Composite empirical likelihood for multisample clustered data

TL;DR

This paper introduces a composite empirical likelihood method for analyzing multisample clustered data, effectively handling cluster structures without parametric assumptions, and provides a bootstrap approach for valid variance estimation.

Contribution

It develops a novel composite empirical likelihood approach for multisample clustered data under a density ratio model, avoiding parametric assumptions and improving inference accuracy.

Findings

The method performs well in simulations, providing accurate variance estimates.

It effectively controls type I errors in hypothesis testing.

Application to real data demonstrates practical utility.

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 generalized 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 utilizes 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.