Robust order selection of mixtures of regression models with random effects

Abstract

Finite mixtures of regression models with random effects are a very flexible statistical tool to model data, as these models allow to model the heterogeneity of the population and to account for multiple correlated observations from the same individual at the same time. The selection of the number of components for these models has been a long-standing challenging problem in statistics. However, the majority of the existent methods for the estimation of the number of components are not robust and, therefore, are quite sensitive to outliers. In this article we study a robust estimation of the number of components for mixtures of regression models with random effects, investigating the performance of trimmed information and classification criteria comparatively to the performance of the traditional information and classification criteria. The simulation study and a real-world application showcase the superiority of the trimmed information and classification criteria in the presence of contaminated data.