Methods and Applications of Longitudinal Data Analysis

Methods and Applications of Longitudinal Data Analysis describes methods for the analysis of longitudinal data in the medical, biological and behavioral sciences. It introduces basic concepts and functions including a variety of regression models, and their practical applications across many areas of research. Statistical procedures featured within the text include:

• descriptive methods for delineating trends over time
• linear mixed regression models with both fixed and random effects
• covariance pattern models on correlated errors
• generalized estimating equations
• nonlinear regression models for categorical repeated measurements
• techniques for analyzing longitudinal data with non-ignorable missing observations

Emphasis is given to applications of these methods, using substantial empirical illustrations, designed to help users of statistics better analyze and understand longitudinal data.

Methods and Applications of Longitudinal Data Analysis equips both graduate students and professionals to confidently apply longitudinal data analysis to their particular discipline. It also provides a valuable reference source for applied statisticians, demographers and other quantitative methodologists.

• From novice to professional: this book starts with the introduction of basic models and ends with the description of some of the most advanced models in longitudinal data analysis
• Enables students to select the correct statistical methods to apply to their longitudinal data and avoid the pitfalls associated with incorrect selection
• Identifies the limitations of classical repeated measures models and describes newly developed techniques, along with real-world examples.

Statisticians, demographers, policymakers and insurance companies involved in longitudinal data analysis, as well as professionals, academics and graduate students of various disciplines including sociology, population studies, economics, psychology, geography and political science, biology, medicine and public health. Applied statisticians and other quantitative methodologists can also use the book as a convenient reference.

• Biography
• Preface
• Chapter 1: Introduction
  • Abstracts
  • 1.1. What is longitudinal data analysis?
  • 1.2. History of longitudinal analysis and its progress
  • 1.3. Longitudinal data structures
  • 1.4. Missing data patterns and mechanisms
  • 1.5. Sources of correlation in longitudinal processes
  • 1.6. Time scale and the number of time points
  • 1.7. Basic expressions of longitudinal modeling
  • 1.8. Organization of the book and data used for illustrations
• Chapter 2: Traditional methods of longitudinal data analysis
  • Abstract
  • 2.1. Descriptive approaches
  • 2.2. Repeated measures ANOVA
  • 2.3. Repeated measures MANOVA
  • 2.4. Summary
• Chapter 3: Linear mixed-effects models
  • Abstract
  • 3.1. Introduction of linear mixed models: three cases
  • 3.2. Formalization of linear mixed models
  • 3.3. Inference and estimation of fixed effects in linear mixed models
  • 3.4. Trend analysis
  • 3.5. Empirical illustrations: application of two linear mixed models
  • 3.6. Summary
• Chapter 4: Restricted maximum likelihood and inference of random effects in linear mixed models
  • Abstract
  • 4.1. Overview of Bayesian inference
  • 4.2. Restricted maximum likelihood estimator
  • 4.3. Computational procedures
  • 4.4. Approximation of random effects in linear mixed models
  • 4.5. Hypothesis testing on variance component G
  • 4.6. Empirical illustrations: linear mixed models with REML
  • 4.7. Summary
• Chapter 5: Patterns of residual covariance structure
  • Abstract
  • 5.1. Residual covariance pattern models with equal spacing
  • 5.2. Residual covariance pattern models with unequal time intervals
  • 5.3. Comparison of covariance structures
  • 5.4. Scaling of time as a classification factor
  • 5.5. Least squares means, local contrasts, and local tests
  • 5.6. Empirical illustrations: estimation of two linear regression models
  • 5.7. Summary
• Chapter 6: Residual and influence diagnostics
  • Abstract
  • 6.1. Residual Diagnostics
  • 6.2. Influence Diagnostics
  • 6.3. Empirical Illustrations on Influence Diagnostics
  • 6.4. Summary
• Chapter 7: Special topics on linear mixed models
  • Abstract
  • 7.1. Adjustment of baseline response in longitudinal data analysis
  • 7.2. Misspecification of the assumed distribution of random effects
  • 7.3. Pattern-mixture modeling
  • 7.4. Summary
• Chapter 8: Generalized linear mixed models on nonlinear longitudinal data
  • Abstract
  • 8.1. A brief overview of generalized linear models
  • 8.2. Generalized linear mixed models and statistical inferences
  • 8.3. Methods of estimating parameters in generalized linear mixed models
  • 8.4. Nonlinear predictions and retransformation of random components
  • 8.5. Some popular specific generalized linear mixed models
  • 8.6. Summary
• Chapter 9: Generalized estimating equations (GEEs) models
  • Abstract
  • 9.1. Basic specifications and inferences of GEEs
  • 9.2. Other GEE approaches
  • 9.3. Relationship between marginal and random-effects models
  • 9.4. Empirical illustration: effect of marital status on disability severity in older Americans
  • 9.5. Summary
• Chapter 10: Mixed-effects regression model for binary longitudinal data
  • Abstract
  • 10.1. Overview of Conventional Logistic and Probit Regression Models
  • 10.2. Specification of Random Intercept Logistic Regression Model
  • 10.3. Specification of Random Coefficient Logistic Regression Model
  • 10.4. Inference of Mixed-Effects Logit Model
  • 10.5. Approximation of Variance for Predicted Response Probability
  • 10.6. Interpretability of Regression Coefficients and Odds Ratios
  • 10.7. Computation of Conditional Effect and Conditional Odds Ratio for a Covariate
  • 10.8. Empirical Illustration: Effect of Marital Status on Probability of Disability Among Older Americans
  • 10.9. Summary
• Chapter 11: Mixed-effects multinomial logit model for nominal outcomes
  • Abstract
  • 11.1. Overview of multinomial logistic regression model
  • 11.2. Mixed-effects multinomial logit models and nonlinear predictions
  • 11.3. Estimation of fixed and random effects
  • 11.4. Approximation of variance–covariance matrix on probabilities
  • 11.5. Conditional effects of covariates on probability scale
  • 11.6. Empirical illustration: marital status and longitudinal trajectories of disability and mortality among older Americans
  • 11.7. Summary
• Chapter 12: Longitudinal transition models for categorical response data
  • Abstract
  • 12.1. Overview of two-time multinomial transition modeling
  • 12.2. Longitudinal transition models with only fixed effects
  • 12.3. Mixed-effects multinomial logit transition models
  • 12.4. Empirical illustration: predicted transition probabilities in functional status and marital status among older Americans
  • 12.5. Summary
• Chapter 13: Latent growth, latent growth mixture, and group-based models
  • Abstract
  • 13.1. Overview of structural equation modeling
  • 13.2. Latent growth model
  • 13.3. Latent growth mixture model
  • 13.4. Group-based model
  • 13.5. Empirical illustration: effect of marital status on ADL count among older Americans revisited
  • 13.6. Summary
• Chapter 14: Methods for handling missing data
  • Abstract
  • 14.1. Mathematical definitions of MCAR, MAR, and MNAR
  • 14.2. Methods handling missing at random
  • 14.3. Methods handling missing not at random
  • 14.4. Summary
• Appendix A: Orthogonal polynomials
• Appendix B: The delta method
• Appendix C: Quasi-likelihood functions and properties
• Appendix D: Model specification and SAS program for random coefficient multinomial logit model on health state among older Americans
• References
• Subject Index