Résumé
This work focuses on generalized linear mixed models (GL2M). In these models, considering a gaussian hypothesis for the random effects distribution, the likelihood based on the marginal distribution of the response cannot be derived in closed form. In the first part of this work, we critically review parameter estimation methods using different kinds of approximations. The second part focuses on model selection for GL2Ms. Two parameter estimation methods are revisited, both leading to iterative model linearisations. We propose simple model selection criteria adapted from classical information criteria and based on the linearised model obtained once the algorithm has converged. In the third and last part, the analysis of mixture models of GL2Ms is considered. The mixture components are defined by GL2Ms and correspond to different possible states of the statistical units. For a mixture of exponential mixed models, we propose a method using a linearisation specific to this distribution. We also propose a second and more general approach which uses a Metropolis-Hastings step to allow construction of an MCEM algorithm. This method can be used for mixtures of any GL2Ms. The different developed methods are tested by simulations.