Finite mixture of regression models based on multivariate scale mixtures of skew-normal distributions

Abstract

The traditional estimation of mixture regression models is based on the assumption of component normality (or symmetry), making it sensitive to outliers, heavy-tailed errors, and asymmetric errors. In this work, we propose addressing these issues simultaneously by considering a finite mixture of regression models with multivariate scale mixtures of skew-normal distributions. This approach provides greater flexibility in modeling data, accommodating both skewness and heavy tails. Additionally, the proposed model allows the use of a specific vector of regressors for each dependent variable. The main advantage of using the mixture of regression models under the class of multivariate scale mixtures of skew-normal distributions is their convenient hierarchical representation, which allows easy implementation of inference. We develop a simple expectation–maximization (EM) type algorithm to perform maximum likelihood inference for the parameters of the proposed model. The observed information matrix is derived analytically to calculate standard errors. Some simulation studies are also presented to examine the robustness of this flexible model against outlying observations. Finally, a real dataset is analyzed, demonstrating the practical value of the proposed method. The R scripts implementing our methods are available on the GitHub repository at https://bit.ly/3CLcI1W.