Parsimonious generalized linear Gaussian cluster-weighted models

Abstract

Mixtures with random covariates are statistical models which can be applied for clustering and for density estimation of a random vector composed by a response variable and a set of covariates. In this class, the generalized linear Gaussian cluster-weighted model (GLGCWM) assumes, in each mixture component, an exponential family distribution for the response variable and a multivariate Gaussian distribution for the vector of real-valued covariates. For parsimony sake, a family of fourteen models is here introduced by applying some constraints on the eigen-decomposed covariance matrices of the Gaussian distribution. The EM algorithm is described to find maximum likelihood estimates of the parameters for these models. This novel family of models is finally applied to a real data set where a good classification performance is obtained, especially when compared with other well-established mixture-based approaches.