Selection of Working Correlation Structure in Generalized Estimating Equations via Empirical Likelihood

Abstract

Generalized estimating equations (GEE) are a popular class of models for analyzing discrete longitudinal data, and do not require the specification of a full likelihood. The GEE estimator for the regression parameter will be the most efficient if the working correlation matrix is correctly specified. Hence it is desirable to choose a working correlation matrix that is the closest to the underlying structure among a set of working structures. In the absence of a parametric likelihood, traditional likelihood-based model selection methods cannot be used for comparing GEE models. Combining the reliability of nonparametric methods with the flexibility and effectiveness of likelihood approaches, empirical likelihood (EL) has the potential to become a model selection tool for GEE. We propose an EL approach to select the working correlation structure in GEE. Our approach is compared to existing methods based on quasi-likelihood or resampling procedures. The effectiveness of the proposed method is demonstrated by simulations. Supplemental materials for this article are available online.

Improving the correlation structure selection approach for generalized estimating equations and balanced longitudinal data

“…In this case, we can more efficiently estimate cov ( Y i ) within the empirical covariance matrix with rather than ( Y i − μ i ) ( Y i − μ i ) T , i = 1, … , N , thus possibly enhancing the selection performances of criteria. For instance, Chen and Lazar proposed criteria based upon empirical likelihood versions of the AIC and BIC, which performed better than the CIC and QIC in their simulation study. However, their criteria assume correctly specified working marginal variances and a common correlation structure, which was only as general as the stationary structure in their simulation study.…”

A moving blocks empirical likelihood method for longitudinal data

“…Until results from future research, currently whether one set of M and L choice is better than the others is still not yet known. Choice of working correlation structures of the methods may be based on prior information or scientific consideration, as well as many existing methods such as CIC (Hin and Wang, ), QIC (Pan, ), and the empirical AIC and BIC (Chen and Lazar, ). If prior or scientific information is available, it may be preferable to use this information to choose working correlation structure, but even in this case it may be desirable to also compare the results with those based on CIC, QIC, and empirical AIC/BIC as sensitivity analysis, since such sensitivity analysis may provide additional insights.…”

Generalized Estimating Equations in Longitudinal Data Analysis: A Review and Recent Developments

“…The author indicated that the covariates were first selected based on QIC, and the variance function could be identified as the one minimizing EQIC given the selected covariates; then "working" correlation structure selection could be achieved based on CIC; in addition, they found out that the covariates selection by EQIC given different working variance functions was more consistent than that based on QIC [45]. Besides those criteria mentioned above, Cantoni et al also discussed the covariate selection for longitudinal data analysis [46]; also, a variance function selection was mentioned by Pan and Mackenzie [30] as well as Wang and Lin [47]; in addition, more work on "working" correlation structure selection was addressed by Chaganty and Joe [48], Wang and Lin [47], Gosho et al [49,50], Jang [51], Chen [52], and Westgate [53][54][55], among others. Overall, the model selection of GEE is nontrivial, where the best selection criterion is still being pursued [56], and the recent work by Wang et al can be followed up as the rule of thumb [45].…”