Applied Linear Regression for Longitudinal Data: With an Emphasis on Missing Observations

Description

This book introduces best practices in longitudinal data analysis at intermediate level, with a minimum number of formulas without sacrificing depths. It meets the need to understand statistical concepts of longitudinal data analysis by visualizing important techniques instead of using abstract mathematical formulas. Different solutions such as multiple imputation are explained conceptually and consequences of missing observations are clarified using visualization techniques. Key features include the following • Provides datasets and examples online • Gives state-of-the-art methods of dealing with missing observations in a non-technical way with a special focus on sensitivity analysis • Conceptualises the analysis of comparative (experimental and observational) studies It is the ideal companion for researcher and students in epidemiological, health, and social and behavioral sciences working with longitudinal studies without a mathematical background. Cover Half Title Series Page Title Page Copyright Page Dedication Table of Contents Preface Acknowledgements Short Description of Research and Simulation Studies Cross-sectional Nutrition study (first used in Section 2.1.1) Cross-sectional Nutrition study with missing observations(first used in Section 2.7.1) Longitudinal Violent-behaviour study (first used in Section 2.3.1) Longitudinal Proximity study (first used in Section 2.4.1) Longitudinal Growth study (first used in Section 3.1.2) Longitudinal Alzheimer study (first used in Section 3.5.1) Longitudinal Salsolinol study (first used in Section 4.2.3) Longitudinal Beating the Blues study (first used in Section 5.2.1) Longitudinal Well-being study (first used in Section 5.2.2) Chapter 1: Scientific Framework of Data Analysis 1.1 Validation Modelling: Comparative Studies 1.2 Predictive Modelling: Predicting a Future Outcome 1.3 Missing Observations 1.3.1 Missing Data Mechanisms 1.3.2 Patterns of Missing Data 1.3.3 Randomised versus Nonrandomised Studies 1.3.4 Concluding Remarks 1.4 Assignments 1.4.1 Assignment 1.4.2 Assignment 1.4.3 Assignment 1.4.4 Assignment Chapter 2: Revisiting and Shortcomings of Standard Linear Regression Models 2.1 Standard Linear Regression Modelling 2.1.1 Formulation of the Research Question: The Cross-Sectional Nutrition Study 2.1.2 The Concept of Pearson (Product-Moment) Correlation 2.1.3 Specification of a Standard Linear Regression Model for the Nutrition Study 2.1.4 Interpretation of the Model Parameters 2.2 Multiple Linear Regression (MLR) Modelling 2.2.1 Specification of a Multiple Linear Regression Model for the Nutrition Study 2.2.2 Interpretation of the Model Parameters of the Nutrition Study 2.3 MLR Conditional on the Subjects 2.3.1 A Longitudinal Case Study: Violent-Behaviour Study 2.3.2 Intermezzo: Dummy Variables 2.3.3 Analysis of Violent Data 2.4 Multiple Piecewise Linear Regression 2.4.1 A Comparative Longitudinal Study: Proximity Study 2.4.2 Specification of the Multiple Piecewise-Linear Regression Model 2.5 Assumptions of the MLR with Uncorrelated Errors 2.5.1 Linearity Assumption 2.5.2 Normality Assumption 2.5.3 The Independence Assumption 2.6 Issues of MLR for a Longitudinal Study 2.6.1 Implication of the Independence Assumption 2.6.2 Shortcomings of the OLS Model 2.7 Handling Missing Observations in Cross-Sectional Designs 2.7.1 Simple Methods 2.7.1.1 Complete-Case Analysis 2.7.1.2 Marginal Mean Substitution 2.7.1.3 Conditional Mean Substitution 2.7.1.4 Stochastic Regression Imputation 2.7.2 Advanced Methods: Direct Likelihood and Multiple Imputation 2.7.3 Generating Imputations 2.7.4 Comparison of Methods 2.7.4.1 Partly Missing Dependent Variable Related to Fully Observed Independent Variables 2.7.4.2 Partly Missing Dependent Variable Related to the Dependent Variable Itself 2.7.4.3 Partly Missing Independent Variable Unrelated to Fully Observed Dependent Variable 2.7.4.4 Partly Missing Independent Variable Related to the Dependent Variable 2.7.5 Conclusion and Recommendations 2.8 Assignments 2.8.1 Assignment 2.8.2 Assignment 2.8.3 Assignment 2.8.4 Assignment 2.8.5 Assignment 2.8.6 Assignment 2.8.7 Assignment 2.8.8 Assignment 2.8.9 Assignment 2.8.10 Assignment 2.8.11 Assignment 2.8.12 Assignment 2.8.13 Assignment 2.8.14 Assignment 2.8.15 Assignment 2.8.16 Assignment 2.8.17 Assignment 2.8.18 Assignment 2.8.19 Assignment Chapter 3: An Introduction to the Analysis of Longitudinal Data 3.1 Examples of Multilevel Designs 3.1.1 Cross-Sectional Multilevel Designs 3.1.1.1 Performance of Pupils in Schools 3.1.1.2 Cross-Country Comparison: Cross-Sectional Design 3.1.2 Longitudinal Designs 3.1.2.1 Cross-Country Comparison: Longitudinal Design 3.1.2.2 Growth Study 3.1.2.3 Interpersonal Proximity Study 3.2 Comparison of the Multilevel Linear Regression Model with the Standard (OLS) Linear Regression 3.2.1 Age-Specific Sex Effect 3.2.2 Sex-Specific Age Effect 3.3 Accounting for the Multilevel Structure 3.3.1 Formulation of the Problem: A Marginal and Subject-Specific Representation 3.3.2 Fixed or Random Factor 3.3.3 Treating Subjects as a Random Factor 3.3.3.1 Random-Intercept Models 3.3.3.2 Random-Slope Models 3.3.3.3 Serial Correlation 3.3.3.4 Example: Random-Effect Model or Marginal Model With and Without Serial Correlation 3.4 Marginal Models 3.5 Handling Missing Observations in Longitudinal Designs 3.5.1 Patterns of Missing Data in Longitudinal Studies 3.5.2 Complete-Case Analysis in Longitudinal Studies 3.5.3 Last Observation Carried Forward in Longitudinal Studies 3.5.4 Advanced Missing Data Methods in Longitudinal Studies 3.5.4.1 Missing Observations in the Dependent Variable Only 3.5.4.2 Missing Observations in the Independent Variables Only 3.5.4.3 Missing Observations in the Dependent and Independent Variables 3.5.5 Conclusion and Recommendations 3.6 Assignments 3.6.1 Assignment 3.6.2 Assignment 3.6.3 Assignment 3.6.4 Assignment 3.6.5 Assignment 3.6.6 Assignment 3.6.7 Assignment 3.6.8 Assignment Chapter 4: Model Building for Longitudinal Data Analysis 4.1 Basic Guidelines 4.1.1 Step 1. Exploratory Analysis 4.1.2 Step 2. Procedure for Choosing the Best Variance-Covariance Structure 4.1.3 Step 3. Interpretation of the Regression Parameter Estimates 4.2 Analysis of Some Case Studies 4.2.1 Best Practice for the Analysis of Proximity Data 4.2.1.1 Step 1. Exploratory Analysis 4.2.1.2 Step 2. Procedure for Choosing the Best Variance-Covariance Structure 4.2.1.3 Step 3. Interpretation of the Parameter Estimates Bonferroni Correction Sidak-Bonferroni Correction 4.2.2 Best Practice for the Analysis of the Growth Study 4.2.3 Best Practice for the Analysis of the Salsolinol Study 4.3 Multiple Imputation of Missing Observations: Building Imputation Models 4.3.1 Data Format: Wide versus Long 4.3.2 Imputation in Wide Format: The Classical Approach 4.3.3 Imputation in a Long Format: The Multilevel Approach 4.4 Summary 4.5 Assignments 4.5.1 Assignment 4.5.2 Assignment 4.5.3 Assignment 4.5.4 Assignment 4.5.5 Assignment 4.5.6 Assignment 4.5.7 Assignment Chapter 5: Analysis of a Pre/Post Measurement Design 5.1 Best Practice for the Analysis of a Pre/Post Measurement Design 5.1.1 The Analysis of Covariance (ANCOVA) Approach 5.1.2 The Gain-Score Approach 5.1.3 A Random Intercept Representation of the Gain-Score and ANCOVA Approach 5.2 Case Studies 5.2.1 An Example of a Randomised Clinical Trial: Beating the Blues 5.2.2 An Example of a Nonexperimental Study: Well-Being, a Life-Event Study 5.3 Handling Missing Observations in Pre/Post Measurement Designs 5.3.1 The ANCOVA Approach 5.3.2 The Gain-Score Approach 5.4 Assignments 5.4.1 Assignment 5.4.2 Assignment 5.4.3 Assignment 5.4.4 Assignment 5.4.5 Assignment 5.4.6 Assignment 5.4.7 Assignment Chapter 6: Analysis of Longitudinal Life-Event Studies 6.1 Best Practice for the Analysis of a Longitudinal Life-Event Study 6.1.1 Choosing between the Gain-Score and ANCOVA Approach 6.1.2 Gain-Score Approach of the Well-Being Study 6.1.2.1 Sensitivity Analysis for Gain-Score Approach using Multiple Imputation 6.1.3 ANCOVA Approach of the Well-Being Study 6.1.3.1 Sensitivity Analysis for ANCOVA Approach Using Multiple Imputation 6.2 Extension to More Than Three Time Points and Groups 6.2.1 Interpretation of the Regression Parameters of a Gain-Score Model 6.2.2 Interpretation of the Regression Parameters of an ANCOVA-Model 6.3 Assignments 6.3.1 Assignment 6.3.2 Assignment 6.3.3 Assignment 6.3.4 Assignment 6.3.5 Assignment 6.3.6 Assignment Note Chapter 7: Analysis of Longitudinal Experimental Studies 7.1 Best Practice for the Analysis of Beating the Blues Trial 7.2 Assignments 7.2.1 Assignment 7.2.2 Assignment 7.2.3 Assignment References Index