Composite empirical likelihood for multisample clustered data

Abstract

In many applications, data cluster. Failing to take the cluster structure into consideration generally leads to underestimated variances of point estimators and inflated type I errors in hypothesis tests. Many circumstance-dependent approaches have been developed to handle clustered data. A working covariance matrix may be used in generalised estimating equations. One may throw out the cluster structure and use only the cluster means, or explicitly model the cluster structure. Our interest is the case where multiple samples of clustered data are collected, and the population quantiles are particularly important. We develop a composite empirical likelihood for clustered data under a density ratio model. This approach avoids parametric assumptions on the population distributions or the cluster structure. It efficiently utilises the common features of the multiple populations and the exchangeability of the cluster members. We also develop a cluster-based bootstrap method to provide valid variance estimation and to control the type I errors. We examine the performance of the proposed method through simulation experiments and illustrate its usage via a real-world example.

Keywords:

• Bootstrap
• clustered data
• composite likelihood
• density ratio model
• empirical likelihood
• multiple sample
• random effect

Acknowledgments

We thank the editor, the Editorial Board member, and two anonymous referees for their constructive suggestions that significantly improved the paper. We are indebted to Drs. Steve Verrill, David Kretschmann, and James Evans at the USDA Forest Products Lab for making their report available as well as for providing the dataset on which their analyses and now ours are based. We are also indebted to the Forest Products Stochastic Modelling Group centred at the University of British Columbia (UBC): members of this group from FPInnovations in Vancouver, Simon Fraser University, and UBC provided stimulating discussions of the long-term monitoring program to which this paper contributes.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The authors gratefully acknowledge funding from Yunnan University, from Natural Sciences and Engineering Research Council of Canada (NSERC) Grants RGPIN-2019-04204 and RGPIN-2020-04964, the National Natural Science Foundation of China (Numbers 11871419, 11771144), and the 111 Project of the Ministry of Education of China (B14019), a Collaborative Research and Development Grant from Natural Sciences and Engineering Research Council of Canada (NSERC) and FPInnovations.