Abstract
Expectile regression, in contrast to classical linear regression, allows for heteroscedasticity and omits a parametric specification of the underlying distribution. This model class can be seen as a quantile-like generalization of least squares regression. Similarly as in quantile regression, the whole distribution can be modeled with expectiles, while still offering the same flexibility in the use of semiparametric predictors as modern mean regression. However, even with no parametric assumption for the distribution of the response in expectile regression, the model is still constructed with a linear relationship between the fitted value and the predictor. If the true underlying relationship is nonlinear then severe biases can be observed in the parameter estimates as well as in quantities derived from them such as model predictions. We observed this problem during the analysis of the distribution of a self-reported hearing score with limited range. Classical expectile regression should in theory adhere to these constraints, however, we observed predictions that exceeded the maximum score. We propose to include a response function between the fitted value and the predictor similarly as in generalized linear models. However, including a fixed response function would imply an assumption on the shape of the underlying distribution function. Such assumptions would be counterintuitive in expectile regression. Therefore, we propose to estimate the response function jointly with the covariate effects. We design the response function as a monotonically increasing P-spline, which may also contain constraints on the target set. This results in valid estimates for a self-reported listening effort score through nonlinear estimates of the response function. We observed strong associations with the speech receptionthreshold.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.