Linear mixed models : a practical guide using statistical software

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Detalles Bibliográficos
Autor principal: West, Brady T.
Otros Autores: Welch, Kathleen B., Gatecki, Andrzej T., Gillespie, Brenda W., 1950-
Formato: Libro
Lenguaje:English
Publicado: : , .
Edición:Second edition.
Materias:
Modelos lineales (Estadística) > Procesamiento de datos.
Tabla de Contenidos:
  • 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.

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