Model-based Clustering of Multi-Dimensional Zero-Inflated Counts via the EM Algorithm

Abstract: Zero-inflated count data arise in various fields, including health, biology, economics, and the social sciences. These data are often modelled using probabilistic distributions such as zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), or zero-inflated binomial (ZIB). To account for heterogeneity in the data, it is often useful to cluster observations into groups that may explain underlying differences in the data-generating process. This paper focuses on model-based clustering for zero-inflated counts when observations are structured in a matrix form rather than a vector. We propose a clustering framework based on mixtures of ZIP or ZINB distributions, with both the count and zero components depending on cluster assignments. Our approach incorporates covariates through a log-linear structure for the mean parameter and includes a size factor to adjust for differences in total sampling or exposure. Model parameters and cluster assignments are estimated via the Expectation-Maximization (EM) algorithm. We assess the performance of our proposed methodology through simulation studies evaluating clustering accuracy and estimator properties, followed by applications to publicly available datasets.