A1847
Title: Scoring-based model choice for conditional transformation models
Authors: Alexander Ritz - Clausthal University of Technology (Germany) [presenting]
Benjamin Saefken - Clausthal University of Technology (Germany)
Abstract: Conditional transformation models (CTMs) offer a flexible and interpretable way to obtain conditional density estimates, allowing for a more complete understanding of the response distribution given the explanatory variables than models focused exclusively on the conditional mean. At the same time, estimates of full conditional distributions are harder to assess in their ability to capture the true data generating process. In order to establish a rigorous approach to model choice for CTMs, it is possible to rely on scoring rules, which are not restricted to evaluating model performance via an implied point estimate. However, in scenarios where data is not abundant, this approach bears the risk of overestimating the model's out-of-sample performance if the same data is used to estimate as well as evaluate model fit. Therefore, it is necessary to correct for this bias in an analogous manner to established covariance penalties for prediction error estimates. A bias correction for proper scoring rules is derived and a scoring-based model choice criterion is constructed, facilitating the rigorous choice of parsimonious distributional regression models. Models chosen by this approach are further assessed in comparison to those selected via established model choice criteria like WAIC.
