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SUPPORT If you have any questions about downloading Bookshelf, creating your account, or accessing and using your ebook edition, please visit http://support.vitalsource.com/ Extending the Linear Model with R Generalized Linear, Mixed Effects and Nonparametric Regression Models SECOND EDITION CHAPMAN & HALL/CRC Texts in Statistical Science Series Series Editors Francesca Dominici, Harvard School of Public Health, USA Julian J. Faraway, University of Bath, UK Martin Tanner, Northwestern University, USA Jim Zidek, University of British Columbia, Canada Statistical Theory: A Concise Introduction Statistics for Technology: A Course in Applied F. Abramovich and Y. Ritov Statistics, Third Edition C. Chatfield Practical Multivariate Analysis, Fifth Edition A. Afifi, S. May, and V.A. Clark Analysis of Variance, Design, and Regression: Linear Modeling for Unbalanced Data, Practical Statistics for Medical Research Second Edition D.G. Altman R. Christensen Interpreting Data: A First Course in Statistics Bayesian Ideas and Data Analysis: An A.J.B. Anderson Introduction for Scientists and Statisticians R. Christensen, W. Johnson, A. Branscum, Introduction to Probability with R and T.E. Hanson K. Baclawski Modelling Binary Data, Second Edition Linear Algebra and Matrix Analysis for D. Collett Statistics S. Banerjee and A. Roy Modelling Survival Data in Medical Research, Third Edition Mathematical Statistics: Basic Ideas and D. Collett Selected Topics, Volume I, Second Edition Introduction to Statistical Methods for P. J. Bickel and K. A. Doksum Clinical Trials T.D. Cook and D.L. DeMets Mathematical Statistics: Basic Ideas and Selected Topics, Volume II Applied Statistics: Principles and Examples P. J. Bickel and K. A. Doksum D.R. Cox and E.J. Snell Analysis of Categorical Data with R Multivariate Survival Analysis and Competing C. R. Bilder and T. M. Loughin Risks Statistical Methods for SPC and TQM M. Crowder D. Bissell Statistical Analysis of Reliability Data Introduction to Probability M.J. Crowder, A.C. Kimber, J. K. Blitzstein and J. Hwang T.J. Sweeting, and R.L. Smith Bayesian Methods for Data Analysis, An Introduction to Generalized Third Edition Linear Models, Third Edition B.P. Carlin and T.A. Louis A.J. Dobson and A.G. Barnett Second Edition Nonlinear Time Series: Theory, Methods, and R. Caulcutt Applications with R Examples R. Douc, E. Moulines, and D.S. Stoffer The Analysis of Time Series: An Introduction, Sixth Edition Introduction to Optimization Methods and C. Chatfield Their Applications in Statistics B.S. Everitt Introduction to Multivariate Analysis C. Chatfield and A.J. Collins Extending the Linear Model with R: Generalized Linear, Mixed Effects and Problem Solving: A Statistician’s Guide, Nonparametric Regression Models, Second Second Edition Edition C. Chatfield J.J. Faraway Linear Models with R, Second Edition Nonparametric Methods in Statistics with SAS J.J. Faraway Applications O. Korosteleva A Course in Large Sample Theory T.S. Ferguson Modeling and Analysis of Stochastic Systems, Second Edition Multivariate Statistics: A Practical V.G. Kulkarni Approach B. Flury and H. Riedwyl Exercises and Solutions in Biostatistical Theory L.L. Kupper, B.H. Neelon, and S.M. O’Brien Readings in Decision Analysis S. French Exercises and Solutions in Statistical Theory L.L. Kupper, B.H. Neelon, and S.M. O’Brien Discrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Design and Analysis of Experiments with R Count Data J. Lawson M. Friendly and D. Meyer Design and Analysis of Experiments with SAS Markov Chain Monte Carlo: J. Lawson Stochastic Simulation for Bayesian Inference, A Course in Categorical Data Analysis Second Edition T. Leonard D. Gamerman and H.F. Lopes Statistics for Accountants Bayesian Data Analysis, Third Edition S. Letchford A. Gelman, J.B. Carlin, H.S. Stern, D.B. 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Gamerman, and Analysis of Failure and Survival Data F. Louzada P. J. Smith Beyond ANOVA: Basics of Applied Statistics Applied Statistics: Handbook of GENSTAT R.G. Miller, Jr. Analyses A Primer on Linear Models E.J. Snell and H. Simpson J.F. Monahan Applied Nonparametric Statistical Methods, Applied Stochastic Modelling, Second Edition Fourth Edition B.J.T. Morgan P. Sprent and N.C. Smeeton Elements of Simulation Data Driven Statistical Methods B.J.T. Morgan P. Sprent Probability: Methods and Measurement Generalized Linear Mixed Models: A. O’Hagan Modern Concepts, Methods and Applications W. W. Stroup Introduction to Statistical Limit Theory A.M. Polansky Survival Analysis Using S: Analysis of Time-to-Event Data Applied Bayesian Forecasting and Time Series M. Tableman and J.S. Kim Analysis A. Pole, M. West, and J. Harrison Applied Categorical and Count Data Analysis W. Tang, H. He, and X.M. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface xi 1 Introduction 1 2 BinaryResponse 25 2.1 HeartDiseaseExample 25 2.2 LogisticRegression 28 2.3 Inference 32 2.4 Diagnostics 34 2.5 ModelSelection 38 2.6 GoodnessofFit 40 2.7 EstimationProblems 44 3 BinomialandProportionResponses 51 3.1 BinomialRegressionModel 51 3.2 Inference 53 3.3 Pearson’sχ2Statistic 54 3.4 Overdispersion 55 3.5 Quasi-Binomial 60 3.6 BetaRegression 64 4 VariationsonLogisticRegression 67 4.1 LatentVariables 67 4.2 LinkFunctions 68 4.3 ProspectiveandRetrospectiveSampling 71 4.4 PredictionandEffectiveDoses 74 4.5 MatchedCase-ControlStudies 75 5 CountRegression 83 5.1 PoissonRegression 83 5.2 DispersedPoissonModel 87 5.3 RateModels 89 5.4 NegativeBinomial 92 5.5 ZeroInflatedCountModels 94 vii viii CONTENTS 6 ContingencyTables 103 6.1 Two-by-TwoTables 103 6.2 LargerTwo-WayTables 108 6.3 CorrespondenceAnalysis 110 6.4 MatchedPairs 112 6.5 Three-WayContingencyTables 114 6.6 OrdinalVariables 121 7 MultinomialData 129 7.1 MultinomialLogitModel 129 7.2 LinearDiscriminantAnalysis 134 7.3 HierarchicalorNestedResponses 136 7.4 OrdinalMultinomialResponses 139 8 GeneralizedLinearModels 151 8.1 GLMDefinition 151 8.2 FittingaGLM 154 8.3 HypothesisTests 156 8.4 GLMDiagnostics 159 8.5 SandwichEstimation 168 8.6 RobustEstimation 169 9 OtherGLMs 175 9.1 GammaGLM 175 9.2 InverseGaussianGLM 181 9.3 JointModelingoftheMeanandDispersion 184 9.4 Quasi-LikelihoodGLM 186 9.5 TweedieGLM 188 10 RandomEffects 195 10.1 Estimation 196 10.2 Inference 201 10.3 EstimatingRandomEffects 207 10.4 Prediction 208 10.5 Diagnostics 210 10.6 BlocksasRandomEffects 211 10.7 SplitPlots 215 10.8 NestedEffects 219 10.9 CrossedEffects 222 10.10MultilevelModels 224 11 RepeatedMeasuresandLongitudinalData 237 11.1 LongitudinalData 238 11.2 RepeatedMeasures 243 11.3 MultipleResponseMultilevelModels 248