Modelling monotonic effects of ordinal predictors in Bayesian regression models

Area of Science:

• Statistics
• Regression Analysis
• Computational Statistics

Background:

• Ordinal predictors are frequently misused in regression, treated as nominal or metric.
• This incorrect handling leads to suboptimal inference and predictions.
• Existing methods may not fully capture the nuanced information within ordinal predictors.

Purpose of the Study:

• To propose a new method for modeling ordinal predictors with monotonic effects.
• To provide a robust framework for analyzing ordinal data that respects its inherent order.
• To improve the accuracy of statistical inference and predictions from regression models.

Main Methods:

• A novel parameterization for monotonic effects using a scale parameter (b) and a simplex parameter.
• Generalization of the method to include interaction terms and multilevel structures.
• Bayesian estimation using Stan, implemented in the R package brms.

Main Results:

• Simulation studies demonstrate the model is well-calibrated.
• The proposed method shows competitive or superior predictive performance when monotonicity is present.
• The Bayesian framework allows for prior incorporation and monotonicity assumption checking.

Conclusions:

• The new method effectively models monotonic effects of ordinal predictors.
• It offers a significant improvement over treating ordinal predictors as nominal or metric.
• The R package brms makes Bayesian estimation of monotonic effects accessible.