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 introducea 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 controlsthe heaviness of the tails of the link. We propose an interesting EM algorithm for computingthe 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 usesclosed-form expressions at the E-step, as opposed to Monte Carlo simulation. Our proposedalgorithm rely on available formulas for the mean and variance of a truncated multivariatet-distribution. To illustrate the new methodology, a real data set on respiratory infection inchildren and a simulation study are presented.