Generalized expectile regression with flexible response function.

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Expectile regression generalizes least squares, modeling entire distributions without parametric assumptions.
• It offers flexibility similar to semiparametric mean regression but assumes linear predictor-response relationships.
• Nonlinear relationships can cause significant bias in parameter estimates and predictions, especially with bounded outcome variables.

Purpose of the Study:

• To address biases in expectile regression caused by nonlinear relationships between predictors and responses.
• To develop a method that ensures predictions remain within the valid range of bounded outcome variables.
• To improve the analysis of self-reported scores, such as hearing ability.

Main Methods:

• Proposed a novel expectile regression framework incorporating an estimated response function.
• Designed the response function as a monotonically increasing P-spline, allowing for constraints.
• Estimated the response function and covariate effects simultaneously.

Main Results:

• The proposed method produced valid estimates for a self-reported listening effort score.
• Nonlinear estimation of the response function corrected biases observed in classical expectile regression.
• Strong associations were found between the model's predictions and the speech reception threshold.

Conclusions:

• Jointly estimating the response function and covariate effects in expectile regression effectively handles nonlinearities and bounded outcomes.
• This approach enhances the reliability of expectile regression for analyzing real-world data with inherent constraints.
• The method shows promise for applications in audiology and other fields analyzing limited-range self-reported data.