. i uccefully enumeraed a, r 0 oherie, i.e. he peron i no uccefully enumeraed a. Uing a logi model, for inance, e can deermine he repone propeniy R of each peron in he above e a a funcion of a vecor of auxiliary variable X : R Pr(r X ). ( L) For any peron () in (i.e., ih r ) he required eigh i. R In diincion from non-repone adumen a ave (Secion.), he e of auxiliary variable (X) can be rich in conen becaue of he informaion available on he non-enumeraed peron from preceding ave. In o far a mo non-repone occur a he houehold (raher han he peronal) level, a maoriy of he relevan auxiliary variable (X) ill be geographical and houehold level variable (region, houehold ize and ype, enure), including conruced variable uch a houehold income and houehold ork au. Many peron-level variable are alo likely o be ueful (gender, age, employmen au) he or of variable correlaed ih peron moving o a ne addre, eing up a ne houehold, remaining raceable, ec. R by definiion. I i neceary o enure ha no negaive, zero, or indeed very mall value of R are alloed. A before, he folloing pracical rimming limi i uggeed: 8 The folloing applie concerning EU-SILC. There are cerain (mall) caegorie of houehold and individual, hich, according o EU-SILC rule, are no folloed-up. Example are houehold no enumeraed a ave or a o conecuive ave hereafer, or even no enumeraed a a ingle ave for ome pecified reaon. Alo, peron belo a cerain age (under, or under 6 in ome counrie) are no folloed up if hey move alone, i.e. ihou being accompanied by an adul ample peron. For he preen purpoe, all hee caegorie are reaed a non-reponden even if hee have no been recorded a uch in he urvey becaue of he paricular racing rule. 7
L (R,B) (R,B) { } (R,D) (R,D) { } L, ih L, for inance. Here each quaniy i divided by i mean, and (R,D) refer o he individual original deign eigh... Deermining eligibiliy and repone au of uni Applicaion of he above procedure require ha for each peron enumeraed a (-), he peron eligibiliy and repone au a i knon. Thi mean ha i i poible o claify each peron in ino one of he folloing caegorie uniquely: he peron () i enumeraed a (i.e., i in e ); () remain in he populaion, bu i no enumeraed a (i in e x ); () ha moved ou of he populaion (i in e ou ). In pracice, for a proporion of non-enumeraed peron, informaion i no available o deermine heher hey belong o caegory () or o caegory (). Each uch peron ha o be aigned o one or he oher of hee o group on he bai of ome appropriae model. The procedure i imilar o ha in Secion. for ave, bu generally impler becaue feer ambiguou caegorie are involved... Bae eigh for oher caegorie of peron In he above, bae eigh have been defined only for he longiudinal ample aring from ave, i.e., for all individual enumeraed in he urvey hroughou he inerval o :..., ih. (8) There are o mall addiional caegorie of peron ho can be aigned non-zero bae eigh on he bai of he bae eigh of hee longiudinal individual in he ame houehold, ihou affecing he eigh of he laer. Thee are: (i) Children born o ample omen. They receive he eigh of he moher. (ii) Peron moving ino ample houehold from ouide he urvey populaion. They receive he average of bae eigh of exiing ample member in he houehold, including (i). 9 A any ime, he ample houehold include addiional caegorie of member ho have o far been aigned zero eigh. The main group among hee are he co-reiden, defined a peron moving ino a ample houehold from anoher non-ample houehold in he populaion. Thee are given zero bae eigh. The ame applie o children born o non-ample omen. In order o conruc longiudinal and cro-ecional eigh decribed in he folloing ecion (hich are he acual arge variable of inere), procedure are required o aign nonzero eigh o ome or all of he zero-eighed peron, o ha hey can be included in analyi of he urvey daa. 5. Longiudinal eigh 5.. Se of ample requiring longiudinal eigh Conider he ample daa becoming available afer urvey reference year in Figure. The oal ample i made up four panel, eleced in year (mo recen), (-), (-) and (- ). For convenience, e ill alo idenify hee by reference o heir curren duraion in year, repecively a (), (), () and (). 9 In deermining he repone propeniie from one ave o he nex a decribed in Secion., hee addiional caegorie can be included in he ample bae being folloed-up. 8
Wih he excepion of he mo recenly inroduced panel (), he oher hree panel conribue o nely available longiudinal daa e. A decribed in Secion., by puing ogeher hee panel e obain hree longiudinal daa e ( L S, LS, LS), repecively of duraion, and year. 0 In erm of panel ()-(), he compoiion of hee ample i a follo. Differen ype of panel egmen are involved: - Panel aring from heir ime of elecion ( ): A: a -year longiudinal ample of panel (), covering year (-) o ; A: a -year longiudinal ample of panel (), covering year (-) o ; A: a -year longiudinal ample of panel (), covering year (-) o. - Panel hich are included from a laer ime ( >): B: a -year longiudinal ample from panel (), covering year (-) o ; B: a -year longiudinal ample from panel (), covering year (-) o ; C: a -year longiudinal ample from panel (), covering year (-) o. The concerned longiudinal daa e becoming available a are (ee equaion ()-(5) in Secion.): L S A + B + C; L S A + B; L S A; ih A ; imilarly A, A ; B ; B ; C. 5.. Longiudinal eigh a diinc from bae eigh The longiudinal eigh dicued in hi ecion are he acual eigh ued in longiudinal analyi baed on he oal available longiudinal ample. For a period 0 o, 0 <, hee are defined for all uni (from all he available panel) ho have been enumeraed in he urvey hroughou hi period. A noed earlier, bae eigh are for he longiudinal ample of each panel, aring from ime hen he panel i fir inroduced ino he urvey. In he pecial cae of 0, here i eenially no difference beeen hee bae and he required longiudinal eigh, excep ha he former are defined for each panel hile differen panel need o be pu ogeher for he laer. Wih 0 >, he longiudinal ample over he period 0 o include cerain addiional caegorie of individual no preen in he longiudinal ample of original ample peron over he full period o, o hich non-zero eigh have o be aigned. The difference from cae (i)-(ii) of Secion. i ha aigning non-zero eigh o hee addiional caegorie ill require aduing he eigh of oher member in he ample. The addiional caegorie include: (iii) longiudinal co-reiden, enering he houehold a or before 0 and remaining a houehold member over he period ( 0 o ); 0 There are alo oher equence of longiudinal daa embedded in he daa e hon in he diagram: a -year longiudinal ample from (-) o (-) in panel (); and hree -year ample, coniing of (-)+(-) and (- )+(-) in panel (), and (-)+(-) in panel (). Thee panel correpond o daa hich have been produced in previou year. 9