Mixtures of common factor analyzers using the restricted multivariate skew-t distribution for clustering high-dimensional data with missing values

Abstract

Mixtures of common restricted skew-$t$ factor analyzers (MCrstFA) have emerged as a parsimonious and practical approach for the model-based clustering of high-dimensional data with asymmetric features and outlying observations in one or more heterogeneous populations. However, missing data has become a ubiquitous problem that frequently adds complexity to the analyses for practitioners. Most existing tools are not adaptable to data with missing values, which is a significant reason for this complexity. This paper proposes an extension of the MCrstFA framework that allows the analyst to parsimoniously model data with missing values, skewness, heavy tails, and multimodality simultaneously. Under the missing at random (MAR) mechanism for nonresponses, a computationally feasible expectation conditional maximization either (ECME) algorithm is developed for computing maximum likelihood (ML) estimates of model parameters. The estimation procedure enables the automatic imputation of missing values and the prediction of unobserved factor scores. To assess the precision of the ML estimators, an information matrix-based approach is employed to approximate the asymptotic covariance matrix of the estimators. Numerical results obtained from the analysis of simulated and real datasets illustrate the effectiveness of the proposed methodology.