Classification in segmented regression problems

Heterogeneity in many datasets stems from the different behaviors of several underlying groups or subpopulations. The aim of this paper is to classify observations in such a dataset into these latent groups when each group’s behavior is piecewise linearly related to a set of covariates. We assume that each group can be represented by a segmented regression model, but the group membership for each observation is unobserved or lost. A full Bayesian approach is proposed to simultaneously classify observations and estimate segmented regression parameters. The estimated marginal likelihood and the Deviance Information Criterion are used to select the number of mixture groups. We demonstrate the accuracy and performance of the proposed MCMC estimators in a simulation study and illustrate the methodology in an empirical study.