A MIXTURE LIKELIHOOD APPROACH FOR GENERALIZED LINEAR-MODELS

A mixture model approach is developed that simultaneously estimates th e posterior membership probabilities of observations to a number of un observable groups or latent classes, and the parameters of a generaliz ed linear model which relates the observations, distributed according to some member of the exponential family, to a set of specified covari ates within each Class. We demonstrate how this approach handles many of the existing latent class regression procedures as special cases, a s well as a host of other parametric specifications in the exponential family heretofore not mentioned in the latent class literature. As su ch we generalize the McCullagh and Nelder approach to a latent class f ramework. The parameters are estimated using maximum likelihood, and a n EM algorithm for estimation is provided. A Monte Carlo study of the performance of the algorithm for several distributions is provided, an d the model is illustrated in two empirical applications.