Bootstrapping clustered data via a weighted Laplace approximation

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 individualcontributions to the joint distribution of outcomes and random effects and theuse of the Laplace approximation method for integrals on this weighted jointdistribution. We show the similarities between the random weighting of theLaplace-approximated log-Likelihood and other bootstrap schemes based on randomweighting of the estimating equations. Through simulations, we provide evidenceof the good quality of the bootstrap approximations of the samplingdistributions for the model parameters as well as evidence of their finitesample properties when applied in a Mixed Logit Model. We further illustratethe properties of our proposal via simulated examples in Accelerated FailureTime Models for clustered data.