Archive ouverte UNIGE | last documents for author 'Daniel Antonio Flores Agreda'https://archive-ouverte.unige.ch/Latest objects deposited in the Archive ouverte UNIGE for author 'Daniel Antonio Flores Agreda'engOn the Inference of Random Effects in Generalized Linear Mixed Modelshttps://archive-ouverte.unige.ch/unige:102003https://archive-ouverte.unige.ch/unige:102003In the first chapter, the problem of Bootstrap inference for the parameters of a GLMM is addressed. We formulate a bootstrapping strategy consisting on the random weighting of the contributions to the Joint Likelihood of Outcomes and Random Effects. Using the Laplace Approximation method for integrals on this function, yields a Random Weighted Log-Likelihood that produces the desired bootstrap replicates after optimization. In order to assess the properties of this procedure, that we name Random Weighted Likelihood Bootstrap (RWLB), we compare analytically their resulting EE to those of the Generalized Cluster Bootstrap for Gaussian LMM and conduct simulation studies both in a LMM and Mixed Logit regression contexts. The second chapter explores adaptations of the RWLB to the estimation of the uncertainty in prediction of random effects in a GLMM, as measured by the Mean Squared Error for the Predictors (MSEP).Fri, 09 Feb 2018 11:17:36 +0100Bootstrap estimation of uncertainty in prediction for generalized linear mixed modelshttps://archive-ouverte.unige.ch/unige:100298https://archive-ouverte.unige.ch/unige:100298In the framework of Mixed Models, it is often of interest to provide an es- timate of the uncertainty in predictions for the random effects, customarily defined by the Mean Squared Error of Prediction (MSEP). To address this computation in the Generalized Linear Mixed Model (GLMM) context, a non-parametric Bootstrap algorithm is proposed. First, a newly developed Bootstrap scheme relying on random weighting of cluster contributions to the joint likelhood function of the model and the Laplace Approximation is used to create bootstrap replicates of the parameters. Second, these replicates yield in turn bootstrap samples for the random effects and for the responses. Third, generating predictions of the random effects employing the bootstrap samples of observations produces bootstrap replicates of the random effects that, in conjunction with their respective bootstrap samples, are used in the estimation of the MSEP. To assess the validity of the proposed method, two simulation studies are presented. The first one in the framework of Gaussian LMM, contrasts the quality of the proposed approach with respect to: (i) an- alytical estimators of MSEP based on second-order correct approximations, (ii) Conditional Variances obtained with a Bayesian representation and (iii) other bootstrap schemes, on the grounds of relative bias, relative efficiency and the coverage ratios of resulting prediction intervals. The second simu- lation study serves the purpose of illustrating the properties of our proposal in a Non-Gaussian GLMM setting, namely a Mixed Logit Model, where the alternatives are scarce.Wed, 13 Dec 2017 17:00:52 +0100