Estimation of linear mixed models with a mixture of distribution for the random effects

The aim of this paper is to propose an algorithm to estimate linear mixed model when random effect distribution is a mixture of Gaussians. This heterogeneous linear mixed model relaxes the classical Gaussian assumption for the random effects and, when used for longitudinal data, can highlight distinct patterns of evolution. The observed likelihood is maximized using a Marquardt algorithm instead of the EM algorithm which is frequently used for mixture models. Indeed, the EM algorithm is computationally expensive and does not provide good convergence criteria nor direct estimates of the variance of the parameters. The proposed method also allows to classify subjects according to the estimated profiles by computing posterior probabilities of belonging to each component. The use of heterogeneous linear mixed model is illustrated through a study of the different patterns of cognitive evolution in the elderly. HETMIXLIN is a free Fortran90 program available on the web site: http://www.isped.u-bordeaux2.fr.