دانلود کتاب Linear Mixed-Effects Models Using R: A Step-by-Step Approach

Linear mixed-effects models (LMMs) are an important class of statistical models that can be used to analyze correlated data. Such data are encountered in a variety of fields including biostatistics, public health, psychometrics, educational measurement, and sociology. This book aims to support a wide range of uses for the models by applied researchers in those and other fields by providing state-of-the-art descriptions of the implementation of LMMs in R. To help readers to get familiar with the features of the models and the details of carrying them out in R, the book includes a review of the most important theoretical concepts of the models. The presentation connects theory, software and applications. It is built up incrementally, starting with a summary of the concepts underlying simpler classes of linear models like the classical regression model, and carrying them forward to LMMs. A similar step-by-step approach is used to describe the R tools for LMMs. All the classes of linear models presented in the book are illustrated using real-life data. The book also introduces several novel R tools for LMMs, including new class of variance-covariance structure for random-effects, methods for influence diagnostics and for power calculations. They are included into an R package that should assist the readers in applying these and other methods presented in this text.Table of ContentsCoverLinear Mixed-Effects Models Using R - A Step-by-Step ApproachISBN 9781461438991 ISBN 9781461439004PrefaceContentsList of TablesList of FiguresList of R PanelsPart I Introduction Introduction 1.1 The Aim of the Book 1.2 Implementation of Linear Mixed-Effects Models in R 1.3 The Structure of the Book 1.4 Technical Notes Case Studies 2.1 Introduction 2.2 Age-Related Macular Degeneration Trial o 2.2.1 Raw Data o 2.2.2 Data for Analysis 2.3 Progressive Resistance Training Study o 2.3.1 Raw Data o 2.3.2 Data for Analysis 2.4 The Study of Instructional Improvement Project o 2.4.1 Raw Data o 2.4.2 Data for Analysis o 2.4.3 Data Hierarchy 2.5 The Flemish Community Attainment-Targets Study o 2.5.1 Raw Data o 2.5.2 Data for Analysis 2.6 Chapter Summary Data Exploration 3.1 Introduction 3.2 ARMD Trial: Visual Acuity o 3.2.1 Patterns of Missing Data o 3.2.2 Mean-Value Profile o 3.2.3 Sample Variances and Correlations of Visual Acuity Measurements 3.3 PRT Study: Muscle Fiber Specifi Force 3.4 SII Project: Gain in the Math Achievement Score o 3.4.1 School-Level Data o 3.4.2 Class-Level Data o 3.4.3 Pupil-Level Data 3.5 FCAT Study: Target Score 3.6 Chapter SummaryPart II Linear Models for Independent Observations Linear Models with Homogeneous Variance 4.1 Introduction 4.2 Model Specifiation o 4.2.1 Model Equation at the Level of the Observation o 4.2.2 Model Equation for All Data 4.3 Offset 4.4 Estimation o 4.4.1 Ordinary Least Squares o 4.4.2 Maximum-Likelihood Estimation o 4.4.3 Restricted Maximum-Likelihood Estimation o 4.4.4 Uncertainty in Parameter Estimates 4.5 Model Diagnostics o 4.5.1 Residuals o 4.5.2 Residual Diagnostics o 4.5.3 Influnce Diagnostics 4.6 Inference o 4.6.1 The Wald, Likelihood Ratio, and Score Tests o 4.6.2 Confidenc Intervals for Parameters 4.7 Model Reduction and Selection o 4.7.1 Model Reduction o 4.7.2 Model Selection Criteria 4.8 Chapter Summary Fitting Linear Models with Homogeneous Variance: The lm() and gls() Functions 5.1 Introduction 5.2 Specifying the Mean Structure Using a Model Formula o 5.2.1 The Formula Syntax o 5.2.2 Representation of RFormula: The terms Class 5.3 From a Formula to the Design Matrix o 5.3.1 Creating a Model Frame o 5.3.2 Creating a Design Matrix 5.4 Using the lm() and gls() Functions to Fit a Linear Model 5.5 Extracting Information from a Model-Fit Object 5.6 Tests of Linear Hypotheses for Fixed Effects 5.7 Chapter Summary ARMD Trial: Linear Model with Homogeneous Variance 6.1 Introduction 6.2 A Linear Model with Independent Residual Errors with Homogeneous Variance 6.3 Fitting a Linear Model Using the lm() Function 6.4 Fitting a Linear Model Using the gls() Function 6.5 Chapter Summary Linear Models with Heterogeneous Variance 7.1 Introduction 7.2 Model Specifiation o 7.2.1 Known Variance Weights o 7.2.2 Variance Function 7.3 Details of the Model Specificatio o 7.3.1 Groups of Variance Functions o 7.3.2 Aliasing in Variance Parameters 7.4 Estimation o 7.4.1 Weighted Least Squares o 7.4.2 Likelihood Optimization o 7.4.3 Constrained Versus Unconstrained Parameterization of the Variance Parameters o 7.4.4 Uncertainty in Parameter Estimation 7.5 Model Diagnostics o 7.5.1 Pearson Residuals o 7.5.2 Influnce Diagnostics 7.6 Inference o 7.6.1 Tests of Statistical Significanc o 7.6.2 Confidenc Intervals for Parameters 7.7 Model Reduction and Selection 7.8 Mean-Variance Models o 7.8.1 Estimation o 7.8.2 Model Diagnostics and Inference 7.9 Chapter Summary Fitting Linear Models with Heterogeneous Variance: The gls() Function 8.1 Introduction 8.2 Variance-Function Representation: The varFunc Class o 8.2.1 Variance-Function Constructors o 8.2.2 Initialization of Objects of Class varFunc 8.3 Inspecting and Modifying Objects of Class varFunc 8.4 Using the gls() Function to Fit Linear Models with Heterogeneous Variance 8.5 Extracting Information From a Model-ft Object of Class gls 8.6 Chapter Summary ARMD Trial: Linear Model with Heterogeneous Variance 9.1 Introduction 9.2 A Linear Model with Independent Residual Errors and Heterogeneous Variance o 9.2.1 Fitting the Model Using the gls() Function 9.3 Linear Models with the varPower(�) Variance-Function o 9.3.1 Fitting the Models Using the gls() Function o 9.3.2 Model-Fit Evaluation 9.4 Chapter SummaryPart III Linear Fixed-Effects Models for Correlated Data Linear Model with Fixed Effects and Correlated Errors 10.1 Introduction 10.2 Model Specificatio 10.3 Details of Model Specificatio o 10.3.1 Variance Structure o 10.3.2 Correlation Structure o 10.3.3 Serial Correlation Structures o 10.3.4 Spatial Correlation Structures 10.4 Estimation o 10.4.1 Weighted Least Squares o 10.4.2 Likelihood-Based Estimation o 10.4.3 Constrained Versus Unconstrained Parameterization of the Variance-Covariance Matrix o 10.4.4 Uncertainty in Parameter Estimation 10.5 Model Diagnostics o 10.5.1 Residual Diagnostics o 10.5.2 Influnce Diagnostics 10.6 Inference and Model Selection 10.7 Mean-Variance Models 10.8 Chapter Summary Fitting Linear Models with Fixed Effects and Correlated Errors: The gls() Function 11.1 Introduction 11.2 Correlation-Structure Representation: The corStruct Class o 11.2.1 Correlation-Structure Constructor Functions 11.3 Inspecting and Modifying Objects of Class corStruct o 11.3.1 Coefficient of Correlation Structures o 11.3.2 Semivariogram o 11.3.3 The corMatrix() Function 11.4 Illustration of Correlation Structures o 11.4.1 Compound Symmetry: The corCompSymm Class o 11.4.2 Autoregressive Structure of Order 1: The corAR1 Class o 11.4.3 Exponential Structure: The corExp Class 11.5 Using the gls() Function 11.6 Extracting Information from a Model-Fit Object of Class gls 11.7 Chapter Summary ARMD Trial: Modeling Correlated Errors for Visual Acuity 12.1 Introduction 12.2 The Model with Heteroscedastic, Independent Residual Errors Revisited o 12.2.1 Empirical Semivariogram 12.3 A Linear Model with a Compound-Symmetry Correlation Structure o 12.3.1 Model Specificatio o 12.3.2 Syntax and Results 12.4 Heteroscedastic Autoregressive Residual Errors o 12.4.1 Model Specificatio o 12.4.2 Syntax and Results 12.5 General Correlation Matrix for Residual Errors o 12.5.1 Model Specificatio o 12.5.2 Syntax and Results 12.6 Model-Fit Diagnostics o 12.6.1 Scatterplots of Raw Residuals o 12.6.2 Scatterplots of Pearson Residuals o 12.6.3 Normalized Residuals 12.7 Inference About the Mean Structure o 12.7.1 Models with the General Correlation Structure and Power Variance Function o 12.7.2 Syntax and Results 12.8 Chapter SummaryPart IV Linear Mixed-Effects Models Linear Mixed-Effects Model 13.1 Introduction 13.2 The Classical Linear Mixed-Effects Model o 13.2.1 Specificatio at a Level of a Grouping Factor o 13.2.2 Specificatio for All Data 13.3 The Extended Linear Mixed-Effects Model 13.4 Distributions Define by the y and b Random Variables o 13.4.1 Unconditional Distribution of Random Effects o 13.4.2 Conditional Distribution of y Given the Random Effects o 13.4.3 Additional Distributions Define by y and b 13.5 Estimation o 13.5.1 The Marginal Model Implied by the Classical Linear Mixed-Effects Model o 13.5.2 Maximum-Likelihood Estimation o 13.5.3 Penalized Least Squares o 13.5.4 Constrained Versus Unconstrained Parameterization of the Variance-Covariance Matrix o 13.5.5 Uncertainty in Parameter Estimation o 13.5.6 Alternative Estimation Approaches 13.6 Model Diagnostics o 13.6.1 Normality of Random Effects o 13.6.2 Residual Diagnostics o 13.6.3 Influnce Diagnostics 13.7 Inference and Model Selection o 13.7.1 Testing Hypotheses About the Fixed Effects o 13.7.2 Testing Hypotheses About the Variance-Covariance Parameters o 13.7.3 Confidenc Intervals for Parameters 13.8 Mean-Variance Models o 13.8.1 Single-Level Mean-Variance Linear Mixed-Effects Models o 13.8.2 Multilevel Hierarchies o 13.8.3 Inference 13.9 Chapter Summary Fitting Linear Mixed-Effects Models: The lme() Function 14.1 Introduction 14.2 Representation of a Positive-Definit Matrix: The pdMat Class o 14.2.1 Constructor Functions for the pdMat Class o 14.2.2 Inspecting and Modifying Objects of Class pdMat 14.3 Random-Effects Structure Representation: The reStruct class o 14.3.1 Constructor Function for the reStruct Class o 14.3.2 Inspecting and Modifying Objects of Class reStruct 14.4 The Random Part of the Model Representation: The lmeStruct Class 14.5 Using the Function lme() to Specify and Fit Linear Mixed-Effects Models 14.6 Extracting Information from a Model-Fit Object of Class lme 14.7 Tests of Hypotheses About the Model Parameters 14.8 Chapter Summary Fitting Linear Mixed-Effects Models: The lmer() Function 15.1 Introduction 15.2 Specificatio of Models with Crossed and Nested Random Effects o 15.2.1 A Hypothetical Experiment with the Effects of Plates Nested Within Machines o 15.2.2 A Hypothetical Experiment with the Effects of Plates Crossed with the Effects of Machines o 15.2.3 General Case 15.3 Using the Function lmer() to Specify and Fit Linear Mixed-Effects Models o 15.3.1 The lmer() Formula 15.4 Extracting Information from a Model-Fit Object of Class mer 15.5 Tests of Hypotheses About the Model Parameters 15.6 Illustration of Computations 15.7 Chapter Summary ARMD Trial: Modeling Visual Acuity 16.1 Introduction 16.2 A Model with Random Intercepts and Homogeneous Residual Variance o 16.2.1 Model Specificatio o 16.2.2 R Syntax and Results 16.3 A Model with Random Intercepts and the varPower(�) Residual Variance-Function o 16.3.1 Model Specificatio o 16.3.2 R Syntax and Results o 16.3.3 Diagnostic Plots 16.4 Models with Random Intercepts and Slopes and the varPower(�) Residual Variance-Function o 16.4.1 Model with a General Matrix D o 16.4.2 Model with a Diagonal Matrix D o 16.4.3 Model with a Diagonal Matrix and a Constant Treatment Effect D 16.5 An Alternative Residual Variance Function: varIdent(�) 16.6 Testing Hypotheses About Random Effects o 16.6.1 Test for Random Intercepts o 16.6.2 Test for Random Slopes 16.7 Analysis Using the Function lmer() o 16.7.1 Basic Results o 16.7.2 Simulation-Based p-Values: The simulate.mer() Method o 16.7.3 Test for Random Intercepts o 16.7.4 Test for Random Slopes 16.8 Chapter Summary PRT Trial: Modeling Muscle Fiber Specific-orce 17.1 Introduction 17.2 A Model with Occasion-Specifi Random Intercepts for Type-1 Fibers o 17.2.1 Model Specificatio o 17.2.2 R Syntax and Results 17.3 A Mean-Variance Model with Occasion-Specifi Random Intercepts for Type-1 Fibers o 17.3.1 R Syntax and Results 17.4 A Model with Heteroscedastic Fiber-Type�Occasion-Specifc Random Intercepts o 17.4.1 Model Specificatio o 17.4.2 R Syntax and Results 17.5 A Model with Heteroscedastic Fiber-Type Occasion-Specifi Random Intercepts (Alter� native Specifcation) o 17.5.1 Model Specificatio o 17.5.2 R Syntax and Results 17.6 A Model with Heteroscedastic Fiber-Type�Occasion-Specifi Random Intercepts and a Structured Matrix D o 17.6.1 Model Specificatio o 17.6.2 R Syntax and Results 17.7 A Model with Homoscedastic Fiber-Type�Occasion-Specifi Random Intercepts and a Structured Matrix D o 17.7.1 Model Specificatio o 17.7.2 R Syntax and Results 17.8 A Joint Model for Two Dependent Variables o 17.8.1 Model Specificatio o 17.8.2 R Syntax and Results 17.9 Chapter Summary SII Project: Modeling Gains in Mathematics Achievement-Scores 18.1 Introduction 18.2 A Model with Fixed Effects for Schooland Pupil-Specifi Covariates and Random Intercepts for Schools and Classes o 18.2.1 Model Specificatio o 18.2.2 R Syntax and Results 18.3 A Model with an Interaction Between Schooland Pupil-Level Covariates o 18.3.1 Model Specificatio o 18.3.2 R Syntax and Results 18.4 A Model with Fixed Effects of Pupil-Level Covariates Only o 18.4.1 Model Specificatio o 18.4.2 R Syntax and Results 18.5 A Model with a Third-Degree Polynomial of a Pupil-Level Covariate in the Mean Structure o 18.5.1 Model Specificatio o 18.5.2 R Syntax and Results 18.6 A Model with a Spline of a Pupil-Level Covariate in the Mean Structure o 18.6.1 Model Specificatio o 18.6.2 R Syntax and Results 18.7 The Final Model with Only Pupil-Level Variables in the Mean Structure o 18.7.1 Model Specificatio o 18.7.2 R Syntax and Results 18.8 Analysis Using the Function lmer() 18.9 Chapter Summary FCAT Study: Modeling Attainment-Target Scores 19.1 Introduction 19.2 A Fixed-Effects Linear Model Fitted Using the Function lm() o 19.2.1 Model Specificatio o 19.2.2 R Syntax and Results 19.3 A Linear Mixed-Effects Model with Crossed Random Effects Fitted Using the Function lmer() o 19.3.1 Model Specificatio o 19.3.2 R Syntax and Results 19.4 A Linear Mixed-Effects Model with Crossed Random Effects Fitted Using the Function lme() 19.5 A Linear Mixed-Effects Model with Crossed Random Effects and Heteroscedastic Residual Errors Fitted Using lme() o 19.5.1 Model Specificatio o 19.5.2 R Syntax and Results 19.6 Chapter Summary Extensions of the R Tools for Linear Mixed-Effects Models 20.1 Introduction 20.2 The New pdMatClass: pdKronecker o 20.2.1 Creating Objects of Class pdKronecker o 20.2.2 Extracting Information from Objects of Class pdKronecker 20.3 Influnce Diagnostics o 20.3.1 Preparatory Steps o 20.3.2 Influnce Diagnostics 20.4 Simulation of the Dependent Variable 20.5 Power Analysis o 20.5.1 Post Hoc Power Calculations o 20.5.2 A Priori Power Calculations for a Hypothetical Study o 20.5.3 Power Evaluation Using SimulationsAcronymsReferencesFunction IndexSubject Index