Assessing proportionality in the proportional odds model for ordinal logistic regression

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Ordinal logistic regression models ordered categorical data.
• The proportional odds model is a common approach for such data.
• Valid application requires assessing the proportional odds assumption.

Purpose of the Study:

• To describe an approach for assessing the proportionality assumption in ordinal logistic regression.
• To develop formal goodness-of-fit measures for this assumption.
• To illustrate the methods with a data example.

Main Methods:

• Comparing correlated fits of underlying binary logistic models.
• Utilizing asymptotic distributional results.
• Constructing formal goodness-of-fit measures.
• Applying bootstrap simulation.

Main Results:

• An approach for assessing the proportional odds assumption is presented.
• Formal goodness-of-fit measures are derived.
• The methods are demonstrated with a practical data example.

Conclusions:

• The described approach provides a formal method for assessing the proportional odds assumption.
• Goodness-of-fit measures and bootstrap simulation aid in validating model application.
• This enhances the reliability of ordinal logistic regression analyses.