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Title: Bootstrapping clustered data via a weighted Laplace approximation Authors:  Daniel Antonio Flores Agreda - Universite de Geneve (Switzerland) [presenting]
Eva Cantoni - University of Geneva (Switzerland)
Stephane Heritier - Monash University (Australia)
Rory Wolfe - Monash University (Australia)
Abstract: The problem of bootstrapping Generalized Linear Mixed Models for exponential families is considered in a non-parametric manner. We propose a method based on the random weighting of the individual contributions to the joint distribution of outcomes and random effects and the use of the Laplace approximation method for integrals on this weighted joint distribution. We show the similarities between the random weighting of the Laplace-approximated log-Likelihood and other bootstrap schemes based on random weighting of the estimating equations. Through simulations, we provide evidence of the good quality of the bootstrap approximations of the sampling distributions for the model parameters as well as evidence of their finite sample properties when applied in a Mixed Logit Model. We further illustrate the properties of our proposal via simulated examples in Accelerated Failure Time Models for clustered data.