Contingency Table Analysis: Methods and Implementation Using R PDF
Preview Contingency Table Analysis: Methods and Implementation Using R
Statistics for Industry and Technology Maria Kateri Contingency Table Analysis Methods and Implementation Using R Statistics for Industry and Technology Series Editor N.Balakrishnan McMasterUniversity Hamilton,ON Canada Editorial Advisory Board MaxEngelhardt EG&GIdaho,Inc. IdahoFalls,ID,USA HarryF.Martz LosAlamosNationalLaboratory LosAlamos,NM,USA GaryC.McDonald NAOResearch&DevelopmentCenter Warren,MI,USA KazuyukiSuzuki UniversityofElectroCommunications Chofu-shi,Tokyo Japan Forfurthervolumes: http://www.springer.com/series/4982 Maria Kateri Contingency Table Analysis Methods and Implementation Using R MariaKateri InstituteofStatistics RWTHAachenUniversity Aachen,Germany ISBN978-0-8176-4810-7 ISBN978-0-8176-4811-4(eBook) DOI10.1007/978-0-8176-4811-4 SpringerNewYorkHeidelbergDordrechtLondon LibraryofCongressControlNumber:2014934697 MathematicsSubjectClassification(2010):62H17,62J12,62H25,62H12,62F10,62H15,62F03 ©SpringerScience+BusinessMediaNewYork2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.birkhauser-science.com) To myparentsAthinaand Dimitris and to mydaughterZenia Preface Thefocusofthisbookisonmodelsforcontingencytableanalysis.Itdealsmainly withlog-linearmodelsandspecialmodelsforordinaldata(log-linearornonlinear). Specialmodelsforordinaldataaredealtwithtoagreaterextent,coveredinChaps.6, 7,and9.Thesemodels,asforexample,associationmodelsfortwo-andmulti-way contingencytablesorsymmetrymodelsforsquaretables,thoughverypowerfuland ofgreatinterpretingvalue,arenotverypopularinuse.Thisismainlybecausethey are notreadily providedas modeloptionsin standard statistical software. Though theycanbefittedinRbysomespecialpackages,theirapplicationusuallyrequires someexpertiseorexperienceonthesemodelsandR.Existingbooksoncontingency tablesorcategoricaldataanalysiseitherdonotincludeassociationmodelsintheir contentsorreferonlyto thesimplesttypesofthem.Thefew exceptions,although treating these models in more detail, remain in the methodological part without providingguidancefor applyingthem in practice. Thus, such modelscan be used mainlybyexpertsonthetopic.Thisascertainmentwasthemotivationandtheidea behindtheconceptofthisbook:to provideareferencethatexploitsthesemodels, explains their features and interpretation aspects in detail, and simultaneously trains the reader to fit them in practice. Additionally, special issues not covered in other books, such as the adjustment of models to account for structural zeros, are addressed.The goalwas to endup with a methodologicalbookthat makesall approaches,models,orgraphspresented,easyreproducible. The aim to familiarize readers with methods and models for the analysis of contingency tables and their use in practice is served by discussing the models’ features and interconnections and by giving special emphasis on the examples’ analysis,theirinterpretation,andtheirimplementationinR.Whenneeded,special R functionsare provided(in the web companionof the book) that automatize the requiredprocedures,simplifyingthustheirapplicability.Forexample,functionsare providedfor derivingthe midrankscoresof a classification variableor computing thelocaloddsratiosofatwo-waycontingencytable(orothertypesofgeneralized odds ratios). Hence, all models, measures, and graphs discussed can easily be realized in R by handy functions. The examples are worked out in R, explaining theuseofthefunctions,sothatthereaderisgraduallytrainedandattheendinthe vii viii Preface positiontoalterthefunctionsandadjustthemtospecialneeds.Thewebcompanion ofthebookistobefoundunder http://cta.isw.rwth-aachen.de Framing this book on model-based analysis, the great body of nonparametric methods (especially for ordinal data) and smoothing methods for contingency tables is not considered. Emphasis is given primarily on models that treat the variablessymmetrically rather than distinguishingbetween response and explana- tory variables. Additionally, since the book deals only with contingency tables, regression-typemodels that involve also continuous explanatoryvariables are not addressed at all. Thus, logistic regression, though very important in categorical data analysis, is partially covered, only for the case of categorical explanatory variables (logit models). Furthermore, clustered categorical data and multivariate responsemodelsarenotconsidered.Onlybivariateresponsemodelsareconsidered for data represented in square two-way contingency tables with commensurable classificationvariables,nominalorordinal.Formorethantwooccasions,werefer tootherspecialreferencesources. Theapproachadoptedistheasymptoticfrequentistapproach.Ashortreference on Bayesian analysis of contingency tables and on small sample inference is providedinthelastchapter. Thereadershiptargetgroupsare(a)graduatestudentsorresearchers(instatistics orinpsychometric,social,biomedical,andpedagogicalsciences)and(b)practition- ers(e.g.,forsocialorconsumers’surveys).Thefirstfivechapters(uptoSect.5.4) addressbothgroups,thoughgroup(a)couldgoquicklythroughit,forfillinggaps andbuildingupgraduallytheRpart.ExpertiseinRisnotrequired.Regardingthe followingmaterial(fromSect.5.5),group(b)wouldprobablybemoreinterestedin thesimplermodels(aslinear-by-linear,row,orcolumneffectassociationmodels), easytopresentandinterpret,whilegroup(a)alsoinmoreadvancedtopics(suchas handlingstructuralzeros,themultiplicativerow–columnassociationmodel,models for the marginal distributions, or the generalized odds ratios). An updated rich literaturereviewonabrightaspectoftopicsisprovidedattheendofeachchapter andismainlyaddressedtogroup(a). ThescopeistosimultaneouslydevelopthetheoreticalandRprogrammingskills required for analyzing contingency tables, as well as evaluating and interpreting the results. Parts of the manuscriptare based on my notes forthe graduatecourse oncategoricaldataanalysis, whichIheldforabout10yearsin theDepartmentof StatisticsandInsuranceScienceoftheUniversityofPiraeusinGreece. I would like to thank those who have been involved in this book project. Special thanks to Alan Agresti who influenced the most my view on categorical data. His Categorical Data Analysis book, in its first 1990 edition, is partly responsibleformyinvolvementwithcategoricaldata.Ialsothankhimforproviding valuablecommentsonthemanuscript,suggestingalterationsandadditions.Ithank Panayiotis Bobotas for proofreading the complete draft, Anna Gottard for her critical comments and suggestions on graphical models, and Anestis Touloumis forhishelpfulcommentsonChaps.5–10.Iappreciateallthosewhoaccompanied my scientific journey, in particular my former supervisor Takis Papaioannou. Preface ix ThanksalsotoNarayanaswamyBalakrishnan,editorinchieffortheseries“Statis- tics for Industry and Technology,” for his interest in this project, and to Mitch Moulton, editorial assistant at Springer, for his help facilitating it. This book wouldnothavebeenpossiblewithoutthe generoussupportof myparents,Athina and Dimitris Kateris, to whom I express my deep gratitude. Finally, I thank my daughterZeniaforherpatienceduringthepreparationperiodandherinterestinthe developmentoftheproject. Aachen,Germany MariaKateri January2014
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