B1212
Title: Parametric transformation models for location-scale regression with unknown response distribution
Authors: Johannes Brachem - Georg-August-University Goettingen (Germany) [presenting]
Paul Wiemann - University of Wisconsin-Madison (United States)
Thomas Kneib - University of Goettingen (Germany)
Abstract: Parametric transformation models for location and scale (PTM-LS) are a novel form of distributional regression for univariate continuous responses. While distributional regression models typically require the assumption of a theoretical response distribution, parametric transformation models infer the response distribution's form directly from the data and incorporate structured additive covariate models for its location and scale. The core of the model is a monotonically increasing transformation function that relates the response distribution to a reference distribution. This transformation function is constructed using a shape-constrained B-spline. PTM-LS can be viewed as a generalisation of well-known location-scale models for normally distributed responses. The model is presented in a Bayesian formulation, which allows for easy uncertainty quantification via credible intervals and for tempering the model's high flexibility through the use of regularising priors. Additionally, the reference distribution can be understood as the researcher's prior belief about the distribution of the data. A simulation study demonstrates the viability of the approach. The model is implemented in Python using the Liesel probabilistic programming framework. In sum, PTM-LS offer an interpretable, coherent approach for location-scale regression with unknown response distribution.
