Modifications of QIC and CIC for Selecting a Working Correlation Structure in the Generalized Estimating Equation Method

Abstract

The generalized estimating equation (GEE) method is a popular method for analyzing longitudinal data. An inappropriate specification of the working correlation structure reduces the efficiency of the GEE estimation. Pan (2001a) and Hin and Wang (2009) proposed a quasi-likelihood under the independence model criterion (QIC) and a correlation information criterion (CIC) for selecting a proper working correlation structure, respectively. In this study, we proposed modifications to the QIC and CIC using the variance estimators of the GEE with improved small-sample properties. In a simulation study, the performance of the modified QIC and CIC was better than that of the original QIC and CIC. The modified methods were illustrated using the data for an air pollution study.

Consistency Inference Property of QIC in Selecting the True Working Correlation Structure for Generalized Estimating Equations

“…For each simulation setting, the success rates of QIC in selecting the true AR-1 structure for ω Q is approximately twice the success rate of QIC in selecting the true AR-1 structure for ω / . The results obtained for ω Q , were similar to results obtained by Gosho [13] who established success rates of between 32.1% and 72% indicating that the probability of QIC selecting the true AR-1 correlation approached one as…”

“…QIC selection rates established for ω Q are similar to results [1,13] who both established success rates of up to 72% for : 0.5 and m=3 and 4 respectively. However the increase in performance of QIC with increase in in m and : established in the study is dissimilar to results [13] whose indicated that simultaneously increasing m to 8 and : to 0.5 resulted to a slight decrease in the selection rates. The results are further presented in figure 2.…”

“…QIC selection rates established for the set ω / in the study are similar to those of Jang [13] who established QIC's performance to be in the range of 0%to 20% and tended to decrease as n increased, those [2] who established correct identification rates of 25-30% for moderately correlated exchangeable structure and the results [14] who established success rates of less than 50% for all combinations of m and :. The study [13] asserted that the performance was due to the estimation of the overparameterized structure which becomes more precise as n increases hence increasing the likelihood of the unstructured matrix to be chosen. QIC selection rates established for ω Q are similar to results [1,13] who both established success rates of up to 72% for : 0.5 and m=3 and 4 respectively.…”

“…The study [13] asserted that the performance was due to the estimation of the overparameterized structure which becomes more precise as n increases hence increasing the likelihood of the unstructured matrix to be chosen. QIC selection rates established for ω Q are similar to results [1,13] who both established success rates of up to 72% for : 0.5 and m=3 and 4 respectively. However the increase in performance of QIC with increase in in m and : established in the study is dissimilar to results [13] whose indicated that simultaneously increasing m to 8 and : to 0.5 resulted to a slight decrease in the selection rates.…”

A robust and unified framework for estimating heritability in twin studies using generalized estimating equations

“…For example, what mean‐level covariate effects should be included, should one use GEE2‐NACE or GEE2‐Falconer (we recommend the later due to the potential bias of GEE2‐NACE demonstrated in Section 3.3), and what covariates should one allow heritability to differ by. Several information criteria have been proposed for model selection in GEE‐type models 33‐35 . It would be interesting to try extending these methods to the GEE2‐NACE and GEE2‐Falconer twin models, especially for deciding which covariates affect heritability.…”