Bayesian estimation of random effects models for multivariate responses of mixed data

A random effects model is presented to estimate multivariate data of mixed data types. Such data typically appear in studies where different response variables are measured repeatedly for one subject. It is possible to relate normal, binary, multinomial and count data by our joint model. Further flexibility with respect to model specification is obtained by including modern variable selection techniques. Auxiliary mixture sampling leads to a Gibbs sampling type scheme which is easy to implement since no additional tuning is needed. The method is illustrated by transaction data of a costumer cohort acquired by an apparel retailer.