Estimation of marginal model with subgroup auxiliary information

Marginal model is a popular instrument for studying longitudinal data and cluster data. This paper investigates the estimator of marginal model with subgroup auxiliary information. To marginal model, we propose a new type of auxiliary information, and combine them with the traditional estimating equations of the quadratic inference function (QIF) method based on the generalized method of moments (GMM). Thus obtaining a more efficient estimator. The asymptotic normality and the test statistics of the proposed estimator are established. The theoretical result shows that the estimator with subgroup information is more efficient than the conventional QIF one. Simulation studies are carried out to examine the performance of the proposed method under finite sample. We apply the proposed method to a real data for illustration.