  Beta-binomial/Poisson models have been used by many authors to model
multivariate count data. Lora and Singer (Statistics in Medicine, 2008)
extended such models to accommodate repeated multivariate count data with
overdipersion in the binomial component. To overcome some of the limitations of
that model, we consider a beta-binomial/gamma-Poisson alternative that also
allows for both overdispersion and different covariances between the Poisson
counts. We obtain maximum likelihood estimates for the parameters using a
Newton-Raphson algorithm and compare both models in a practical example.
