Studies in which data are collected repeatedly on a sample of
individuals over time (or some other condition) are ubiquitous in the
health, social, and behavioral sciences; agricultural and biological
sciences; education; economics; and business. Questions of interest in
the context of such longitudinal data often focus on patterns of
change of outcomes of interest over time and on elucidating factors
that are associated with patterns of change in relevant populations of
individuals. Because the study of change is so pervasive across almost
all disciplines, statistical models and methods for the analysis of
longitudinal data have become essential tools for practicing
statisticians. Moreover, as studies and technologies giving rise to
longitudinal data become increasingly complex, development of new
methodology continues to be an active research area.
This course will provide an overview of statistical models and methods
for longitudinal data analysis. Fundamental modeling strategies and
methodological developments will be presented in detail and their
properties studied via theoretical arguments carried out at a
heuristic level. Implementation in R and SAS will also be discussed.
The course will begin with a conceptual framework for thinking about
longitudinal data, followed by a brief review of "classical" methods,
whose limitations will be highlighted. The rest of the course will
focus on more modern methods. Selected advanced topics will also be
covered. This course is background for study of areas such as
semiparametric theory, functional data analysis, and analysis in the
presence of missing data.
Course prerequisites
ST 522,
Statistical Theory II, and
ST 552,
Linear Models and Variance Components, or equivalents. Students should also
have been exposed to SAS and R and have reasonable proramming skills.
Course topics

Introduction and Motivation:
Objectives, Examples, Overview
 Modeling Longitudinal Data:
Data structure and notation, Conceptual framework for continuous
response, Populationaveraged vs. subjectspecific modeling, Models for
correlation structure, Discrete resonpse
 Repeated Measures Analysis of Variance:
Univariate repeated measures ANOVA, Specialized tests, Multivariate
repeated Measures ANOVA
 Modern Methods: Preliminaries:
Drawbacks of classical methods; Review of large sample inference and
estimating equations
 Populationaveraged Linear Models for
Continuous Response: Model specification, Maximum
likelihood undr normality, Restricted maximum likelihood, Large sample
inference, Implications of missing data
 Linear Mixed Effects Models:
Model specification, Maximum likelihood and restricted maximumm
likelihood, Large sample inference and implications of missing data,
Best linear unbiased prediction and empirical Bayes, Implementation
via the EM algorithm, Testing variance components
 Review of Generalized and Nonlinear
Models for Univariate Response: Nonlinear and Generalized
(non)linear models, Estimating equations and variance function
estimation, Large sample inference
 PopulationAveraged Models and
Generalized Estimating Equations: Model specification,
Linear and quadratic estimating equations for fixed effects, Quadratic
estimating equations for covariance parameters, Large sample
inference, Modeling issues, Implications of missing data
 Generalized Linear and Nonlinear Mixed Effects Models:
Model specification, Maximum likelihood, Empirical Bayes estimators
for random effects, Approximate inference based on individual
estimates, Approximate inference based on linearization,"Exact"
inference, Implications of missing data
 Advanced Topics: Bayesian
formulation, Complex nonlinear models, Timedependent covariates,
Multilevel models, Distribution of random effects
See the class notes for more detailed information