Generalized empirical likelihood methods for analyzing longitudinal data

Abstract

<jats:title>Abstract</jats:title> <jats:p>Efficient estimation of parameters is a major objective in analyzing longitudinal data. We propose two generalized empirical likelihood-based methods that take into consideration within-subject correlations. A nonparametric version of the Wilks theorem for the limiting distributions of the empirical likelihood ratios is derived. It is shown that one of the proposed methods is locally efficient among a class of within-subject variance-covariance matrices. A simulation study is conducted to investigate the finite sample properties of the proposed methods and compares them with the block empirical likelihood method by You et al. (2006) and the normal approximation with a correctly estimated variance-covariance. The results suggest that the proposed methods are generally more efficient than existing methods that ignore the correlation structure, and are better in coverage compared to the normal approximation with correctly specified within-subject correlation. An application illustrating our methods and supporting the simulation study results is presented.</jats:p>

Selection of working correlation structure in generalized estimating equations

“…Empirical likelihood provides a valuable approach for parameter estimation and hypothesis tests in nonparametric or distribution‐free contexts . It has good properties, performs well especially for small and moderate sample sizes, and hence has received considerable attention in analyzing longitudinal data .…”

Comparison of Extended Empirical Likelihood Methods: Size and Shape of Test Based Confidence Regions

“…Since its introduction by Owen (1988Owen ( , 1990, the methodology has been extended to the analysis of censored data (Li, Li & Zhou (2005)), longitudinal data (e.g., Wang, Qian & Carroll (2010)) and semi-parametric regression model (e.g., Shi & Lau Statistica Sinica: Newly accepted Paper (accepted version subject to English editing) (2000)). In a wide range of applications as outlined in Owen (2001) empirical likelihood ratio statistics were shown to have limiting chi-square distributions, that is, observe a Wilks theorem.…”

Generalized Empirical Likelihood Inference in Generalized Linear Models for Longitudinal Data

“…To consider the within correlation, Li et al (2008) considered an empirical likelihood method by introducing the working covariance matrix in partially linear model. Wang et al (2010) proposed two generalized empirical likelihood-based methods.…”