A comparison between the varying-thresholds model and quantile regression

The varying-thresholds model is a new modelling approach capable of estimating the whole conditional distribution of a response variable in a regression setting. The varying-thresholds model can be used for continuous, ordinal and count responses. Conditional quantiles estimated through the varying-thresholds method are compared to those of quantile regression. The comparison is based on models' simulations to assess the performance of the two methodologies regarding the coverage and width of prediction intervals. The simulation study encompasses eight different settings with several functional forms and types of errors. In addition, a discrete variation of the continuous ranked probability score is proposed as a way to choose the best link function for the binary models used to estimate the varying-thresholds model. The comparison shows that the varying thresholds model performs better whenever the functional form of the true data generating model is non-linear.