Parsimonious modeling of category-specific effects in partial proportional odds models based on trees

The proportional odds model is arguably the most widely applied regression approach for ordinal response variables. It assumes that the effects of the covariates are constant across the response categories allowing a parsimonious model specification. A violation of this assumption, however, may lead to biased effect estimates and decreased predictive ability. To overcome this issue, partial proportional odds models, where proportionality is only enforced for a smaller subset of covariates, can be applied. While statistical tests to check the proportional odds assumption are available, a generalized framework for data-driven selection of category-specific effects has not been established. In this paper, we introduce a novel tree-structured algorithm that forms clusters of categories sharing the same effect on the ordinal response, with a focus on model parsimony and ease of interpretation. The proposed model appeared to be superior to alternatives in a clinical application to data from the University Hospital Bonn on patients presenting in the emergency department. The predictive ability and selection properties of the proposed approach were also compared to alternative approaches, such as LASSO-penalized regression, in a simulation study.