Bootstrapping for highly unbalanced clustered data

We apply the generalized cluster bootstrap to both Gaussian quasi-likelihood and robust estimates in the context of highly unbalanced clustered data. We compare it with the transformation bootstrap where the data are generated by the random effect and transformation models and all the random variables have different distributions. We also develop a fast approach (proposed by Salibian-Barrera et al. (2008)) and show that it produces some encouraging results. We show that the generalized bootstrap performs better than the transformation bootstrap for highly unbalanced clustered data. We apply the generalized cluster bootstrap to a sample of income data for Australian workers.