TABLE OF CONTENTS In Chapter 4 we gave a brief description of generalised linear models and showed how they have unified regression analysis for discrete and continuous independent response variables. An obvious question is how might such models be adapted to be suitable for correlated response variables, in particular the repeated measurements taken in a longitudinal study? The multivariate regression model for correlated normally distributed response variables found in Chapter 6 provides the first part of the answer, and in this chapter the extension to non-normal responses, in particular, categorical responses, will be considered.
In the linear model for Gaussian data in Chapter 6 estimation of the regression parameters needed to take account of the correlations in the data, but their interpretation was essentially independent of the correlation structure. One potentially troublesome aspect of modelling non-normal longitudinal data is that this independence of estimation and interpretation no longer always holds. Different assumptions about the source of correlations between the observations can lead to regression coefficients with distinct interpretations as we shall see later. The three principal approaches to introducing correlations are marginal, random effects and transition models. Each type will now be considered relatively briefly; fuller accounts are available in Diggle, et al. (1994).
Longitudinal data can be considered as a series of cross-sections, and marginal models for such data use the generalised linear model discussed in Chapter 4, to fit to each cross-section. In this approach, the relationship of...
