Tesis Doctorado
Extensións et applicatións de l algorithme saem pour les modeles mixtes
Autor
Foulley, Jean Louis
Lavielle, Marc
Universite Paris
Institución
Resumen
ii this thesis, we are interested in parametric estimation in rnixed models. This kind
of model is treated as a missing data problem and we use a stochastic approximation version of
tlie EM algorithm to compute the estimators of parameters of such modeis. Many applications and
extensions of SAEM algorithrn both for nonlinear mixed modeis and for generalized linear mixed
models (GLMM) are proposes. in particular the SAEM algorithm is adapt.ed to and implemented
in the context of gerietic analysis of growth curves. The model in this case is a norilinear mixed
model which includes both the permanent environmental effects and the animal genetic effects. We
propose an extension of SAEM which increases the speed of convergence of the algorithm arid which
aliows to avoid local maxima of the likelihood. This new algorithm, called PX-SAEM (as combinirig
PX- EM and SAEM), introduces an expanded complete-data model with a larger set of pararneters
and substantially improves the speed of convergence towards the maximum likelihood estimate. Tbe
third part of this work is devoted to a new estimation procedure for the variance components in
nonlinear mixed modeis miming the Restricted Ma.ximum Likelihood (REML) via an integrated ukelihood.
This method is implemented via the SAEM algorithrn and it allows to reduce considerably
the bias observed in the ML estimation. The last chapter of this thesis is devoted to the application
of SAEM to GLMM context in particular to the mixed-effects probit model for dichotomous outcomes.
An adaptation of the SAEM is proposed to compute the ML estimators of the parameters
which also includes a speed np option via PX-EM arid a REML version for para.meter estimation.