  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.
