Bayesian Discrete Conditional Transformation Models

TL;DR

This paper introduces a flexible Bayesian framework for modeling discrete ordinal and count data using conditional transformation functions, accommodating excess zeros and complex covariate effects.

Contribution

It presents a novel Bayesian, distribution-free approach for count and ordinal data, including models for excess zeros and category-specific effects, with a modular MCMC inference scheme.

Findings

Effective modeling of count data with excess zeros.

Flexible ordinal response modeling with covariate effects.

Applications demonstrate versatility in real-world data.

Abstract

We propose a novel Bayesian model framework for discrete ordinal and count data based on conditional transformations of the responses. The conditional transformation function is estimated from the data in conjunction with an a priori chosen reference distribution. For count responses, the resulting transformation model is novel in the sense that it is a Bayesian fully parametric yet distribution-free approach that can additionally account for excess zeros with additive transformation function specifications. For ordinal categoric responses, our cumulative link transformation model allows the inclusion of linear and nonlinear covariate effects that can additionally be made category-specific, resulting in (non-)proportional odds or hazards models and more, depending on the choice of the reference distribution. Inference is conducted by a generic modular Markov chain Monte Carlo algorithm where multivariate Gaussian priors enforce specific properties such as smoothness on the functional effects. To illustrate the versatility of Bayesian discrete conditional transformation models, applications to counts of patent citations in the presence of excess zeros and on treating forest health categories in a discrete partial proportional odds model are presented.