Robust clustering via mixtures of t factor analyzers with incomplete data

Mixtures of t $$ t $$ factor analysers with censored responses and external covariates: An application to educational data from Peru

Analysing data from educational tests allows governments to make decisions for improving the quality of life of individuals in a society. One of the key responsibilities of statisticians is to develop models that provide decision-makers with pertinent information about the latent process that educational tests seek to represent. Mixtures oft $$ t $$ factor analysers (MtFA) have emerged as a powerful device for model-based clustering and classification of high-dimensional data containing one or several groups of observations with fatter tails or anomalous outliers. This paper considers an extension of MtFA for robust clustering of censored data, referred to as the MtFAC model, by incorporating external covariates. The enhanced flexibility of including covariates in MtFAC enables cluster-specific multivariate regression analysis of dependent variables with censored responses arising from upper and/or lower detection limits of experimental equipment. An alternating expectation conditional maximization (AECM) algorithm is developed for maximum likelihood estimation of the proposed model. Two simulation experiments are conducted to examine the effectiveness of the techniques presented. Furthermore, the proposed methodology is applied to Peruvian data from the 2007 Early Grade Reading Assessment, and the results obtained from the analysis provide new insights regarding the reading skills of Peruvian students.

A Multivariate Flexible Skew-Symmetric-Normal Distribution: Scale-Shape Mixtures and Parameter Estimation via Selection Representation

Multivariate skew-symmetric-normal (MSSN) distributions have been recognized as an appealing tool for modeling data with non-normal features such as asymmetry and heavy tails, rendering them suitable for applications in diverse areas. We introduce a richer class of MSSN distributions based on a scale-shape mixture of (multivariate) flexible skew-symmetric normal distributions, called the SSMFSSN distributions. This very general class of SSMFSSN distributions can capture various shapes of multimodality, skewness, and leptokurtic behavior in the data. We investigate some of its probabilistic characterizations and distributional properties which are useful for further methodological developments. An efficient EM-type algorithm designed under the selection mechanism is advocated to compute the maximum likelihood (ML) estimates of parameters. Simulation studies as well as applications to a real dataset are employed to illustrate the usefulness of the presented methods. Numerical results show the superiority of our proposed model in comparison to several existing competitors.