  Generalized estimating equations (GEE) are widely used to analyze
longitudinal data; however, they are not appropriate for heteroscedastic data,
because they only estimate regressor effects on the mean
response{\textemdash}and therefore do not account for data heterogeneity. Here,
we combine the GEE with the asymmetric least squares (expectile) regression to
derive a new class of estimators, which we call generalized expectile
estimating equations (GEEE). The GEEE model estimates regressor effects on the
expectiles of the response distribution, which provides a detailed view of
regressor effects on the entire response distribution. In addition to capturing
data heteroscedasticity, the GEEE extends the various working correlation
structures to account for within-subject dependence. We derive the asymptotic
properties of the GEEE estimators and propose a robust estimator of its
covariance matrix for inference (see our R package,
github.com/AmBarry/expectgee). Our simulations show that the GEEE estimator is
non-biased and efficient, and our real data analysis shows it captures
heteroscedasticity.
