A finite mixture approach to joint clustering of individuals and multivariate discrete outcomes

In this work, we modify finite mixtures of factor analysers to provide a method for simultaneous clustering of subjects and multivariate discrete outcomes. The joint clustering is performed through a suitable reparameterization of the outcome (column)-specific parameters. We develop an expectation–maximization-type algorithm for maximum likelihood parameter estimation where the maximization step is divided into orthogonal sub-blocks that refer to row and column-specific parameters, respectively. Model performance is evaluated via a simulation study with varying sample size, number of outcomes and row/column-specific clustering (partitions). We compare the performance of our model with the performance of standard model-based biclustering approaches. The proposed method is also demonstrated on a benchmark data set where a multivariate binary response is considered.