Suppose I have 3 response variables (Y1, Y2, Y3, which are vectors of count data). Assume I also have multiple co-variates that are both categorical (e.g. X1, X2, X3) and numerical (e.g. Z1, Z2, Z3). The goal is to, for instance, predict the response variables as a function of the co-variates, and also assess for any interaction between the categorical co-variates. By considering only a single response Y1, I can use e.g. a Binomial or Poisson distribution to model the data. But I want to model the whole data set as a multivariate distribution. Does anyone know of an "R" library for this problem? Any suggestions?