A fast implementation of generalized linear mixed models for correlated binary data

We propose a new EM algorithm for computing the maximum likelihood
for generalized linear mixed probit-normal models for correlated binary data.
In contrast with recent developments (Tan et al., 2007; Meza et al., 2009), this
algorithm used closed-form expressions at the E step, as opposed to Monte
Carlo simulation. Our proposed algorithm rely on formulas for the mean and
variance of a truncated multinormal distribution, and can be computed using
available formula. A real data set from the childrens wheeze study is analyzed
to illustrate the proposed method and for comparison with existing methods.