Weighted asymmetric least squares regression for longitudinal data using GEE
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The well-known generalized estimating equations (GEE) is widely used to estimate the effect of the covariates on the mean of the response variable. We apply the GEE method using the asymmetric least-square regression (expectile) to analyze the longitudinal data. Expectile regression naturally extends the classical least squares method and has properties similar to quantile regression. Expectile regression allows the study of the heterogeneity of the effects of the covariates over the entire distribution of the response variable, while also accounting for unobserved heterogeneity. In this paper, we present the generalized expectile estimating equations estimators, derive their asymptotic properties and propose a robust estimator of their variance-covariance matrix for inference. The performance of the new estimators is evaluated through exhaustive simulation studies, and their advantages in relation to existing methods are highlighted. Finally, the labor pain dataset is analyzed to illustrate the usefulness of the proposed model.
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