Ordinal Regression Models in Psychology: A Tutorial

Abstract

Ordinal variables, although extremely common in psychology, are almost exclusively analyzed with statistical models that falsely assume them to be metric. This practice can lead to distorted effect-size estimates, inflated error rates, and other problems. We argue for the application of ordinal models that make appropriate assumptions about the variables under study. In this Tutorial, we first explain the three major classes of ordinal models: the cumulative, sequential, and adjacent-category models. We then show how to fit ordinal models in a fully Bayesian framework with the R package brms, using data sets on opinions about stem-cell research and time courses of marriage. The appendices provide detailed mathematical derivations of the models and a discussion of censored ordinal models. Compared with metric models, ordinal models provide better theoretical interpretation and numerical inference from ordinal data, and we recommend their widespread adoption in psychology.