Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model

TL;DR

This paper introduces a robust contaminated Gaussian cluster-weighted model for regression analysis that effectively handles outliers and leverage points without prior parameter specification, enhancing clustering robustness.

Contribution

The paper proposes a novel contaminated Gaussian CWM with flexible outlier and leverage point control parameters that do not require pre-specification, improving robustness in clustering and regression.

Findings

The model effectively identifies outliers and leverage points within clusters.

Monte Carlo experiments demonstrate improved estimator robustness over Gaussian CWM.

Application to real data shows practical utility and enhanced classification accuracy.

Abstract

The Gaussian cluster-weighted model (CWM) is a mixture of regression models with random covariates that allows for flexible clustering of a random vector composed of response variables and covariates. In each mixture component, it adopts a Gaussian distribution for both the covariates and the responses given the covariates. To robustify the approach with respect to possible elliptical heavy tailed departures from normality, due to the presence of atypical observations, the contaminated Gaussian CWM is here introduced. In addition to the parameters of the Gaussian CWM, each mixture component of our contaminated CWM has a parameter controlling the proportion of outliers, one controlling the proportion of leverage points, one specifying the degree of contamination with respect to the response variables, and one specifying the degree of contamination with respect to the covariates. Crucially, these parameters do not have to be specified a priori, adding flexibility to our approach. Furthermore, once the model is estimated and the observations are assigned to the groups, a finer intra-group classification in typical points, outliers, good leverage points, and bad leverage points - concepts of primary importance in robust regression analysis - can be directly obtained. Relations with other mixture-based contaminated models are analyzed, identifiability conditions are provided, an expectation-conditional maximization algorithm is outlined for parameter estimation, and various implementation and operational issues are discussed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments and compared to the estimators from the Gaussian CWM. A sensitivity study is also conducted based on a real data set.