Graphical diagnostics to check model misspecification for the proportional odds regression model.

Area of Science:

• Statistics
• Biostatistics
• Regression Modeling

Background:

• The proportional odds (PO) regression model is widely applied for analyzing ordinal response data.
• Assessing the adequacy of the PO model is crucial for reliable interpretation of covariate effects.
• Existing diagnostic methods may not fully capture model misspecification in ordinal regression.

Purpose of the Study:

• To develop and evaluate novel graphical and numerical methods for assessing the proportional odds regression model.
• To extend existing residual-based diagnostic techniques for binary logistic regression to ordinal responses.
• To compare the performance of proposed methods against traditional goodness-of-fit statistics.

Main Methods:

• Generalization of cumulative sum of residuals methods for ordinal responses.
• Development of graphical diagnostic tools for evaluating functional form misspecification.
• Numerical methods for assessing covariate effects and link function adequacy.
• Simulation studies to compare diagnostic method performance.

Main Results:

• The proposed graphical methods demonstrate superior power in detecting model misspecification compared to Hosmer-Lemeshow-type statistics.
• The methods effectively identify functional misspecification in covariate effects.
• The framework accommodates assessment of link function misspecification.

Conclusions:

• The developed graphical and numerical methods provide valuable tools for validating proportional odds regression models.
• These methods enhance the reliability of analyses involving ordinal outcomes.
• The study offers practical advancements for applied statisticians and researchers using ordinal regression.