Longitudinal Data and Linear Mixed Effects Models

Abstract

Longitudinal data are measurements or observations taken from multiple subjects repeatedly over time. The main theme of this book is to describe autoregressive linear mixed effects models for longitudinal data analysis. This model is an extension of linear mixed effects models and autoregressive models. This chapter introduces longitudinal data and linear mixed effects models before the main theme in the following chapters. Linear mixed effects models are popularly used for the analysis of longitudinal data of a continuous response variable. They are an extension of linear models by including random effects and variance covariance structures for random errors. Marginal models, which do not include random effects, are also introduced in the same framework. This chapter explains examples of popular linear mixed effects models and marginal models: means at each time point with a random intercept, means at each time point with an unstructured variance covariance, and linear time trend models with a random intercept and a random slope. The corresponding examples of group comparisons are also provided. This chapter also discusses the details of mean structures and variance covariance structures and provides estimation methods based on maximum likelihood and restricted maximum likelihood.