Comparing flexible modelling approaches: the varying-thresholds model versus quantile regression

The varying-thresholds model (VTM) is a novel methodology proposed by Tutz (Flexible predictive distributions from varying-thresholds modelling. https://doi.org/10.48550/arXiv.2103.13324, arXiv:2103.13324 2021) capable of estimating the whole conditional distribution of a response variable in a regression setting. It can be used for continuous, ordinal and count responses. In this study, conditional quantiles and prediction intervals estimated through VTM are compared with those of quantile regression. The comparison is based on a set of data-generating models to assess the performance of the two methodologies regarding the coverage and width of prediction intervals. The simulation study encompasses settings with several functional forms and types of errors. In addition, a discrete version of the continuous ranked probability score is proposed as a tool to choose the best link function for the binary models used in the fitting of VTM. In summary, the varying-thresholds model is a flexible methodology that can be broadly applied with light assumptions; it is advantageous over quantile regression when the conditional quantile function is misspecified.