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Title: Mixture of longitudinal factor analysis for modelling heterogeneous longitudinal multivariate data Authors:  Amine Ounajim - University of Poitiers (France) [presenting]
Yousri Slaoui - University of Poitiers (France)
Pierre-Yves Louis - AgroSup Dijon University of Bourgogne Franche-Comte (France)
Denis Frasca - University Hospital Centre Poitiers (France)
Philippe Rigoard - University Hospital Centre Poitiers - PRISMATICS Lab (France)
Abstract: In order to study the evolution of several observed outcomes among patients, it is important to focus on longitudinal trends among latent variables using joint modeling based on covariance structures between these observed outcomes. However, this type of data might represent heterogeneity over time and among groups of individuals. To address this problem, some authors have proposed factor analyzer mixture models, which estimate different factor loadings for different subpopulations, which are represented by a latent class variable. We propose here an extension to the factor analysis framework where group non-invariance is taken into account using a mixture model. We start by defining the mixture of the longitudinal factor analysis model and its parameters. Then, we propose an EM algorithm to estimate the model. We also develop a Bayesian information criterion to identify the number of components in the mixture. We then discuss the comparability of the latent factors obtained between subjects in different latent groups. Finally, we apply the model to simulated and real data of patients with postoperative chronic pain.