Daniel Flores-Agreda, Eva Cantoni - Under Review We consider the problem of bootstrapping Generalized Linear Mixed Models for exponential families 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 good finite sample properties when applied in a Mixed Logit Model. As a further illustration of the breadth of our proposal, we implement the method in a Mixed Poisson Model to analyze longitudinal data on the number of epileptic seizures.
Article currently under review