Clustering Multivariate Longitudinal Data using Mixture of Matrix-Variate t-distributions

The finite mixture model is considered as an appropriate instrument for data clustering.Different parsimonious multivariate mixture distributions are introduced for skewed and/or heavy-tailed longitudinal data.The eigenvalue or modified Cholesky decomposition of covariance matrices develops the families of parsimonious mixture models.Thus, the finite mixture of matrix-variate t-distributions for clustering a three-way dataset with heavy-tailed or outlier observations (e.g., multivariate longitudinal data) is more appropriate compared to matrix-variate normal distributions.Accordingly, the present study considered a parsimonious family of the finite mixture of matrix-variate t-distributions using the eigenvalue and modified Cholesky decomposition for within and between covariance matrices, respectively.Finally, parameter estimates were calculated using the expectation-maximization algorithm, and simulations studies and real data analyses were conducted to confirm the obtained results.