Within-cluster resampling for multilevel models under informative cluster size

A within-cluster resampling method is proposed for fitting a multilevel model in the presence of informative cluster size. Our method is based on the idea of removing the information in the cluster sizes by drawing bootstrap samples which contain a fixed number of observations from each cluster.We then estimate the parameters by maximising an average, over the bootstrap samples, of a suitable composite log-likelihood. The consistency of the proposed estimator is shown 15 and does not require that the correct model for cluster size is specified. We give an estimator of the covariance matrix of the proposed estimator, and a test for the non-informativeness of the cluster sizes. A simulation study shows, as in Neuhaus & McCulloch (2011), that the standard maximum likelihood estimator exhibits little bias for some regression coefficients. However, for those parameters which exhibit non-negligible bias, the proposed method is successful in cor- 20 recting for this bias.