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Regression: Models, Methods and Applications PDF

713 Pages·2013·15.682 MB·English
by  FahrmeirL.KneibTh.LangS.MarxB.
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Regression Ludwig Fahrmeir (cid:2) Thomas Kneib (cid:2) StefanLang (cid:2) Brian Marx Regression Models, Methods and Applications 123 LudwigFahrmeir StefanLang DepartmentofStatistics DepartmentofStatistics UniversityofMunich UniversityofInnsbruck Munich Innsbruck Germany Austria ThomasKneib BrianMarx ChairofStatistics ExperimentalStatistics UniversityofGo¨ttingen LouisianaStateUniversity Go¨ttingen BatonRouge,LA Germany USA ISBN978-3-642-34332-2 ISBN978-3-642-34333-9(eBook) DOI10.1007/978-3-642-34333-9 SpringerHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2013934096 (cid:2)c Springer-VerlagBerlinHeidelberg2013 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.springer.com) Preface Regression is the most popular and commonly used statistical methodology for analyzing empirical problems in social sciences, economics, and life sciences. Correspondingly,thereexistalargevarietyofmodelsandinferentialtools,ranging from conventional linear models to modern non- and semiparametric regression. Currently available textbooks mostly focus on particular classes of regression models, however, strongly varying in style, mathematical level, and orientation towards theory or application. Why then another book on regression? Several introductorytextbooksareavailableforstudentsandpractitionersindiversefields ofapplications,buttheydealalmostexclusivelywithlinearregression.Ontheother hand,mosttextsconcentratingonmodernnon-andsemiparametricmethodsprimar- ilyaddressreaderswithstrongtheoreticalinterestandmethodologicalbackground, presupposinga correspondinglyhigh-levelmathematicalbasis. Theyare therefore lessaccessibletoreadersfromappliedfieldswhoneedtoemploythesemethods. Theaimofthisbookisanappliedandunifiedintroductionintoparametric,non-, andsemiparametricregressionthatclosesthegapbetweentheoryandapplication. The most important models and methods in regression are presented on a solid formal basis, and their appropriate application is shown through many real data examplesandcasestudies.Availabilityof(user-friendly)softwarehasbeenamajor criterion for the methods selected and presented. In our view, the interplay and balance between theory and application are essential for progress in substantive disciplines, as well as for the development of statistical methodology, motivated andstimulatedthroughnewchallengesarisingfrommultidisciplinarycollaboration. A similar goal, but with somewhat different focus, has been pursued in the book SemiparametricRegressionbyRuppert,Wand,andCarroll(2003). Thus,ourbookprimarilytargetsanaudiencethatincludesstudents,teachers,and practitionersinsocial,economic,andlifesciences,aswellasstudentsandteachers instatisticsprogramsandmathematiciansandcomputerscientistswithinterestsin statisticalmodelinganddataanalysis.Itiswrittenatanintermediatemathematical level and assumes only knowledge of basic probability, calculus, and statistics. Short parts in the text dealing with more complex details or providing additional informationstartwiththesymbol andendwith .Thesepartsmaybeomitted in a first reading without loss of continuity. The most important definitions and v vi Preface statements are concisely summarized in boxes. Two appendices describe required matrixalgebra,aswellaselementsofprobabilitycalculusandstatisticalinference. Dependingontheparticularinterests,partsofthebookcanbereadindependently ofremainingpartsoralsoinmodifiedorder: (cid:129) Chapter2providesanintroductoryoverviewonparametric,non-,andsemipara- metric regressionmodels,deliberatelyomittingtechnicaldetailsandinferential tools. (cid:129) Chapters1–4canbereadasanintroductiontolinearmodels. (cid:129) Linear mixed models (Sects.7.1–7.4) can be studied immediately after Chaps.1–4andbeforereadingChaps.5and 6. (cid:129) Sections 10.1 and 10.2 on linear quantile regression can be read immediately afterChaps.1–4. (cid:129) Chapters1–4,Sects.7.1–7.4,andChaps.8–10canbereadasanintroductionto parametric and semiparametric regression for continuous responses (including semiparametricquantileregression). (cid:129) Chapters1–6compriseparametricregressionmodelsforcontinuousanddiscrete responses. Anoverviewofpossiblereadingalternativesisgiveninthefollowingtable(chapters inbrackets[:::]couldbeomitted): Description Chapters Linearmodels 1,2,3,4,[Sects.10.1,10.2] Linearmixedmodels 1,2,3,4,Sects.7.1–7.4,[Sects.10.1–10.2] Variableselectioninlinearmodels 3,Sects.4.2–4.4 Generalizedlinearmodels 1,2,3,4,5,[6] Generalizedlinearmixedmodels 1,2,3,4,5,[6],7 Semiparametricregressionforcontinuous 1,2,3,4,8(excl.pages481ff.),9(excl. responses(excludingmixedmodels) Sects.9.4,9.6.2),[10] Semiparametricregressionforcontinuous 1,2,3,4,Sects.7.1–7.4,8,9,[10] responses(includingmixedmodels) Manyexamplesandapplicationsfromdiversefieldsillustratemodelsandmeth- ods.Mostof thedata sets are availablevia theurlhttp://www.regressionbook.org/ andthesymbol addedtoanexampleindicatestheavailabilityofcorresponding software code from the web site. This facilitates independent work and studies through real data applications and small case studies. In addition, the web site providesinformationaboutstatisticalsoftwareforregression. Highlightsofthebookinclude: (cid:129) An introductionof regression modelsfromfirst principles, i.e., a complete and comprehensiveintroductiontothelinearmodelinChaps.3,4,and10 (cid:129) Acoverageoftheentirerangeofregressionmodelsstartingwithlinearmodels, coveringgeneralizedlinear and mixedmodelsand also including(generalized) additivemodelsandquantileregression Preface vii (cid:129) ApresentationofbothfrequentistandBayesianapproachestoregression (cid:129) Theinclusionofalargenumberofworkedoutexamplesandcasestudies (cid:129) Althoughthebookiswrittenintextbookstyl esuitableforstudents,thematerial isclosetocurrentresearchonadvancedregressionanalysis ThisbookispartlybasedonaprecedingGermanversionthathasbeentranslated and considerably extended. We are indebted to Alexandra Reuber for translating largepartsoftheGermanversion.WealsothankHerwigFriedl,ChristianHeumann, Torsten Hothorn, and Helga Wagner for acting as referees of the book. They all did a great job and were very helpful in improving the manuscript. Many thanks to Jesus Crespo Cuaresma, Kathrin Dallmeier, Martin Feldkircher, Oliver Joost, Franziska Kohl, Jana Lehmann,LorenzOberhammer,Cornelia Oberhauser, AlexanderRazen, Helene Roth, Judith Santer, Sylvia Schmidt, Nora Seiwald, Iris Burger,Sven Steinert,NikolausUmlauf,Janette Walde, Elisabeth Waldmann,and Peter Wechselbergerforsupportandassistance in variousways.Lastbutnotleast wethankAliceBlanck,AlphonserajaSagayaraj,UlrikeStricker-KombaandNiels PeterThomasfromSpringerVerlagfortheircontinuedsupportandpatienceduring thepreparationofthemanuscript. Mu¨nchen,Germany LudwigFahrmeir Go¨ttingen,Germany ThomasKneib Innsbruck,Austria StefanLang BatonRouge,LA BrianMarx January2013 Table of Contents 1 Introduction................................................................. 1 1.1 ExamplesofApplications............................................ 4 1.2 FirstSteps............................................................. 11 1.2.1 UnivariateDistributionsoftheVariables.................. 11 1.2.2 GraphicalAssociationAnalysis............................ 13 1.3 NotationalRemarks.................................................. 19 2 RegressionModels.......................................................... 21 2.1 Introduction........................................................... 21 2.2 LinearRegressionModels........................................... 22 2.2.1 SimpleLinearRegressionModel ......................... 22 2.2.2 MultipleLinearRegression ................................ 26 2.3 RegressionwithBinaryResponseVariables:TheLogitModel.... 33 2.4 MixedModels........................................................ 38 2.5 SimpleNonparametricRegression .................................. 44 2.6 AdditiveModels...................................................... 49 2.7 GeneralizedAdditiveModels........................................ 52 2.8 GeoadditiveRegression.............................................. 55 2.9 BeyondMeanRegression............................................ 61 2.9.1 RegressionModelsforLocation,Scale,andShape....... 62 2.9.2 QuantileRegression........................................ 66 2.10 ModelsinaNutshell................................................. 68 2.10.1 LinearModels(LMs,Chaps.3and4)..................... 68 2.10.2 LogitModel(Chap.5)...................................... 68 2.10.3 PoissonRegression(Chap.5).............................. 68 2.10.4 GeneralizedLinearModels(GLMs,Chaps.5and6)..... 69 2.10.5 LinearMixedModels(LMMs,Chap.7)................... 69 2.10.6 AdditiveModelsand Extensions(AMs, Chaps.8and9).............................................. 70 2.10.7 Generalized Additive (Mixed) Models (GA(M)Ms,Chap.9) ....................................... 70 2.10.8 StructuredAdditiveRegression(STAR,Chap.9)......... 71 2.10.9 QuantileRegression(Chap.10)............................ 71 ix

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