Estimation dans les modèles linéaires généralisés à effets aléatoires

Abstract : In this work, we consider parameter estimation methods for gene\-ralized linear mixed models (GL2M). Considering a gaussian hypothesis for the random effects ($\xi$) distribution, the likelihood based on the marginal distribution of the response $Y$ cannot be described explicitely in these models. Several approximations can be applied. We distinguish two kinds of approaches : a conditional one and a marginal one. Following the first one, we propose a method based on the maximization of the joint distribution of $(Y,\xi)$ previous to going into an estimation step. This corresponds to a conditional linearization of the model. Following the second approach, we study a marginal reasoning based on the approximation of the first two marginal moments of $Y$ and the use of the quasi-likelihood. We extend to other distributions and link functions the method developed by Gilmour et al. in the case of a probit link binomial model. We then compare the different methods on a deconditioning scale. The second part of this work introduces a notion of heterogeneity for the GL2M. This heterogeneity enables us to distinguish between the different behaviours of random effects depending on the actual environment. To take this into account in the model, we assume a specific random effects variance for each environment. We propose an estimation method, which combines the linearization of the former conditional approach and the use of the EM algorithm, which is particularly appropriate for the linear case in this heterogeneity framework.
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• HAL Id : tel-00004908, version 1

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Catherine Trottier. Estimation dans les modèles linéaires généralisés à effets aléatoires. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 1998. Français. ⟨tel-00004908⟩

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