Flexible Bayesian modelling of concomitant covariate effects in mixture models

Mixture models provide a useful tool to account for 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 of the mixture can be linked to the covariates through a multinomial logistic regression model, where each component weight is a function of the linear predictor involving one or more covariates. The proposed contribution extends this approach by replacing the linear predictor, used for the component weights, with an additive structure, where each term is a smooth function of the covariates considered. An estimation procedure within the Bayesian paradigm is suggested. 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. The performance of the proposed methodology is investigated via simulation experiments, and an application to an original dataset about UK parliamentary votes on Brexit is discussed.