Bayesian Approaches to Assessing the Parallel Lines Assumption in Cumulative Ordered Logit Models

Abstract

We first review existing literature on cumulative logit models along with various ways to test the parallel lines assumption. Building on the traditional frequentist framework, we introduce a method of Bayesian assessment of null values to provide an alternative way to examine the parallel lines assumption using highest density intervals and regions of practical equivalence. Second, we propose a new hyperparameter cumulative logit model that can improve upon existing ones in addressing several challenges where traditional modeling techniques fail. We use two empirical examples from health research to showcase the Bayesian approaches.