Generalized estimating equation (GEE) is widely adopted for regression
modeling for longitudinal data, taking account of potential correlations within
the same subjects. Although the standard GEE assumes common regression
coefficients among all the subjects, such assumption is not realistic when
there are potential heterogeneity in regression coefficients among subjects. In
this paper, we develop a flexible and interpretable approach, called grouped
GEE analysis, to modeling longitudinal data with allowing heterogeneity in
regression coefficients. The proposed method assumes that the subjects are
divided into a finite number of groups and subjects within the same group share
the same regression coefficient. We provide a simple algorithm for grouping
subjects and estimating the regression coefficients simultaneously, and show
asymptotic properties of the proposed estimator. The number of groups can be
determined by the cross validation with averaging method. We demonstrate the
proposed method through simulation studies and an application to a real
dataset.Comment: 64 page