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

Area of Science:

• Psychology
• Statistics
• Data Analysis

Background:

• Ordinal data (e.g., Likert scales, ratings) are common in psychology but often analyzed with metric models, leading to statistical inference and prediction issues.
• Challenges in understanding ordinal regression parameters and conducting power analyses may hinder their adoption.

Purpose of the Study:

• To present ordinal regression models using an accessible simulation-based approach.
• To clarify parameter interpretation and demonstrate data simulation techniques for ordinal predictors.
• To illustrate power analysis for ordinal regression models.

Main Methods:

• Introduced the general ordinal regression model, its components, and assumptions.
• Explained parameter interpretation for logit and probit ordinal models.
• Demonstrated data simulation with examples of 2x2 interactions and numeric-categorical predictor interactions.

Main Results:

• Provided a simulation-based framework for understanding ordinal regression.
• Showcased practical data simulation methods applicable to complex designs.
• Presented an example of power analysis for ordinal regression, extendable to multiple predictors.

Conclusions:

• Simulation-based approaches and custom R functions can demystify ordinal regression models.
• This tutorial facilitates better statistical inference and prediction for ordinal data in psychological research.
• Accessible code and functions are available for reproducing simulations and applying ordinal regression.