Generalized linear mixed models for correlated binary data with t-link

A critical issue in modelling binary response data is the choice of the links. We introduce a new link based on the Student t-distribution (t-link) for correlated binary data. The t-link relates to the common probit-normal link adding one additional parameter which purely controls the heaviness of the tails of the link. We propose an interesting EM algorithm for computing the maximum likelihood for generalized linear mixed t-link models for correlated binary data. In contrast with recent developments (Tan et al., 2007; Meza et al., 2009), this algorithm uses closed-form expressions at the E-step, as opposed to Monte Carlo simulation. Our proposed algorithm rely on available formulas for the mean and variance of a truncated multivariate t-distribution. To illustrate the new methodology, a real data set on respiratory infection in children and a simulation study are presented.