Testing for Dependence in Mixed Effect Models for Multivariate Mixed Responses

In regression modelling for multivariate responses of mixed type, the association between outcomes may be modeled through dependent, outcome-specific, latent effects. Parametric specifications of this model already exist in the literatre: in this paper, we focus on model parameter estimation in a Finite Mixture (FM) framework. a relevant issues arises when independence should be tested vs dependence. We review the performance of LRT and penalized likelihood criteria to assess the presence of dependence between outcome-specific random effects. The model behavior investigated through the analysis of simulated datasets shows that AIC and BIC are of little help to test for dependence, while bootstrapped LRT statistics performs well even with small sample sizes and limited number of bootstrap samples.