Robust mixture regression modeling based on the normal mean-variance mixture distributions

Mixture regression models (MRMs) are widely used to capture the heterogeneity of relationships between the response variable and one or more predictors coming from several non-homogeneous groups. Since the conventional MRMs are quite sensitive to departures from normality caused by extra skewness and possible heavy tails, various extensions built on more flexible distributions have been put forward in the last decade. The class of normal mean-variance mixture (NMVM) distributions that arise from scaling both the mean and variance of a normal random variable with a common mixing distribution encompasses many prominent (symmetric or asymmetrical) distributions as special cases. A unified approach to robustifying MRMs is proposed by considering the class of NMVM distributions for component errors. An expectation conditional maximization either (ECME) algorithm, which incorporates membership indicators and the latent scaling variables as the missing data, is developed for carrying out maximum likelihood (ML) estimation of model parameters. Four simulation studies are conducted to examine the finite-sample property of ML estimators and the robustness of the proposed model against outliers for contaminated and noisy data. The usefulness and superiority of our methodology are demonstrated through applications to two real datasets.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

Mixture regression models (MRMs) are widely used to capture the heterogeneity of relationships between the response variable and predictors from non-homogeneous groups. However, conventional MRMs are sensitive to departures from normality. A unified approach using normal mean-variance mixture (NMVM) distributions is proposed to robustify MRMs. An ECME algorithm is developed for ML estimation, and simulation studies demonstrate the finite-sample properties and robustness of the proposed model. Real data applications further illustrate the usefulness and superiority of the methodology.