Multilevel models applications to the analysis of longitudinal data

Abstract

This work is an introduction to repeated measurement analysis for longitudinal studies. It uses a two stage modelling framework, using hierarchical linear models with two levels. The first level pertains to the repeated measures, the second level pertains to the individual. For the last 25 years, hierarchical linear models have been used in the Social Sciences to analyse data coming from organizations with multiple levels. Their applications have been extended to the study of change in populations, both to describe the average change in an outcome variable in a population and to analyse the factors associated with variability in the individual trajectories of change. In this article, the basic concepts are introduced: between subjects and within subjects variability, the person-specific model for the individual trajectory and the between person model to describe how individuals vary in their trajectories, fixed and random effects, linear and quadratic growth models. At the end of each section, an illustration is given for the study of cognitive function of the older people cohort Aging in Leganés, followed in four occasions between 1993 and 1999. Results from fitting the models to answer the most frequently asked research questions in the description and analysis of individual change are presented. Lastly, we present possible generalizations of these linear models to non linear situations which arise when outcomes are dichotomous, nominal or ordinal.