Robust Mixture of Linear Regression Models

Abstract

This article proposes a robust model for parameter estimation when modeling in the presence of latent heterogeneity of population. Mixture of regression models are used for modeling when the data are a mixture of subgroups to allow for heterogeneity of the population. Parameter estimates from standard mixture of linear regression models are sensitive to atypical observations. To study mixtures of linear regression models, we introduce a class of robust estimators, called S-estimators. We investigate their breakdown point in mixture of linear regression models. It is expected that the robust S-estimators can achieve the high breakdown point in the contaminated data from the heterogenous populations. This model presents a unified, robust framework and parameter estimation is achieved via an expectation-conditional maximization (ECM) algorithm. This new family of robust mixture models is validated through Monte Carlo simulations. The application to real life data sets has shown that use of robust S-estimators in mixture of linear regression models accommodates the outliers producing stable estimates as compared to maximum likelihood estimators from mixture of linear regression models.