REGRESSION-MODELS FOR DISCRETE LONGITUDINAL RESPONSES

In this paper, we review analytic methods for regression models for lo ngitudinal categorical responses. We focus on both likelihood-based ap proaches and non-likelihood approaches to analysing repeated binary re sponses. In both approaches, interest is focussed primarily on the reg ression parameters for the marginal expectations of the binary respons es. The association or time dependence between the responses is largel y regarded as a nuisance characteristic of the data. We consider these approaches for both the complete and incomplete data cases. We descri be the generalized estimating equations (GEE) approach, a non-likeliho od approach, and some proposed extensions of it. We also discuss likel ihood-based approaches that are based on a log-linear representation o f the joint probabilities of the binary responses. We describe how a l ikelihood-based ''mixed parameter'' model yields likelihood equations for the regression parameters that are of exactly the same form as the GEE. An outline of the desirable features and drawbacks of each appro ach is presented. In addition, we provide some comparisons in terms of asymptotic relative efficiency for the complete data case, and in ter ms of asymptotic bias for the incomplete data case. Finally, we make s ome recommendations concerning the application of these methods.