Robust mixtures of factor analysis models using the restricted multivariate skew-t distribution. (February 2018)

• Record Type: Journal Article
• Authors: Lin, Tsung-I; Wang, Wan-Lun; McLachlan, Geoffrey J.; Lee, Sharon X.
• Is Part Of: Statistical modelling. Volume 18:Number 1(2018)
• Page Start: 50
• Page End: 72
• Publication Date: 2018-02
• Subjects: model-based clustering -- Factor analysis -- heavy tails -- missing values -- rMST distribution -- robustness; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X17718119
• Languages: English
• ISSNs: 1471-082X

Abstract

This article introduces a robust extension of the mixture of factor analysis models based on the restricted multivariate skew- t distribution, called mixtures of skew- t factor analysis (MSTFA) model. This model can be viewed as a powerful tool for model-based clustering of high-dimensional data where observations in each cluster exhibit non-normal features such as heavy-tailed noises and extreme skewness. Missing values may be frequently present due to the incomplete collection of data. A computationally feasible EM-type algorithm is developed to carry out maximum likelihood estimation and create single imputation of possible missing values under a missing at random mechanism. The numbers of factors and mixture components are determined via penalized likelihood criteria. The utility of our proposed methodology is illustrated through analysing both simulated and real datasets. Numerical results are shown to perform favourably compared to existing approaches.