Description
Taylor & Francis Ltd Multivariate Generalized Linear Mixed Models Using R 2011 Edition by Damon Mark Berridge, Robert Crouchley
Multivariate Generalized Linear Mixed Models Using R presents robust and methodologically sound models for analyzing large and complex data sets, enabling readers to answer increasingly complex research questions. The book applies the principles of modeling to longitudinal data from panel and related studies via the Sabre software package in R.A Unified Framework for a Broad Class of Models The authors first discuss members of the family of generalized linear models, gradually adding complexity to the modeling framework by incorporating random effects. After reviewing the generalized linear model notation, they illustrate a range of random effects models, including three-level, multivariate, endpoint, event history, and state dependence models. They estimate the multivariate generalized linear mixed models (MGLMMs) using either standard or adaptive Gaussian quadrature. The authors also compare two-level fixed and random effects linear models. The appendices contain additional information on quadrature, model estimation, and endogenous variables, along with SabreR commands and examples. Improve Your Longitudinal StudyIn medical and social science research, MGLMMs help disentangle state dependence from incidental parameters. Focusing on these sophisticated data analysis techniques, this book explains the statistical theory and modeling involved in longitudinal studies. Many examples throughout the text illustrate the analysis of real-world data sets. Exercises, solutions, and other material are available on a supporting website. Introduction Generalized Linear Models for Continuous/Interval Scale Data Introduction Continuous/interval scale data Simple and multiple linear regression models Checking assumptions in linear regression models Likelihood: multiple linear regressionComparing model likelihoods Application of a multiple linear regression modelGeneralized Linear Models for Other Types of Data Binary dataOrdinal dataCount dataFamily of Generalized Linear Models Introduction The linear model Binary response models Poisson modelLikelihoodMixed Models for Continuous/Interval Scale Data Introduction Linear mixed model The intraclass correlation coefficient Parameter estimation by maximum likelihood Regression with level-two effects Two-level random intercept models General two-level models including random intercepts LikelihoodResiduals Checking assumptions in mixed models Comparing model likelihoods Application of a two-level linear model Two-level growth modelsLikelihoodExample on linear growth modelsMixed Models for Binary Data Introduction The two-level logistic model General two-level logistic models Intraclass correlation coefficient LikelihoodExample on binary dataMixed Models for Ordinal Data Introduction The two-level ordered logit model LikelihoodExample on mixed models for ordered dataMixed Models for Count Data Introduction The two-level Poisson model LikelihoodExample on mixed models for count dataFamily of Two-Level Generalized Linear Models Introduction The mixed linear model Mixed binary response models Mixed Poisson model Likelihood Three-Level Generalized Linear Models Introduction Three-level random intercept models Three-level generalized linear models Linear models Binary response models LikelihoodExample on three-level generalized linear modelsModels for Multivariate Data Introduction Multivariate two-level generalized linear model Bivariate Poisson model: Example Bivariate ordered response model: Example Bivariate linear-probit model: Example Multivariate two-level generalized linear model likelihoodModels for Duration and Event History Data IntroductionDuration data in discrete timeRenewal dataCompeting risk dataStayers, Non-Susceptibles, and Endpoints Introduction Mover-stayer model Likelihood with mover-stayer modelExample 1: Stayers in Poisson data Example 2: Stayers in binary dataHandling Initial Conditions/State Dependence in Binary Data Introduction to key issues: heterogeneity, state dependence and non-stationarity Motivational example Random effects model Initial conditions problem Initial treatment of initial conditions problem Example: Depression data Classical conditional analysis Classical conditional model: Depression example Conditioning on initial response but allowing random effect u0j to be dependent on zj Wooldridge conditional model: Depression example Modeling the initial conditions Same random effect in the initial response and subsequent response models with a common scale parameter Joint analysis with a common random effect: Depression example Same random effect in models of the initial response and subsequent responses but with different scale parametersJoint analysis with a common random effect (different scale parameters): Depression example Different random effects in models of the initial response and subsequent responses Different random effects: Depression example Embedding the Wooldridge approach in joint models for the initial response and subsequent responses Joint model plus the Wooldridge approach: Depression example Other link functionsIncidental Parameters: An Empirical Comparison of Fixed Effects and Random Effects ModelsIntroduction Fixed effects treatment of the two-level linear model Dummy variable specification of the fixed effects model Empirical comparison of two-level fixed effects and random effects estimators Implicit fixed effects estimator Random effects models Comparing two-level fixed effects and random effects models Fixed effects treatment of the three-level linear modelAppendix A: SabreR Installation, SabreR Commands, Quadrature, Estimation, Endogenous EffectsAppendix B: Introduction to R for SabreBibliographyExercises appear at the end of most chapters.