Bootstrapped inference for variance parameters, measures of heterogeneity and random effects in multilevel logistic regression models

We used Monte Carlo simulations to assess the performance of three bootstrap procedures for use with multilevel data (the parametric bootstrap, the residuals bootstrap, and the nonparametric bootstrap) for estimating the sampling variation of three measures of cluster variation and heterogeneity when using a multilevel logistic regression model: the variance of the distribution of the random effects, the variance partition coefficient (equivalent here to the intraclass correlation coefficient), and the median odds ratio. We also described a novel parametric bootstrap procedure to estimate the standard errors of the predicted cluster-specific random effects. Our results suggest that the parametric and residuals bootstrap should, in general, be used to estimate the sampling variation of key measures of cluster variation and heterogeneity. The performance of the novel parametric bootstrap procedure for estimating the standard errors of predicted cluster-specific random effects tended to exceed that of the model-based estimates.