A MODIFIED EM ALGORITHM FOR ESTIMATION IN GENERALIZED MIXED MODELS

Application of the EM algorithm for estimation in the generalized mixe d model has been largely unsuccessful because the E-step cannot be det ermined in most instances. The E-step computes the conditional expecta tion of the complete data log-likelihood and when the random effect di stribution is normal, this expectation remains an intractable integral . The problem can be approached by numerical or analytic approximation s; however, the computational burden imposed by numerical integration methods and the absence of an accurate analytic approximation have lim ited the use of the EM algorithm. In this paper, Laplace's method is a dapted for analytic approximation within the E-step. The proposed algo rithm is computationally straightforward and retains much of the conce ptual simplicity of the conventional EM algorithm, although the usual convergence properties are not guaranteed. The proposed algorithm acco mmodates multiple random factors and random effect distributions besid es the normal, e.g., the log-gamma distribution. Parameter estimates o btained for several data sets and through simulation show that this mo dified EM algorithm compares favorably with other generalized mixed mo del methods.