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Bootstrap estimation of uncertainty in prediction for generalized linear mixed models

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Year 2017
Abstract In this article, we focus on the estimation of the Mean Squared Error for the Predictors (MSEP) of Random Effects (RE) in Generalized Linear Mixed Models (GLMM) by means of non-parametric bootstrap methods. In the frequentist paradigm, the MSEP is used as a measure of the uncertainty in prediction and has been shown to be affected by the estimation of the model parameters. In the particular case of linear mixed models (LMM), two solutions are provided to practitioners: on one hand, second- order correct approximations which yield estimators of this quantity and, on the other hand, several Parametric Bootstrap algorithms. We propose a non-parametric bootstrap scheme, consisting of an adaptation of the Random Weighted Laplace Bootstrap (RWLB) that can be used in the entire class of GLMM. On a first stage, the RWLB is used to generate bootstrap replicates of the parameters while, on a second stage, simulation is used to generate bootstrap samples of standardized RE. We conduct a first simulation study in the framework of Gaussian LMM to contrast the quality of our approach with respect to: (i) analytical estimators of MSEP based on approxi- mations, (ii) Conditional Variances obtained with a Bayesian representation and (iii) other bootstrap schemes, on the grounds of their relative bias, relative efficiency and the coverage ratios of resulting prediction intervals. A second simulation study serves the purpose to illustrate the use and benefits of our proposal against other feasible alternatives in a pure, Non-Gaussian, GLMM setting.
Keywords BootstrapGLMMPredictionRandom EffectMSEPLaplace Approximation
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FLORES AGREDA, Daniel Antonio, CANTONI, Eva. Bootstrap estimation of uncertainty in prediction for generalized linear mixed models. 2017 https://archive-ouverte.unige.ch/unige:100298

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Deposited on : 2017-12-13

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