Growth curve mixture models with unknown covariance structures

Though playing an important role in longitudinal data analysis, the uses of growth curve models are constrained by the crucial assumption that the grouping design matrix is known. In this paper we propose a Gaussian mixture model within the framework of growth curve models which handles the problem caused by the unknown grouping matrix. This allows for a greater degree of flexibility in specifying the model and freeing the response matrix from following a single multivariate normal distribution. The new model is considered under two parsimonious covariance structures together with the unstructured covariance. The maximum likelihood estimation of the proposed model is studied using the ECM algorithm, which clusters growth curve data simultaneously. Data-driving methods are proposed to find various model parameters so as to create an appropriate model for complex growth curve data. Simulation studies are conducted to assess the performance of the proposed methods and real data analysis on gene expression clustering is made, showing that the proposed procedure works well in both, model fitting and growth curve data clustering.