An alternative estimation approach to fit a heterogeneity linear mixed model

International audienceAn alternative estimation approach is proposed to fit a linear mixed effects model where the random effects follow a finite mixture of normal distributions. This model, called a heterogeneity linear mixed model, is an interesting tool since it relaxes the classical normality assumption and is also perfectly suitable for classification purposes, based on longitudinal profiles. Instead of fitting directly the heterogeneity linear mixed model, we propose to fit an equivalent mixture of linear mixed models under some restrictions which is computationally simpler. Indeed, unlike the former model, the latter can be maximized analytically using an EM-algorithm and the obtained parameter estimates can be easily used to compute the parameter estimates of interest. We study and compare the behaviour of our approach on simulations. Finally, the use of our approach is illustrated on a real data set