Finite Mixture Models for Mixed Data: EM Algorithms and Parafac Representations

We propose a flexible regression model for multivariate mixed responses, where different numbers of locations are used for each margin, and joined by a full association structure, which can be simplified by using a Parafac-based representation. This structure of dependence is more general, and properly nests the independence model, but it does not come at no cost. In fact, by adopting this representation, the numberof parameters can be shown to increase exponentially with the number of the analysed outcomes. Therefore, we propose a parsimonious representation of this multi-way array through the Parafac model, Harshman, 1970 and Kapteyn et al., 1986. This helps us define a flaexible model that can account for profile-specific heterogeneity, general form of dependence between profiles and a parsiomious representations of the latter.