Cluster-Weighted Models with Changepoints

Abstract

A flexible family of mixture models known as cluster-weighted models (CWMs) arise when the joint distribution of a response variable and a set of covariates can be modelled by a weighted combination of several component distributions. We introduce an extension to CWMs where changepoints are present. Similar to the finite mixture of regressions (FMR) with changepoints, CWMs with changepoints are more flexible than standard CWMs if we believe that changepoints are present within the data. We consider changepoints within the linear Gaussian CWM, where both the marginal and conditional densities are assumed to be Gaussian. Furthermore, we consider changepoints within the Poisson and Binomial CWM. Model parameter estimation and performance of some information criteria are investigated through simulation studies and two real-world datasets.