Titre : Mixture of varying coefficient models with random effects 

Auteur: Amine Ounajim, Pierre-Yves Louis and Yousri Slaoui 

Résumé: 

With technological advances, massive amounts of longitudinal data have become available which makes parametric and non- parametric modeling techniques for longitudinal data very useful. Varying coefficient models have received a lot of attention because they allow to model the links between a time varying response variable and time varying covariates using regression coefficients represented by smooth time functions which makes them very useful in the analysis of longitudinal data. Varying coefficient models are generally used without taking into account both data heterogeneity and within-subject correlation. In this paper, we propose a mixture of varying coefficient models with random effects incorporated into stochastic processes. This model allows to take into account inter-individual heterogeneity and intra-individual variations. We present a two-step procedure for estimating mixture proportions, smooth functions and covariance parameters using a modified expectation-maximization method and the back-fitting algorithms. A cross-validation method is proposed for the selection of smoothing hyper-parameters which impact the model performance. The proposed model is evaluated on simulated data. We show that the model allows to cluster subjects into homogenous groups and get better estimates of the model effects.