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

• Published in: Journal of applied statistics Vol. 49; no. 14; pp. 3564 - 3590
• Main Authors: Barry, Amadou, Oualkacha, Karim, Charpentier, Arthur
• Format: Journal Article
• Language: English
• Published: England Taylor & Francis 26.10.2022; Taylor & Francis Ltd
• Subjects: Asymmetry; Asymptotic properties; cluster data; Covariance matrix; Data analysis; Estimators; Expectile regression; GEE working correlation; Heterogeneity; Least squares; longitudinal data; quantile regression; Statistical methods; quantile regression; GEE working correlation; Expectile regression; cluster data; longitudinal data
• ISSN: 0266-4763; 1360-0532; 1360-0532
• DOI: 10.1080/02664763.2021.1957789

Generalized estimating equations 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 with the asymmetric least squares (expectile) regression to derive a new class of estimators, which we call generalized expectile estimating equations . The 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 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.