Author:
West, Brady T.
Edition Statement:Second edition.
Imprint:Boca Raton : CRC Press, Taylor & Francis Group, [2015]
Descriptionxxv, 414 pages : illustrations ; 27 cm
Note:"A Chapman & Hall Book."
Note:"First edition published in 2006."
Note:1. Introduction -- What are linear mixed models (LMMs)? -- Models with random effects for clustered data -- Models for longitudinal or repeated-measures data -- A brief history of LMMs -- Key theoretical developments -- Key software development -- 2. Linear mixed models : an overview -- Types and structures of data sets -- Clustered data vs. repeated-measures and longitudinal data -- Levels of data -- Types of factors and their related effects in an LMM -- Fixed factors -- Random factors -- Nested vs. crossed factors and their corresponding effects -- Specifications of LMMs -- General specification for an individual observation -- General matrix specification -- Covariance structures -- Group-specific covariance parameter values -- Alternative matrix specification for all subjects -- Hierarchical linear model (HLM) -- The marginal linear model -- Estimation in LMMs -- Maximum likelihood (ML) estimation -- REML estimation -- Computational issues -- algorithms for likelihood function optimization -- Computational problems with estimation of covariance parameters -- Tools for model selection -- Basic concepts in model selection -- Nested models -- Hypotheses : specification and testing -- Likelihood ratio tests (LRTs) -- Alternative tests -- Information criteria -- Model-building strategies -- The top-down strategy -- The step-up strategy -- Checking model assumptions (diagnostics -- Residual diagnostics -- Raw residuals -- Standardized and studentized residuals -- Influence diagnostics -- Diagnostics for random effects -- Other aspects of LMMs -- Predicting random effects : best linear unbiased predictors -- Intraclass correlation coefficients (ICCs) -- Problems with model specification (aliasing) -- Missing data -- Centering covariates -- Fitting linear mixed models to complex sample survey data -- Power analysis for linear mixed models -- Direct power computations -- Examining power via simulation -- 3. Two-level models for clustered data : the rat pup example -- The rat pup study -- Overview of the rat pup data analysis -- Analysis steps in the software procedures -- Results of hypothesis tests -- Comparing results across the software procedures -- Interpreting parameter estimates in the final model -- Estimating the intraclass correlation coefficients (ICCs) -- Calculating predicted values -- Diagnostics for the final model -- Residual diagnostics -- Influence diagnostics -- Software notes and recommendations -- Data structure -- Syntax vs. menus -- Heterogeneous residual variances for level 2 groups -- Display of the marginal covariance and correlation matrices -- Differences in model fit criteria -- Differences in tests for fixed effects -- Calculation of EBLUPs -- Tests for covariance parameters -- Reference categories for fixed factors. 4. Three-level models for clustered data : the classroom example -- The classroom study -- Overview of the classroom data analysis -- Hypothesis tests -- Analysis steps in the software procedures -- Results of the hypothesis tests -- Comparing results across the software procedures -- INterpreting parameter estimates in the final model -- Estimating the intraclass correlation coefficients (ICCs) -- Calculating predicted values -- Diagnostics for the final model -- Plots of the EBLUPs -- Residual diagnostics -- Software notes -- Setting up three-level models in HLM -- Analyzing cases with complete data -- Miscellaneous differences -- Recommendations -- 5. Models for repeated-measures data : the rat brain example -- The rat brain study -- Overview of the rat brain data analysis -- Hypothesis tests -- Analysis steps in the software procedures -- Results of hypothesis tests -- Comparing results across the software procedures -- INterpreting parameter estimates in the final model -- The implied marginal variance-covariance matrix for the final model -- Software notes -- Heterogeneous residual variances for level 1 groups -- EBLUPs for multiple random effects -- Other analytic approaches -- Kronecker product for more flexible residual covariance structures -- Fitting the marginal model -- Repeated-measures ANOVA -- Recommendations -- 6. Random coefficient models for longitudinal data : the autism example -- The autism study -- Overview of the autism data analysis -- Analysis steps in the software procedures -- Results of hypothesis tests -- Comparing results across the software procedures -- Interpreting parameter estimates in the final model -- Calculating predicted values -- Diagnostics for the final model -- Software note : computational problems with the D matrix -- Recommendations -- An alternative approach : fitting the marginal model with an unstructured covariance matrix -- 7. The dental veneer study -- Overview of the dental veneer data analysis -- Analysis steps in the software procedures -- Results of hypothesis tests -- Comparing results across the software procedures -- Interpreting parameter estimates in the final model -- The implied marginal variance-covariance matrix for the final model -- Diagnostics for the final model -- Software notes and recommendations -- ML v. REML estimation -- The ability to remove random effects from a model -- Considering alternative residual covariance structures -- Aliasing of covariance parameters -- Displaying the marginal covariance and correlation matrices -- Other analytic approaches -- Modeling the covariance structure -- The step-up vs. step-down approach to model building -- Alternative uses of baseline values for the dependent variable -- 8. Models for data with crossed random factors : the SAT score example -- The SAT score study -- Overview of the SAT score data analysis -- Analysis steps in the software procedures -- Results of hypothesis tests -- Likelihood ratio tests for random effects -- Testing the fixed year effect -- Comparing results across the software procedures -- Interpreting parameter estimates in the final model -- The implied marginal variance-covariance matrix for the final model -- Recommended diagnostics for the final model -- Software notes and additional recommendations -- Appendix A. Statistical software resources -- Appendix B. Calculation of the marginal variance-covariance matrix -- Appendix C. Acronyms / abbreviations.
Bibliography Note:Includes bibliographical references (pages 401-405) and index.
