Multivariate probit models are used to study clustered data with binary and continuous responses. In these models, random effects are often assumed to follow a normal distribution. However this assumption is difficult to verify in practice, resulting in potential misspecification. Misspecification may be a serious problem for maximum likelihood fitting, which is commonly used in the estimation of generalized linear mixed models. A possible solution is to model random effects by a normal mixture, in the so-called heterogeneity model, and to apply an EM algorithm for estimating fixed and random effects parameters. Similar algorithms were proposed in previous studies, which suffered from being slow to converge.;In this work, it is shown that misspecification has a severe impact on ML estimates in correlated probit models with continuous and binary responses, when clusters belong to two latent classes that significantly differ in their random effects. Also a Stochastic Approximation ECM algorithm is proposed for fitting the heterogeneity model, and its performance is studied through simulations.
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