This article is concerned with the analysis of correlated count data. A cla
ss of models is proposed in which the correlation among the counts is repre
sented by correlated latent effects. Special cases of the model are discuss
ed and a tuned and efficient Markov chain Monte Carlo algorithm is develope
d to estimate the model under both multivariate normal and multivariate-t a
ssumptions on the latent effects. The methods are illustrated with two real
data examples of six and sixteen variate correlated counts.