Correlation structure and variable selection in generalized estimating equations via composite likelihood information criteria

TL;DR

This paper introduces a weighted scores method for generalized linear models with correlated data, utilizing composite likelihood criteria for effective variable and correlation structure selection, outperforming existing GEE methods.

Contribution

It proposes a likelihood-based weighted scores approach combined with composite likelihood criteria for improved model and correlation structure selection in GEE.

Findings

Outperforms existing model selection methods in simulations

Allows for correct analysis and potentially different inferential results

Effective in selecting correlation structures and variables

Abstract

The method of generalized estimating equations (GEE) is popular in the biostatistics literature for analyzing longitudinal binary and count data. It assumes a generalized linear model (GLM) for the outcome variable, and a working correlation among repeated measurements. In this paper, we introduce a viable competitor: the weighted scores method for GLM margins. We weight the univariate score equations using a working discretized multivariate normal model that is a proper multivariate model. Since the weighted scores method is a parametric method based on likelihood, we propose composite likelihood information criteria as an intermediate step for model selection. The same criteria can be used for both correlation structure and variable selection. Simulations studies and the application example show that our method outperforms other existing model selection methods in GEE. From the example, it can be seen that our methods allow for correct analysis, and may change the inferential results.