Flexible clustering via Gaussian parsimonious mixture models with censored and missing values

The Gaussian mixture model (GMM) is a versatile and widely used tool for model-based clustering and classification of multivariate data with heterogeneity. While there are existing software packages designed to fit the GMM with varying numbers of mixture components and covariance structures, they are inapplicable when dealing with data containing both censored and missing values. This paper addresses this limitation by proposing an extended framework of the GMM, called the GPMM-CM, which incorporates 14 specifications of parsimonious component–covariance matrices to accommodate the complex situation of existing censored and missing values. Under the missing at random mechanism, an analytically feasible expectation conditional maximization algorithm is devised for carrying out maximum likelihood estimation of the GPMM-CM approach. The superiority and utility of the proposed methodology are demonstrated through analyses of both real and simulated datasets.