Title: Flexible Bayesian modelling of concomitant covariate effects in mixture models
Authors: Marco Berrettini - University of Bologna (Italy)
Giuliano Galimberti - University of Bologna (Italy) [presenting]
Saverio Ranciati - Universita di Bologna (Italy)
Thomas Brendan Murphy - University College Dublin (Ireland)
Abstract: Mixtures provide a useful tool to model unobserved heterogeneity and are at the basis of many model-based clustering methods. In order to gain additional flexibility, some model parameters can be expressed as functions of concomitant covariates. In particular, component weights can be linked to concomitant covariates through a multinomial logistic regression model, where each component weight is associated with a linear predictor involving one or more than one concomitant covariate. This approach is extended by replacing the linear predictors with additive ones, where the contributions of some/all concomitant covariates can be represented by smooth functions. In particular, splines are used to approximate these smooth functions. An estimation procedure within the bayesian paradigm is proposed. In particular, a data augmentation scheme based on differenced random utility models is exploited, and smoothness of the covariate effects is controlled by suitable choices for the prior distributions of the spline coefficients. Performances of the proposed methodology are investigated via simulation experiments and some examples on real data are discussed.