Conditional versus Marginal Covariance Representation for Linear and Nonlinear Models

Abstract

Grouped data, such as repeated measures and longitudinal data, are increasingly collected in different areas of application, as varied as clinical trials, epidemiological studies, and educational testing. It is often of interest, for these data, to explore possible relationships between one or more response variables and available covariates. Because of the within-group correlation typically present with this type of data, special regression models that allow the joint estimation of mean and covariance parameters need to be used. Two main approaches have been proposed to represent the covariance structure of the data with these models: (i) via the use of random effects, the so-called conditional model and (ii) through direct representation of the covariance structure of the responses, known as the marginal approach. Here we discuss and compare these two approaches in the context of linear and non-linear regression models with additive Gaussian errors, using a real data example to motivate and illustrate the discussion.