Ordinal regression models made easy: A tutorial on parameter interpretation, data simulation and power analysis

Abstract

Ordinal data such as Likert items, ratings or generic ordered variables are widespread in psychology. These variables are usually analysed using metric models (e.g., standard linear regression) with important drawbacks in terms of statistical inference (reduced power and increased type-1 error) and prediction. One possible reason for not using ordinal regression models could be difficulty in understanding parameters or conducting a power analysis. The tutorial aims to present ordinal regression models using a simulation-based approach. Firstly, we introduced the general model highlighting crucial components and assumptions. Then, we explained how to interpret parameters for a logit and probit model. Then we proposed two ways for simulating data as a function of predictors showing a 2 × 2 interaction with categorical predictors and the interaction between a numeric and categorical predictor. Finally, we showed an example of power analysis using simulations that can be easily extended to complex models with multiple predictors. The tutorial is supported by a collection of custom R functions developed to simulate and understand ordinal regression models. The code to reproduce the proposed simulation, the custom R functions and additional examples of ordinal regression models can be found on the online Open Science Framework repository ( https://osf.io/93h5j).