Finite mixtures of matrix-variate normal distributions on censored and missing data

Incomplete data, such as missing or censored values, frequently arise in matrix-variate datasets. At the same time, latent heterogeneity–manifested as subpopulations or clusters–is often present. To our knowledge, no finite mixture model has yet been proposed that can simultaneously handle matrix-variate data with both missing and censored values. To address this gap, we introduce a novel model based on the matrix-variate normal distribution that accommodates missingness and various censoring types while capturing latent group structure through clustering. The missing/censoring mechanism is assumed to be missing at random, implying a non-informative (ignorable) mechanism. An efficient expectation-conditional maximization algorithm is developed for maximum likelihood estimation. Simulations demonstrate accurate parameter recovery under a variety of censoring and missingness patterns. Applications of the method to environmental data from the Chesapeake Bay and clinical data from the Age-Related Eye Disease Study illustrate its ability to reveal ecologically and clinically meaningful structures in complex, incomplete datasets.