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

Amadou Barry; Karim Oualkacha; Arthur Charpentier

doi:10.1080/02664763.2021.1957789

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

J Appl Stat. 2021 Jul 26;49(14):3564-3590. doi: 10.1080/02664763.2021.1957789. eCollection 2022.

Authors

Amadou Barry^{1

2}, Karim Oualkacha³, Arthur Charpentier³

Affiliations

¹ Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montréal, QC, Canada.
² Lady Davis Institute, Jewish General Hospital, Montréal, QC, Canada.
³ Department of Mathematics and Statistics, Université du Québec à Montréal, Montréal, QC, Canada.

Abstract

Generalized estimating equations $(G E E)$ 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 - and therefore do not account for data heterogeneity. Here, we combine the $G E E$ with the asymmetric least squares (expectile) regression to derive a new class of estimators, which we call generalized expectile estimating equations $(G E E E)$ . The $G E E E$ 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 $G E E E$ 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.

Keywords: Expectile regression; GEE working correlation; cluster data; longitudinal data; quantile regression.