Nonparametric bootstrapping for hierarchical data

Abstract

Nonparametric bootstrapping for hierarchical data is relatively underdeveloped and not straightforward: certainly it does not make sense to use simple nonparametric resampling, which treats all observations as independent. We have provided some resampling strategies of hierarchical data, proved that the strategy of nonparametric bootstrapping on the highest level (randomly sampling all other levels without replacement within the highest level selected by randomly sampling the highest levels with replacement) is better than that on lower levels, analyzed real data and performed simulation studies.

Keywords:

• random effects model
• hierarchical data
• nonparametric bootstrapping
• resampling schemes
• unbalanced data

Acknowledgements

This research was supported by grants from the National Institute on Drug Abuse (DA12777) of United States of America. The authors are grateful to the editor and two referees for comments which improved this paper.