Estimation of marginal generalized linear model with subgroup auxiliary information

Abstract

Marginal generalized linear model (MGLM) is a popular instrument for studying longitudinal and cluster data. This paper investigates an estimator for regression coefficients in MGLM, which incorporates subgroup auxiliary information. We propose to use the conditional expectation of the response in each subgroup as auxiliary information, and combine that information with the estimating equations of the quadratic inference function (QIF) method based on the framework of generalized method of moments (GMM). The asymptotic normality and test statistics of the proposed estimator are established, which indicate that the estimator of the proposed estimator is more efficient than the QIF one. Simulation studies are carried out to examine the performance of the proposed method under finite sample sizes, and an education data is used to illustrate our approach.

Keywords:

• Auxiliary information
• estimation efficiency
• generalized method of moments
• marginal generalized linear model
• quadratic inference function

Acknowledgments

The authors thank the reviewer, the associate editor and the Editor-in-Chief for their constructive and insightful comments that led to significant improvements in the article.

Additional information

Funding

This research was supported by the Fundamental Research Funds for the Central Universities SKZZB2015022 (Li) and the National Natural Science Foundation of China grant 11771049 (Duan).