The perils of quasi‐likelihood information criteria

Abstract

In this paper, we consider some potential pitfalls of the growing use of quasi-likelihood-based information criteria for longitudinal data to select a working correlation structure in a generalized estimating equation framework. In particular, we examine settings where the fully conditional mean does not equal the marginal mean as well as hypothesis testing following selection of the working correlation matrix. Our results suggest that the use of any information criterion for selection of the working correlation matrix is inappropriate when the conditional mean model assumption is violated. We also find that type I error differs from the nominal level in moderate sample sizes following selection of the form of the working correlation but improves as sample size is increased as the selection is then concentrated on a single correlation structure. Our results serve to underline the potential dangers that can arise when using information criteria to select correlation structure in routine data analysis.

Co‐occurrence of herbivorous fish functional groups correlates with enhanced coral reef benthic state

“…Unlike GLMs, GEEs are not based on the maximum likelihood theory; therefore, statistics derived under this theory, such as Akaike's information criterion, cannot be applied to GEEs. The quasi‐likelihood information criterion (QIC; Pan, 2001) was introduced as an alternative method of model selection in a GEE setting; however, these methods are commonly disputed and can give rise to errors (Wang et al, 2015). Model choice and correlation structure can therefore be guided by the data (Wang et al, 2015).…”

“…The quasi‐likelihood information criterion (QIC; Pan, 2001) was introduced as an alternative method of model selection in a GEE setting; however, these methods are commonly disputed and can give rise to errors (Wang et al, 2015). Model choice and correlation structure can therefore be guided by the data (Wang et al, 2015). Given that the premise of our study was based around the statistical tests between models, use of the QIC here was deemed inappropriate.…”