Latent Variable Mixture Modelling of Treated Drug Misuse in Ireland


 Spencer Burns
 3 years ago
 Views:
Transcription
1 Metodološk zvezk, Vol. 1, No. 1, 2004, Latent Varable Mxture Modellng of Treated Drug Msuse n Ireland Paul Cahll and Brendan Buntng 1 Abstract Ths study provdes analyses and profles of llegal drug usage n the Republc of Ireland. Two questons are addressed: a) can ndvduals be grouped nto homogeneous classes based upon ther type of drug consumpton, and b) how do these classes dffer n terms of other key background varables? The data reported n ths study s from the Natonal Drug Treatment Reportng System database n the Republc of Ireland. All analyses were carred out n collaboraton wth the Drug Msuse Research Dvson (the Irsh REITOX / EMCDDA focal pont). Ths database contans nformaton on all 6994 ndvduals who receved treatment for drug problems n the Republc of Ireland durng The analyss was conducted n four steps. Frst, a sngle class model was examned n order to establsh the respectve probablty assocated wth each drug type. Second, a seres of uncondtonal latent class models was examned. Ths was done to establsh the optmal number of latent classes requred to descrbe the data, and to establsh the relatve sze of each latent class. From ths analyss the condtonal probabltes for each ndvdual, wthn a gven class, were examned for typcal profles. Thrd, a seres of condtonal models was then examned n terms of key predctors (age and early school leavers). Ths analyss was conducted usng MPlus In the fnal stage of the research, the parameter estmates obtaned from the multnomal logstc regresson model (that was prevously used to express the probablty of an ndvdual beng n a gven latent class, condtonal on a seres of covarates) were graphcally modelled wthn EXCEL and the respectve functons descrbed. The results from ths analyss wll be descrbed n terms of a) the proflng of typcal serous drug msuse n Ireland, b) the clusterng of drug types and, c) the respectve mportance of key background varables. The varous profles obtaned are dscussed n terms of health care strateges n Ireland. 1 School of Psychology, Unversty of Ulster at Magee Campus, Northern Ireland; Ths research has been awarded a Health Servces Research fellowshp and s beng carred out n collaboraton wth the Drug Msuse Research Dvson, Health Research Board, Dubln, Ireland.
2 214 Paul Cahll and Brendan Buntng 1 Introducton The constant battle between the competng needs of healthcare and socal resources necessary for effectve drug treatment has been apparent for the last three decades. These resources are not only fnancal: people, facltes, expertse and even tme are all fnte, and the most effcent use of them needs to be found wthn the drugtreatment servces. The underlyng constructs of drug msuse and ts characterstcs can only be nvestgated ndrectly usng observable measures and ndcators. Latent varable mxture modellng allows for unobserved heterogenety n the sample (Muthén and Muthén, 2003) where dfferent ndvduals can be seen to belong to dfferent subpopulatons, and can uncover some of the unque characterstcs of ths hdden and vulnerable populaton. Over the last three decades large scale evaluaton studes Drug Abuse Reportng Program (DARP) (Smpson and Sells, 1990), and the Natonal Treatment Outcome Research Study (NTORS) (Gossop, Martn, and Stewart, 2003) have examned the effectveness of drug treatment, n both the UK and US. Despte these consderable efforts, addctontreatment researchers are stll confronted wth many of the same core questons as those of thrty years ago. These questons nclude: can ndvduals be grouped nto homogeneous classes based upon ther type of drug consumpton, and how do these classes dffer n terms of other key background varables? 2 Method 2.1 Partcpants Partcpants were 6994 ndvduals who receved treatment for problem drug use n the Republc of Ireland durng the 2000 calendar year. Data returns for the 6994 clents attendng treatment servces durng 2000 were provded by 154 treatment servces (O Bren, Kelleher, and Cahll, 2002). 2.2 Measures The Natonal Drug Treatment Reportng System (NDTRS) s an epdemologcal database on treated drug msuse n the Republc of Ireland. The reportng system was orgnally developed n lne wth the Pompdou Group s Defntve Protocol
3 Latent Varable Mxture Modellng and subsequently refned n accordance wth the Treatment Demand Indcator Protocol (European Montorng Centre for Drugs and Drug Addcton & Pompdou Group, 2000). Drug treatment data are vewed as an ndrect ndcator of drug msuse. These data are used at natonal and European levels to provde nformaton on the characterstcs of clents enterng treatment, and on patterns of drug msuse, such as types of drugs used and consumpton behavours. They are valuable from a publc health perspectve to assess needs and to plan and evaluate servces (EMCDDA, 2002: 23). The montorng role of the NDTRS s recognsed by the Irsh Government, and data collecton for the Natonal Drug Treatment Reportng System s one of the actons dentfed by the government for mplementaton by all health authortes: All treatment provders should cooperate n returnng nformaton on problem drug use to the NDTRS (Department of Toursm, Sport and Recreaton 2001: 118). 2.3 Analyses The basc premse of the latent class analyses, relevant to ths study s that the covaraton found among the observed varables s due to each observed varable s relatonshp to the latent varable (Hagenaars and McCutcheon, 2002). Fgure 1: Latent classes wth covarates. In ths study, the observed drug consumpton behavours (u) are dchotomous n nature, representng the presence or absence of the partcular drug n each
4 216 Paul Cahll and Brendan Buntng ndvdual s drug usng career. C denotes the latent classes to be determned. Once the optmal number of latent classes s calculated, the key background varables of age (contnuous) and early school leavers (dchotomous) are ntroduced. The Bayesan Informaton Crteron (BIC) together wth the Akake Informaton Crteron (AIC) were used to determne the optmal number of uncondtonal latent classes necessary to adequately ft the data. The Bayesan nformaton crteron, as proposed by Schwarz (1978), calculates the crteron for one or more ftted model obects for whch a loglkelhood value can be obtaned. 2*loglkelhood + npar*log(nobs) (1.1) where npar represents the number of parameters and nobs the number of observatons n the ftted model. BIC s a "parsmony crtera" used to perform model comparson and dscrmnaton. A seres of condtonal models was examned n terms of key predctors. Multnomal logstc regresson s an extenson of bnary logstc regresson that allows for the comparson of more than one contrast, smultaneously estmatng the log odds of a number of contrasts. Logstc regresson apples maxmum lkelhood estmaton after transformng the dependent nto a logt varable (the natural log of the odds of the dependent occurrng or not). In ths way, logstc regresson estmates the probablty of βa certan event occurrng. In the multnomal logt model t s assumed that the logodds of each response follow a lnear model. The logt model usng the baselnecategory logts wth predctors x has the form π ( x ) ' log = α + x, (2.1) π ( x ) J where β α s a constant and ' s a vector of regresson coeffcents of x, for J = 6, = 1, 2,, J1, (Agrest, 2002). Ths model s analogous to a logstc regresson model, except that the probablty dstrbuton of the response s multnomal nstead of bnomal and we have J1 equatons nstead of one. The multnomal logt model may also be wrtten n terms of the orgnal probabltes π rather than the logodds. Startng from Equaton 2.1, then π ( x ) = J 1 αβ'β ( α ) + x ' ( x ) exp 1 + exp + k = 1 k k (2.2) where x are the explanatory varables age (years) and early school leavers, and = 1, 2, 5 for each of the sx latent classes respectvely. The denomnator
5 Latent Varable Mxture Modellng remans the same for each probablty, and the numerators for all sum to the denomnator, π =. The parameters for the baselne category n the logt ( x ) 1 expressons equal to zero, therefore the model wth category J as the baselne for the demonnator (equaton 2.1), has α β= 0, (Hosmer and Lemeshow, 2000). J = J 2.4 Instruments / Psychometrc software Database preparaton and data cleanng were completed usng SPSS (11.0). There were no mssng data. MPlus 2.13 was used, and all analyses were carred out n a snglestep. MSExcel 2000 was used graphcally to llustrate the multnomal logstc regresson. 3 Results 0,8 0,7 0,6 Reponse Probabltes 0,5 0,4 0,3 0,2 0,1 0 heron cannabs benzo's ecstasy methadone cocane Drug of Msuse alcohol amphetamnes other opates hallucnogens hypnotcs volatle nhalants other drugs Fgure 2: Postve response probabltes for the thrteen drug types. Fgure 2 llustrates the respectve probabltes assocated wth each of the ten drug types among ndvduals recevng drug treatment durng The maorty of those seekng treatment (75%) reported heron as one of ther drugs of msuse. Cannabs was the next most probable drug of msuse among those seekng treatment (42%), and only one percent of those recevng treatment n 2000 reported use of volatle nhalants.
6 218 Paul Cahll and Brendan Buntng Tests of Model Ft (Informaton Crtera) Numbers of classes Akake (AIC) Bayesan (BIC) 1 Class 2 Classes 3 Classes 4 Classes 5 Classes 6 Classes 7 Classes Akake (AIC) 60177, , , , , , ,581 Bayesan (BIC) 60286, , , , , , ,303 Fgure 3: Inf. Crteron (BIC&AIC) testng model ft for seven modelsolutons. Table 1: Sx latent classes, the average class probabltes by class and the assocated probabltes of problem drug use. Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Class n = sze % = Average Class Probabltes by Class Class Class Class Class Class Class Msuse of: Probabltes of Problem Use of Drug Heron Methadone Other Opates Cocane Amphetamnes Ecstasy Hypnotcs Benzo s Hallucnogens Volatle nhalants Cannabs Alcohol Other drugs Clubbers Novces Polydrug users Methadon e msusers Benzo msusers Heron msusers
7 Latent Varable Mxture Modellng Goodness of ft The AIC and BIC ft ndces mprove as addtonal latent classes are added to the model, (for example, a threeclass soluton BIC value , entropy of 0.849, whereas the 6class soluton yelds BIC value of , wth entropy of 0.767). As the BIC ftndex plateaus there s no addtonal beneft n ncreasng the number of latent classes n the model. BIC and AIC logc dctate that the optmal model s one wth the lowest value, as s evdent from Fgure 3, the sxclass soluton was selected as the optmal model. 3.2 Latent classes Table 1 llustrates the unque characterstcs for each of the sx homogeneous latent classes, together wth the average class probabltes and anecdotal labels used to descrbe them. Class 5 s relatvely small n sze (n= 183), however ths class proves very valuable n terms of the emergng trends n drug consumpton patterns and renforces anecdotal evdence (EMCDDA, 2002). Class 1, ttled Clubbers conssts of 950 ndvduals (13.6%), charactersed by a hgh probablty of cannabs and ecstasy use (0.88 and 0.84 respectvely) wth alcohol and amphetamnes (speed) the next most probable drugs of msuse (0.39 and 0.43). The Clubbers are the class most lkely to msuse hallucnogenc drugs such as LSD or magc mushrooms (16.8) and are unlkely to use the harder drugs, such as heron and methadone (0.07 and 0.01). Class 2, enttled Novces represents 8.3% of the total sample (n=577). Indvduals n ths class have a very hgh probablty of cannabs use (0.93) and are also most lkely to msuse volatle nhalants such as glue and/or solvents (0.10). There s a low probablty of msuse of harder drugs such as amphetamnes, cocane or heron (0.02, 0.03 and 0.08). Class 3, Polydrug users (n = 1013, 14.5%) are those recevng treatment for multple drugs of msuse, n ths case three or more drugs. Ths class has a very hgh probablty of msuse of heron (0.97), wth the next most probable drug of msuse beng cannabs (0.65). Indvduals classed as Polydrug users are the most lkely to abuse cocane (0.29). The 999 ndvduals (14.3%) n class 4 have a probablty of 1.0 of msusng methadone. These ndvduals have a hgh probablty of heron use (0.86) and benzodazepnes (0.36) n combnaton wth methadone. The harder drugs domnate ths class and there s a low probablty of abuse of softer drugs (ecstasy 0.05 and amphetamnes 0.01) as well as alcohol (0.02). Class 5 s the smallest of all the classes representng 183 ndvduals (2.6%). Indvduals n ths Benzodazepne msusers class msuse
8 220 Paul Cahll and Brendan Buntng benzodazepnes, such as valum, dalmane and rohypnol (1.0). Included n ths class are ndvduals who also msuse other opates, such as codene and dstalgescs (0.40) or alcohol (0.25). Anecdotal evdence suggests the msuse of benzodazepnes as an emergng trend (EMCDDA, 2002), and thereby ths evdence from 2000 warrants close nvestgaton. Class 6 s the largest of all the latent classes wth 3272 ndvduals, representng 46.8% of the sample. Ths class, enttled Heron msusers s domnated by the abuse of heron (1.0). For members of ths class, f more than one drug was beng msused, the next most common drugs together wth heron were benzodazepnes (0.30) and cannabs (0.12). The average class probabltes ndcate the level of accurate classfcaton wthn each of the latent classes (dagonal, Table 1). The class probabltes on the offdagonal represent msclassfcatons between each of the classes, for example, the msclassfcaton between Methadone addcts (Class 4) and Clubbers (Class1) was Respondents were assgned to classes based on ther probablty of ncluson n that class; t was ths condtonal probablty score that was correlated wth covarates for the multnomal logstc regresson. In ths way, the probablty of beng ncluded n a specfc class was not constraned to be certan (1.0), as ths would have ntroduced assgnment error. 3.3 Multnomal logstc regresson Table 2: Multnomal logstc regresson equatons for the latent classes regressed on age (x) and early school leavers (y). Age α + β x, Age and Early School Leavers α + β x + β y Class 1 equaton = *(age) *(age) *(school) Class 2 equaton = * (age) *(age) *(school) Class 3 equaton = *(age) *(age) *(school) Class 4 equaton = *(age) *(age) *(school) Class 5 equaton = *(age) *(age) *(school) The estmated probabltes of class membershp for a gven age (Equaton 2.2) equal ( 0.129x ) exp π = 1 1+ exp( x ) + exp( x ) + exp( x ) + exp( x ) + exp( x )
9 Latent Varable Mxture Modellng exp( x ) π = 2 1+ exp( x ) + exp( x ) + exp( x ) + exp( x ) + exp( x ) through to 1 π = 6 1+ exp( x ) + exp( x ) + exp( x ) + exp( x ) + exp( x ) The 1 term n each of the denomnators and n the numerator of the π 6 represents exp( α + β ) usng α β = 0, where J s class 6. The sx probabltes J J J = J add to 1 as the numerators sum to the common denomnator. The Novces class domnates the younger ages and almost dsappears by the early thrtes. The probablty of membershp n the Clubbers class peaks at 20 years of age and declnes slowly through the thrtes. The Methadone and Polydrug classes reman very robust over the spectrum of ages. From the earlytwentes through to the latefortes, ndvduals recevng treatment for drug msuse are most lkely to be members of the heron addcts class. For older drug users, (40 years +), there s a sharp rse n the probablty of membershp of the Benzodazepne msuser class. Fgure 4 llustrates the multnomal logstc regresson paths for each of the classes regressed upon age (contnuous varable) graphcally modelled wthn MSExcel. 0,7 0,6 Probablty of class ncluson 0,5 0,4 0,3 0,2 0,1 'Clubbers' 'Novces' 'Polydrug users' 'Methadone msusers' 'Benzo msusers' 'Heron msusers' Age Fgure 4: Sx Latent Classes regressed on Drug Users Age. Fgure 5 llustrates the regresson paths for each of the sx latent classes regressed on drug user s age, and also regressed on those who left school before aged 15, and those who stayed n school after the age of 15 years. All the sold lnes represent those who left school early. Indvduals who stayed n school longer were more lkely to be members of the Clubbers class (recreatonal drugs use), whle the probablty of early school leavers beng n the Novces class declnes sharply n the late teens. It s also apparent that early school leavers are
10 222 Paul Cahll and Brendan Buntng more lkely to be members of the Heron class over all of the ages and less lkely to be members of the Benzodazepne msuser class n later years. It should be noted that the actual number of drug users n treatment decreases wth age and although the probablty of membershp of the Benzodazepne msusers class ncreases wth age, ths may be as a functon of a declnng proporton n the other latent classes. 0,6 Probablty of class ncluson 0,5 0,4 0,3 0,2 0,1 'Clubbers_1' 'Clubbers_2' 'Novces_1' 'Novces_2' 'Polydrug users_1' 'Polydrug users_2' 'Methadone msusers_1' 'Methadone msusers_2' 'Benzo msusers_1' 'Benzo msusers_2' 'Heron msusers_1' 'Heron msusers_2' Age Fgure 5: Sx Latent Classes regressed on Drug User s Age, and those who left school before age 15 sold lne_1) and those who stayed n school after age 15 years (broken lne_2). 4 Conclusons The current study utlsed latent varable mxture models to examne profles of drug msusers and ncorporated these methodologes for the analyss of treated drug msuse n the Republc of Ireland Usng both the Bayesan and Akake nformaton crtera (BIC and AIC) a sxclass soluton was selected as the optmal number of latent classes bestfttng the data. From the subsequent uncondtonal latent class analyses, the characterstcs of each of the classes were uncovered and each of the typcal profles was developed. The dverse drug msusng behavours of the 6994 ndvduals who receved treatment for drug msuse were structured nto sx dstnct and homogeneous classes (Clubbers n=950, Novces n=577, Polydrug users n=1013, Methadone msusers n=999, Benzodazepne msusers n=183 and Heron msusers n=3272). Gven the complex nature of problems assocated wth drug msuse, ths research hghlghted the need to avod a sngle treatment modalty for problem drug use, and showed that a range of treatment optons may need to be consdered for the unque characterstcs of each class. A seres of condtonal models was then examned n terms of the key covarates 1) age and 2) age and early school leavers. The parameter estmates
11 Latent Varable Mxture Modellng obtaned from the multnomal logstc regresson were graphcally modelled wth MSExcel and the respectve functons descrbed. Stemmng from a better understandng of the probablty of an ndvdual beng n a gven latent class dependent on age (contnuous) and early school leavers (dchotomous), nterventon strateges both reactve (health care polces) and proactve (socal and educatonal ntatves) may be more fully evaluated. References [1] Agrest, A. (2002): Categorcal Data Analyss (2 nd ed). NY: Wley and Sons. [2] Department of Toursm, Sport and Recreaton. (2001): Buldng on Experence. Natonal Drugs Strategy Dubln: The Statonery Offce. [3] EMCDDA (2002): European montorng centre on drugs and drug addcton. Annual Report on the State of the Drugs Problem n the European Unon. Luxembourg: Offce for Offcal Publcatons of the European Communtes. [4] EMCDDA and Pompdou Group (2000): Treatment Demand Indcator: Standard Protocol 2.0. Lsbon: European Montorng Centre for Drugs and Drug Addcton. [5] Gossop, M., Marsden, J., and Stewart, D. (2001): NTORS. After Fve Years. The Natonal Treatment Outcome Research Study. London: Natonal Addcton Centre. [6] Hagenaars, J.A. and McCutcheon, A.L. (Eds.) (2002): Appled Latent Class Analyss Models. UK: Cambrdge Unversty Press. [7] Hosmer, D.W. and Lemeshow, S. (2000): Appled Logstc Regresson. New York: John Wley and Sons. [8] Muthén, L. and Muthén B. (2003): MPlus short courses. Specal Topcs n Latent Varable Modellng Usng Mplus. Fulda, Germany. [9] O Bren, M., Kelleher, T., and Cahll, P. (2002): Trends n Treated Drug Msuse n Health Boards Health Research Board, Dubln. [10] Schwarz, G. (1978): Estmatng the dmensons of a model. Annals of Statstcs, 6, [11] Smpson, D.D. and Sells, S.B. (Eds.). (1990): Opod Addcton and Treatment: A 12Year Followup. Malabar, Florda: Kreger.
benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationLatent Class Regression. Statistics for Psychosocial Research II: Structural Models December 4 and 6, 2006
Latent Class Regresson Statstcs for Psychosocal Research II: Structural Models December 4 and 6, 2006 Latent Class Regresson (LCR) What s t and when do we use t? Recall the standard latent class model
More informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationStatistical Methods to Develop Rating Models
Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationStudy on CET4 Marks in China s Graded English Teaching
Study on CET4 Marks n Chna s Graded Englsh Teachng CHE We College of Foregn Studes, Shandong Insttute of Busness and Technology, P.R.Chna, 264005 Abstract: Ths paper deploys Logt model, and decomposes
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract  Stock market s one of the most complcated systems
More informationA Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy Scurve Regression
Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy Scurve Regresson ChengWu Chen, Morrs H. L. Wang and TngYa Hseh Department of Cvl Engneerng, Natonal Central Unversty,
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationAn Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services
An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces Charles V. Trappey a,1, Hsnyng Wu b a Professor (Management Scence), Natonal Chao
More informationAn empirical study for credit card approvals in the Greek banking sector
An emprcal study for credt card approvals n the Greek bankng sector Mara Mavr George Ioannou Bergamo, Italy 1721 May 2004 Management Scences Laboratory Department of Management Scence & Technology Athens
More informationEvaluating the Effects of FUNDEF on Wages and Test Scores in Brazil *
Evaluatng the Effects of FUNDEF on Wages and Test Scores n Brazl * Naérco MenezesFlho Elane Pazello Unversty of São Paulo Abstract In ths paper we nvestgate the effects of the 1998 reform n the fundng
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? ChuShu L Department of Internatonal Busness, Asa Unversty, Tawan ShengChang
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes causeandeffect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationThe Analysis of Outliers in Statistical Data
THALES Project No. xxxx The Analyss of Outlers n Statstcal Data Research Team Chrysses Caron, Assocate Professor (P.I.) Vaslk Karot, Doctoral canddate Polychrons Economou, Chrstna Perrakou, Postgraduate
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationCalculating the high frequency transmission line parameters of power cables
< ' Calculatng the hgh frequency transmsson lne parameters of power cables Authors: Dr. John Dcknson, Laboratory Servces Manager, N 0 RW E B Communcatons Mr. Peter J. Ncholson, Project Assgnment Manager,
More informationOverview of monitoring and evaluation
540 Toolkt to Combat Traffckng n Persons Tool 10.1 Overvew of montorng and evaluaton Overvew Ths tool brefly descrbes both montorng and evaluaton, and the dstncton between the two. What s montorng? Montorng
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationExtending Probabilistic Dynamic Epistemic Logic
Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σalgebra: a set
More informationExhaustive Regression. An Exploration of RegressionBased Data Mining Techniques Using Super Computation
Exhaustve Regresson An Exploraton of RegressonBased Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The
More informationHOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA*
HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* Luísa Farnha** 1. INTRODUCTION The rapd growth n Portuguese households ndebtedness n the past few years ncreased the concerns that debt
More informationHollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )
February 17, 2011 Andrew J. Hatnay ahatnay@kmlaw.ca Dear Sr/Madam: Re: Re: Hollnger Canadan Publshng Holdngs Co. ( HCPH ) proceedng under the Companes Credtors Arrangement Act ( CCAA ) Update on CCAA Proceedngs
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More informationThe Analysis of Covariance. ERSH 8310 Keppel and Wickens Chapter 15
The Analyss of Covarance ERSH 830 Keppel and Wckens Chapter 5 Today s Class Intal Consderatons Covarance and Lnear Regresson The Lnear Regresson Equaton TheAnalyss of Covarance Assumptons Underlyng the
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationSingle and multiple stage classifiers implementing logistic discrimination
Sngle and multple stage classfers mplementng logstc dscrmnaton Hélo Radke Bttencourt 1 Dens Alter de Olvera Moraes 2 Vctor Haertel 2 1 Pontfíca Unversdade Católca do Ro Grande do Sul  PUCRS Av. Ipranga,
More informationLogistic Regression. Steve Kroon
Logstc Regresson Steve Kroon Course notes sectons: 24.324.4 Dsclamer: these notes do not explctly ndcate whether values are vectors or scalars, but expects the reader to dscern ths from the context. Scenaro
More informationPRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIGIOUS AFFILIATION AND PARTICIPATION
PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIIOUS AFFILIATION AND PARTICIPATION Danny CohenZada Department of Economcs, Benuron Unversty, BeerSheva 84105, Israel Wllam Sander Department of Economcs, DePaul
More informationFREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES
FREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES Zuzanna BRO EKMUCHA, Grzegorz ZADORA, 2 Insttute of Forensc Research, Cracow, Poland 2 Faculty of Chemstry, Jagellonan
More informationSIMPLE LINEAR CORRELATION
SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.
More informationA 'Virtual Population' Approach To Small Area Estimation
A 'Vrtual Populaton' Approach To Small Area Estmaton Mchael P. Battagla 1, Martn R. Frankel 2, Machell Town 3 and Lna S. Balluz 3 1 Abt Assocates Inc., Cambrdge MA 02138 2 Baruch College, CUNY, New York
More informationHeterogeneous Paths Through College: Detailed Patterns and Relationships with Graduation and Earnings
Heterogeneous Paths Through College: Detaled Patterns and Relatonshps wth Graduaton and Earnngs Rodney J. Andrews The Unversty of Texas at Dallas and the Texas Schools Project Jng L The Unversty of Tulsa
More informationNPAR TESTS. OneSample ChiSquare Test. Cell Specification. Observed Frequencies 1O i 6. Expected Frequencies 1EXP i 6
PAR TESTS If a WEIGHT varable s specfed, t s used to replcate a case as many tmes as ndcated by the weght value rounded to the nearest nteger. If the workspace requrements are exceeded and samplng has
More informationHow Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence
1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh
More informationProceedings of the Annual Meeting of the American Statistical Association, August 59, 2001
Proceedngs of the Annual Meetng of the Amercan Statstcal Assocaton, August 59, 2001 LISTASSISTED SAMPLING: THE EFFECT OF TELEPHONE SYSTEM CHANGES ON DESIGN 1 Clyde Tucker, Bureau of Labor Statstcs James
More informationThe Use of Analytics for Claim Fraud Detection Roosevelt C. Mosley, Jr., FCAS, MAAA Nick Kucera Pinnacle Actuarial Resources Inc.
Paper 18372014 The Use of Analytcs for Clam Fraud Detecton Roosevelt C. Mosley, Jr., FCAS, MAAA Nck Kucera Pnnacle Actuaral Resources Inc., Bloomngton, IL ABSTRACT As t has been wdely reported n the nsurance
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationLecture 9: Logit/Probit. Prof. Sharyn O Halloran Sustainable Development U9611 Econometrics II
Lecture 9: Logt/Probt Prof. Sharyn O Halloran Sustanable Development U96 Econometrcs II Revew of Lnear Estmaton So far, we know how to handle lnear estmaton models of the type: Y = β 0 + β *X + β 2 *X
More informationGender differences in revealed risk taking: evidence from mutual fund investors
Economcs Letters 76 (2002) 151 158 www.elsever.com/ locate/ econbase Gender dfferences n revealed rsk takng: evdence from mutual fund nvestors a b c, * Peggy D. Dwyer, James H. Glkeson, John A. Lst a Unversty
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationTransition Matrix Models of Consumer Credit Ratings
Transton Matrx Models of Consumer Credt Ratngs Abstract Although the corporate credt rsk lterature has many studes modellng the change n the credt rsk of corporate bonds over tme, there s far less analyss
More informationTHE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES
The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered
More informationCriminal Justice System on Crime *
On the Impact of the NSW Crmnal Justce System on Crme * Dr Vasls Sarafds, Dscplne of Operatons Management and Econometrcs Unversty of Sydney * Ths presentaton s based on jont work wth Rchard Kelaher 1
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationRegression Models for a Binary Response Using EXCEL and JMP
SEMATECH 997 Statstcal Methods Symposum Austn Regresson Models for a Bnary Response Usng EXCEL and JMP Davd C. Trndade, Ph.D. STATTECH Consultng and Tranng n Appled Statstcs San Jose, CA Topcs Practcal
More informationLogistic Regression. Lecture 4: More classifiers and classes. Logistic regression. Adaboost. Optimization. Multiple class classification
Lecture 4: More classfers and classes C4B Machne Learnng Hlary 20 A. Zsserman Logstc regresson Loss functons revsted Adaboost Loss functons revsted Optmzaton Multple class classfcaton Logstc Regresson
More informationEfficient Project Portfolio as a tool for Enterprise Risk Management
Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse
More informationBinomial Link Functions. Lori Murray, Phil Munz
Bnomal Lnk Functons Lor Murray, Phl Munz Bnomal Lnk Functons Logt Lnk functon: ( p) p ln 1 p Probt Lnk functon: ( p) 1 ( p) Complentary Log Log functon: ( p) ln( ln(1 p)) Motvatng Example A researcher
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationAn Empirical Study of Search Engine Advertising Effectiveness
An Emprcal Study of Search Engne Advertsng Effectveness Sanjog Msra, Smon School of Busness Unversty of Rochester Edeal Pnker, Smon School of Busness Unversty of Rochester Alan RmmKaufman, RmmKaufman
More informationTo manage leave, meeting institutional requirements and treating individual staff members fairly and consistently.
Corporate Polces & Procedures Human Resources  Document CPP216 Leave Management Frst Produced: Current Verson: Past Revsons: Revew Cycle: Apples From: 09/09/09 26/10/12 09/09/09 3 years Immedately Authorsaton:
More informationTesting GOF & Estimating Overdispersion
Testng GOF & Estmatng Overdsperson Your Most General Model Needs to Ft the Dataset It s mportant that the most general (complcated) model n your canddate model lst fts the data well. Ths model s a benchmark
More informationCourse outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy
Fnancal Tme Seres Analyss Patrck McSharry patrck@mcsharry.net www.mcsharry.net Trnty Term 2014 Mathematcal Insttute Unversty of Oxford Course outlne 1. Data analyss, probablty, correlatons, vsualsaton
More information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 /  Communcaton Networks II (Görg) SS20  www.comnets.unbremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More informationStart me up: The Effectiveness of a SelfEmployment Programme for Needy Unemployed People in Germany*
Start me up: The Effectveness of a SelfEmployment Programme for Needy Unemployed People n Germany* Joachm Wolff Anton Nvorozhkn Date: 22/10/2008 Abstract In recent years actvaton of meanstested unemployment
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationAPPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT
APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT Toshhko Oda (1), Kochro Iwaoka (2) (1), (2) Infrastructure Systems Busness Unt, Panasonc System Networks Co., Ltd. Saedocho
More informationA DATA MINING APPLICATION IN A STUDENT DATABASE
JOURNAL OF AERONAUTICS AND SPACE TECHNOLOGIES JULY 005 VOLUME NUMBER (5357) A DATA MINING APPLICATION IN A STUDENT DATABASE Şenol Zafer ERDOĞAN Maltepe Ünversty Faculty of Engneerng BüyükbakkalköyIstanbul
More informationThe Current Employment Statistics (CES) survey,
Busness Brths and Deaths Impact of busness brths and deaths n the payroll survey The CES probabltybased sample redesgn accounts for most busness brth employment through the mputaton of busness deaths,
More informationIs There A Tradeoff between EmployerProvided Health Insurance and Wages?
Is There A Tradeoff between EmployerProvded Health Insurance and Wages? Lye Zhu, Southern Methodst Unversty October 2005 Abstract Though most of the lterature n health nsurance and the labor market assumes
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More information2.4 Bivariate distributions
page 28 2.4 Bvarate dstrbutons 2.4.1 Defntons Let X and Y be dscrete r.v.s defned on the same probablty space (S, F, P). Instead of treatng them separately, t s often necessary to thnk of them actng together
More informationx f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60
BIVARIATE DISTRIBUTIONS Let be a varable that assumes the values { 1,,..., n }. Then, a functon that epresses the relatve frequenc of these values s called a unvarate frequenc functon. It must be true
More informationA Secure PasswordAuthenticated Key Agreement Using Smart Cards
A Secure PasswordAuthentcated Key Agreement Usng Smart Cards Ka Chan 1, WenChung Kuo 2 and JnChou Cheng 3 1 Department of Computer and Informaton Scence, R.O.C. Mltary Academy, Kaohsung 83059, Tawan,
More informationSTATISTICAL DATA ANALYSIS IN EXCEL
Mcroarray Center STATISTICAL DATA ANALYSIS IN EXCEL Lecture 6 Some Advanced Topcs Dr. Petr Nazarov 1401013 petr.nazarov@crpsante.lu Statstcal data analyss n Ecel. 6. Some advanced topcs Correcton for
More informationHigh Correlation between Net Promoter Score and the Development of Consumers' Willingness to Pay (Empirical Evidence from European Mobile Markets)
Hgh Correlaton between et Promoter Score and the Development of Consumers' Wllngness to Pay (Emprcal Evdence from European Moble Marets Ths paper shows that the correlaton between the et Promoter Score
More informationSearching and Switching: Empirical estimates of consumer behaviour in regulated markets
Searchng and Swtchng: Emprcal estmates of consumer behavour n regulated markets Catherne Waddams Prce Centre for Competton Polcy, Unversty of East Angla Catherne Webster Centre for Competton Polcy, Unversty
More informationCS 2750 Machine Learning. Lecture 3. Density estimation. CS 2750 Machine Learning. Announcements
Lecture 3 Densty estmaton Mlos Hauskrecht mlos@cs.ptt.edu 5329 Sennott Square Next lecture: Matlab tutoral Announcements Rules for attendng the class: Regstered for credt Regstered for audt (only f there
More informationThe covariance is the two variable analog to the variance. The formula for the covariance between two variables is
Regresson Lectures So far we have talked only about statstcs that descrbe one varable. What we are gong to be dscussng for much of the remander of the course s relatonshps between two or more varables.
More informationApproximating Crossvalidatory Predictive Evaluation in Bayesian Latent Variables Models with Integrated IS and WAIC
Approxmatng Crossvaldatory Predctve Evaluaton n Bayesan Latent Varables Models wth Integrated IS and WAIC Longha L Department of Mathematcs and Statstcs Unversty of Saskatchewan Saskatoon, SK, CANADA
More informationADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET *
ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER * We are grateful to Jeffrey Brown, PerreAndre
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationSmall pots lump sum payment instruction
For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested
More informationAn InterestOriented Network Evolution Mechanism for Online Communities
An InterestOrented Network Evoluton Mechansm for Onlne Communtes Cahong Sun and Xaopng Yang School of Informaton, Renmn Unversty of Chna, Bejng 100872, P.R. Chna {chsun,yang}@ruc.edu.cn Abstract. Onlne
More informationThe Economic Impacts of Cigarette Tax Reductions on Youth Smoking in Canada
The Economc Impacts of Cgarette Tax Reductons on Youth Smokng n Canada Dane P. Dupont and Anthony J. Ward Economcs, Brock Unversty December 2002 Abstract Cgarettes are the most commonly consumed recreatonal
More informationQuantification of qualitative data: the case of the Central Bank of Armenia
Quantfcaton of qualtatve data: the case of the Central Bank of Armena Martn Galstyan 1 and Vahe Movssyan 2 Overvew The effect of nonfnancal organsatons and consumers atttudes on economc actvty s a subject
More informationLIFETIME INCOME OPTIONS
LIFETIME INCOME OPTIONS May 2011 by: Marca S. Wagner, Esq. The Wagner Law Group A Professonal Corporaton 99 Summer Street, 13 th Floor Boston, MA 02110 Tel: (617) 3575200 Fax: (617) 3575250 www.ersalawyers.com
More informationFeature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College
Feature selecton for ntruson detecton Slobodan Petrovć NISlab, Gjøvk Unversty College Contents The feature selecton problem Intruson detecton Traffc features relevant for IDS The CFS measure The mrmr measure
More informationForecasting and Stress Testing Credit Card Default using Dynamic Models
Forecastng and Stress Testng Credt Card Default usng Dynamc Models Tony Bellott and Jonathan Crook Credt Research Centre Unversty of Ednburgh Busness School Verson 4.5 Abstract Typcally models of credt
More informationMarginal Benefit Incidence Analysis Using a Single Crosssection of Data. Mohamed Ihsan Ajwad and Quentin Wodon 1. World Bank.
Margnal Beneft Incdence Analyss Usng a Sngle Crosssecton of Data Mohamed Ihsan Ajwad and uentn Wodon World Bank August 200 Abstract In a recent paper, Lanjouw and Ravallon proposed an attractve and smple
More informationModelling the Cocaine and Heroin Markets in the Era of Globalization and Drug Reduction Policies Claudia Costa Storti and Paul De Grauwe
Modellng the Cocane and Heron Markets n the Era of Globalzaton and Drug Reducton Polces Clauda Costa Stort and Paul De Grauwe Modellng the Cocane and Heron Markets n the Era of Globalzaton and Drug Reducton
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationTrivial lump sum R5.0
Optons form Once you have flled n ths form, please return t wth your orgnal brth certfcate to: Premer PO Box 2067 Croydon CR90 9ND. Fll n ths form usng BLOCK CAPITALS and black nk. Mark all answers wth
More informationEvaluating the generalizability of an RCT using electronic health records data
Evaluatng the generalzablty of an RCT usng electronc health records data 3 nterestng questons Is our RCT representatve? How can we generalze RCT results? Can we use EHR* data as a control group? *) Electronc
More informationReturns to Experience in Mozambique: A Nonparametric Regression Approach
Returns to Experence n Mozambque: A Nonparametrc Regresson Approach Joel Muzma Conference Paper nº 27 Conferênca Inaugural do IESE Desafos para a nvestgação socal e económca em Moçambque 19 de Setembro
More informationMulticlass sparse logistic regression for classification of multiple cancer types using gene expression data
Computatonal Statstcs & Data Analyss 51 (26) 1643 1655 www.elsever.com/locate/csda Multclass sparse logstc regresson for classfcaton of multple cancer types usng gene expresson data Yongda Km a,, Sunghoon
More informationFinancial Instability and Life Insurance Demand + Mahito Okura *
Fnancal Instablty and Lfe Insurance Demand + Mahto Okura * Norhro Kasuga ** Abstract Ths paper estmates prvate lfe nsurance and Kampo demand functons usng householdlevel data provded by the Postal Servces
More information1 De nitions and Censoring
De ntons and Censorng. Survval Analyss We begn by consderng smple analyses but we wll lead up to and take a look at regresson on explanatory factors., as n lnear regresson part A. The mportant d erence
More information14.74 Lecture 5: Health (2)
14.74 Lecture 5: Health (2) Esther Duflo February 17, 2004 1 Possble Interventons Last tme we dscussed possble nterventons. Let s take one: provdng ron supplements to people, for example. From the data,
More informationWORKING PAPERS. The Impact of Technological Change and Lifestyles on the Energy Demand of Households
ÖSTERREICHISCHES INSTITUT FÜR WIRTSCHAFTSFORSCHUNG WORKING PAPERS The Impact of Technologcal Change and Lfestyles on the Energy Demand of Households A Combnaton of Aggregate and Indvdual Household Analyss
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationTime Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6  The Time Value of Money. The Time Value of Money
Ch. 6  The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21 Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important
More informationDetecting Credit Card Fraud using Periodic Features
Detectng Credt Card Fraud usng Perodc Features Alejandro Correa Bahnsen, Djamla Aouada, Aleksandar Stojanovc and Björn Ottersten Interdscplnary Centre for Securty, Relablty and Trust Unversty of Luxembourg,
More informationMeasuring Customer Satisfaction for Various Services Using Multicriteria Analysis
Measurng Customer Satsfacton for Varous Servces Usng Multcrtera Analyss Yanns Sskos and Evangelos Grgorouds Techncal Unversty of Crete Decson Support Systems Laboratory Unversty Campus, 73100 Chana, GREECE
More informationActivity Scheduling for CostTime Investment Optimization in Project Management
PROJECT MANAGEMENT 4 th Internatonal Conference on Industral Engneerng and Industral Management XIV Congreso de Ingenería de Organzacón Donosta San Sebastán, September 8 th 10 th 010 Actvty Schedulng
More information