Longitudinal Data Analysis for the Behavioral Sciences Using R

✍ Scribed by Jeffrey D. Long

• Publisher: SAGE Publications, Inc
• Year: 2011
• Tongue: English
• Leaves: 766
• Edition: 1
• Category: Library

✦ Table of Contents

Dedication
Title
Copyright
Brief Contents
Detailed Contents
About the Author
Preface
1 Introduction
1.1 Statistical Computing
1.2 Preliminary Issues
1.2.1 Means Versus Correlations
1.2.2 Measurement Issues
1.2.3 Response Variable Assumptions
1.3 Conceptual Overview of Linear Mixed Effects Regression
1.3.1 Goals of Inference
1.3.2 Random Effects
1.3.3 How Important Are Random Effects?
1.4 Traditional Approaches
1.5 MPLS Data Set
1.6 Statistical Strategy
1.7 LMER and Multimodel Inference
1.7.1 Statistical Hypotheses
1.8 Overview of the Remainder of the Book
2 Brief Introduction to R
2.1 Obtaining and Installing R
2.2 Functions and Packages
2.3 Essential Syntax
2.3.1 Prompt Versus Script Files
2.3.2 Input and Output Appearance in This Book
2.3.3 Quitting R
2.3.4 Terminating a Process
2.3.5 Basic Calculations
2.3.6 Objects
2.3.7 Concatenation
2.3.8 Statistical Functions
2.4 Data Types
2.4.1 Missing Values
2.5 Matrices, Data Frames, and Lists
2.5.1 Vector
2.5.2 Matrix
2.5.3 Data Frame
2.5.4 List
2.6 Indexing
2.6.1 Matrix and Data Frame
2.6.2 Vector
2.6.3 List
2.6.4 Sorting
2.6.5 Recoding
2.6.6 Saving Objects
2.6.7 Loading and Listing Objects
2.7 User-Defined Functions
2.8 Repetitive Operations
2.8.1 rdply()
2.8.2 for() Loop
2.9 Linear Regression
2.10 Getting Help
2.11 Summary of Functions
3 Data Structures and Longitudinal Analysis
3.1 Longitudinal Data Structures
3.1.1 Wide Format
3.1.2 Long Format
3.2 Reading an External File
3.2.1 Reading a Text File With read.table()
3.2.2 Displaying the Data Frame
3.2.3 Converting and Recoding Variables
3.3 Basic Statistics for Wide-Format Data
3.3.1 Means, Variances, and Correlations
3.3.2 Missing Data Statistics
3.3.3 Conditioning on Static Predictors
3.4 Reshaping Data
3.4.1 Wide to Long Format
3.4.2 Long to Wide Format
3.5 Basic Statistics for Long-Format Data
3.5.1 Means, Variances, and Correlations
3.5.2 Missing Data Statistics
3.5.3 Conditioning on Static Predictors
3.6 Data Structures and Balance on Time
3.7 Missing Data in LMER Analysis
3.7.1 Retain or Omit Missing Data Rows?
3.8 Missing Data Concepts
3.8.1 Missing Completely at Random
3.8.2 Missing at Random
3.8.3 Not Missing at Random
3.8.4 Missing Data Mechanisms and Statistical Analysis
3.8.5 Missing Data Simulation
3.8.6 LMER Analysis
3.9 Extensions to More Complex Data Structures
3.9.1 Multiple Dynamic Variables
3.9.2 Unbalanced Data
4 Graphing Longitudinal Data
4.1 Graphing and Statistical Strategy
4.2 Graphing With ggplot2
4.2.1 Graph Components
4.2.2 Layering
4.3 Graphing Individual-Level Curves
4.3.1 Superimposed Individual Curves
4.3.2 Facet Plots of Individual Curves
4.3.3 Selecting Subsets
4.3.4 Graphing Fitted Curves
4.4 Graphing Group-Level Curves
4.4.1 Curve of the Means
4.4.2 Graphing Fitted Curves
4.4.3 Graphing Individual-Level and Group-Level Curves
4.5 Conditioning on Static Predictors
4.5.1 Categorical Static Predictors
4.5.2 Quantitative Static Predictors
4.6 Customizing Graphs
4.6.1 Customizing Axes
4.6.2 Customizing Facets
4.6.3 Customizing the Legend
4.7 Summary of ggplot2 Components
5 Introduction to Linear Mixed Effects Regression
5.1 Traditional Regression and the Linear Model
5.2 Regression Examples
5.2.1 Single Quantitative Predictor
5.2.2 Analysis of Covariance
5.2.3 Interaction Model
5.3 Linear Mixed Effects Regression
5.3.1 LMER as a Multilevel Model
5.3.2 Random Effects as Errors
5.3.3 Assumptions Regarding Random Effects and Random Error
5.3.4 Random Effects and Correlated Observations
5.4 Estimating the LMER Model
5.4.1 Time as a Predictor
5.4.2 Anchoring the Intercept
5.5 LMER With Static Predictors
5.5.1 Intercept Effects
5.5.2 Slope and Intercept Effects
5.5.3 Initial Status as a Static Predictor
5.5.4 Extensions to More Complex Models
5.5.5 Summary of lmer() Syntax
5.6 Additional Details of LMER
5.6.1 General Form of the LMER Model
5.6.2 Variance-Covariance Matrix Among Repeated Measures
5.6.3 Importance of Random Effects
5.6.4 Working With Matrices in R
6 Overview of Maximum Likelihood Estimation
6.1 Conceptual Overview
6.2 Maximum Likelihood and LM
6.2.1 Several Unknown Parameters
6.2.2 Exhaustive Search and Numerical Methods
6.2.3 Restricted Maximum Likelihood
6.2.4 Extracting the Log-Likelihood and the Deviance
6.2.5 Comparing Models
6.3 Maximum Likelihood and LMER
6.3.1 LMER Deviance Function
6.3.2 ML Standard Errors
6.3.3 Additional SE Details
6.3.4 Default lmer() Output
6.3.5 Assumptions Regarding Missing Data
6.4 Additional Details of ML for LMER
7 Multimodel Inference and Akaike’s Information Criterion
7.1 Objects of Inference
7.2 Statistical Strategy
7.3 AIC and Predictive Accuracy
7.3.1 Extension to LMER
7.3.2 AIC Corrected
7.4 AICc and Effect Size
7.4.1 Delta
7.4.2 Weight of Evidence
7.4.3 Evidence Ratio
7.5 AICc and Multimodel Inference
7.5.1 Contrast With NHST
7.6 Example of Multimodel Analysis
7.6.1 Guidelines for Model Formulation
7.6.2 Example Set of Models
7.6.3 Bar Graphs of Results
7.6.4 Interpretation of Global Results
7.6.5 Details of Models
7.6.6 Comments Regarding the Multimodel Approach
7.6.7 Post Hoc Models
7.7 Example Write-up
7.8 Parametric Bootstrap of the Evidence Ratio
7.8.1 Performing the Parametric Bootstrap
7.8.2 Caveats Regarding the Parametric Bootstrap
7.9 Bayesian Information Criterion
8 Likelihood Ratio Test
8.1 Why Use the Likelihood Ratio Test?
8.2 Fisher and Neyman-Pearson
8.3 Evaluation of Two Nested Models
8.3.1 Calibrating p-Values Based on Predictive Accuracy
8.4 Approaches to Testing Multiple Models
8.5 Step-Up Approach
8.5.1 Order of Testing
8.5.2 Comments on the Step-Up Approach
8.6 Top-Down Approach
8.7 Comparison of Approaches
8.8 Parametric Bootstrap
8.8.1 Comments on the Parametric Bootstrap
8.9 Planning a Study
8.9.1 Comment on the Procedure
9 Selecting Time Predictors
9.1 Selection of Time Transformations
9.2 Group-Level Selection of Time Transformations
9.3 Multimodel Inference
9.3.1 Analysis Without Static Predictors
9.3.2 Analysis With Static Predictors
9.4 Likelihood Ratio Test
9.4.1 Analysis Without Static Predictors
9.4.2 Analysis With Static Predictors
9.5 Cautions Concerning Group-Level Selection
9.6 Subject-Level Selection of Time Transformations
9.6.1 Level 1 Polynomial Model
9.6.2 Missing Data
9.6.3 Subject-Level Fits
9.6.4 Pooled Measures of Fit
9.6.5 Clustering of Subject Curves
10 Selecting Random Effects
10.1 Automatic Selection of Random Effects
10.2 Random Effects and Variance Components
10.2.1 Restricted Maximum Likelihood
10.2.2 Random Effects and Correlated Data
10.3 Descriptive Methods
10.3.1 OLS Estimates
10.3.2 Examining Residuals
10.3.3 Residuals and Normality
10.4 Inferential Methods
10.4.1 Likelihood Ratio Test
10.4.2 AICc
10.5 Variance Components and Static Predictors
10.6 Predicted Random Effects
10.6.1 Evaluating the Normality Assumption
10.6.2 Predicted Values for an Individual
11 Extending Linear Mixed Effects Regression
11.1 Graphing Fitted Curves
11.2 Static Predictors With Multiple Levels
11.2.1 Evaluating Sets of Dummy Variables
11.2.2 Evaluating Individual Dummy Variables
11.3 Interactions Among Static Predictors
11.3.1 Static Predictor Interactions With lmer()
11.3.2 Interpreting Interactions
11.3.3 Nonlinear Static Predictor Effects
11.4 Indexes of Absolute Effect Size in LMER
11.4.1 Alternative Indexes
11.5 Additional Transformations
11.5.1 Time Units and Variances
11.5.2 Transforming for Standardized Change
11.5.3 Standardizing and Compositing
12 Modeling Nonlinear Change
12.1 Data Set and Analysis Strategy
12.2 Global Versus Local Models
12.3 Polynomials
12.3.1 Mean-Corrected Polynomials
12.3.2 Orthogonal Polynomials
12.3.3 The poly() Function
12.3.4 Polynomial Example
12.4 Alternatives to Polynomials
12.5 Trigonometric Functions
12.6 Fractional Polynomials
12.6.1 First-Order Fractional Polynomials
12.6.2 Second-Order Fractional Polynomials
12.6.3 Static Predictors
12.6.4 Caveats Regarding the Use of Fractional Polynomials
12.7 Spline Models
12.7.1 Linear Spline Models
12.7.2 Higher Order Regression Splines
12.8 Additional Details
12.8.1 Computing Orthogonal Polynomials
12.8.2 General Form of Fractional Polynomials*
13 Advanced Topics
13.1 Dynamic Predictors
13.1.1 Dynamic Predictor as a Single Effect
13.1.2 Dynamic Predictor With a Time Variable
13.2 Multiple Response Variables
13.2.1 Reading and Mathematics
13.2.2 Analyzing Two Responses With lmer()
13.3 Additional Levels of Nesting
13.3.1 Three-Level Model
13.3.2 Static Predictors in Three-Level Models
Appendix: Soft Introduction to Matrix Algebra
A.1 Matrices
A.2 Transpose
A.3 Matrix Addition
A.4 Multiplication of a Matrix by a Scalar
A.5 Matrix Multiplication
A.6 Determinant
A.7 Inverse
A.8 Matrix Algebra and R Functions
References
Author Index
Subject Index