REGRESSION-MODELS FOR MIXED DISCRETE AND CONTINUOUS RESPONSES WITH POTENTIALLY MISSING VALUES

In this paper a likelihood-based method for analyzing mixed discrete a nd continuous regression models is proposed. We focus on marginal regr ession models, that is, models in which the marginal expectation of th e response vector is related to covariates by known link functions. Th e proposed model is based on an extension of the general location mode l of Olkin and Tate (1961, Annals of Mathematical Statistics 32, 448-4 65), and can accommodate missing responses. When there are no missing data, our particular choice of parameterization yields maximum likelih ood estimates of the marginal mean parameters that are robust to missp ecification of the association between the responses. This robustness property does not, in general, hold for the case of incomplete data. T here are a number of potential benefits of a multivariate approach ove r separate analyses of the distinct responses. First, a multivariate a nalysis can exploit the correlation structure of the response vector t o address intrinsically multivariate questions. Second, multivariate t est statistics allow for control over the inflation of the type I erro r that results when separate analyses of the distinct responses are pe rformed without accounting for multiple comparisons. Third, it is gene rally possible to obtain more precise parameter estimates by accountin g for the association between the responses. Finally, separate analyse s of the distinct responses may be difficult to interpret when there i s nonresponse because different sets of individuals contribute to each analysis. Furthermore, separate analyses can introduce bias when the missing responses are missing at random (MAR). A multivariate analysis can circumvent both of these problems. The proposed methods are appli ed to two biomedical datasets.