Measuring change in controlled longitudinal studies

This paper examines the implications of the correlational structure of repeated measurements for three indices of change that can be used to evaluate treatment effects in longitudinal studies with scheduled assessment times and fixed total duration. The generalized least squares (GLS) regression of repeated measurements on time, which is usually reserved for complex mixed model solutions, takes the correlational structure of the repeated measurements into account, whereas simple gain scores and ordinary least squares (OLS) regression calculations do not. Nevertheless, the GLS solution is equivalent to OLS under conditions of compound symmetry and is equivalent to the analysis of simple gain scores in the presence of an autoregressive (order 1) correlational structure. The understanding of these relationships is important with regard to the frequently heard criticisms of the simpler definitions of treatment response in repeated measurement designs.