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Generalized estimating equations (GEE) are widely used to analyzelongitudinal data; however, they are not appropriate for heteroscedastic data,because they only estimate regressor effects on the meanresponse{\textemdash}and therefore do not account for data heterogeneity. Here,we combine the GEE with the asymmetric least squares (expectile) regression toderive a new class of estimators, which we call generalized expectileestimating equations (GEEE). The GEEE model estimates regressor effects on theexpectiles of the response distribution, which provides a detailed view ofregressor effects on the entire response distribution. In addition to capturingdata heteroscedasticity, the GEEE extends the various working correlationstructures to account for within-subject dependence. We derive the asymptoticproperties of the GEEE estimators and propose a robust estimator of itscovariance matrix for inference (see our R package,github.com/AmBarry/expectgee). Our simulations show that the GEEE estimator isnon-biased and efficient, and our real data analysis shows it capturesheteroscedasticity.

A new GEE method to account for heteroscedasticity, using asymmetric least-square regressions