Assessing Proportionality in the Proportional Odds Model for Ordinal Logistic Regression

TLDR

The proportional odds model extends binary logistic regression to ordinal outcomes by fitting a series of logistic regressions with common parameters that embody the proportional odds assumption. The study aims to assess the proportionality assumption, which is essential for valid application of the model. An approach based on comparing correlated fits of the underlying binary logistic models and on asymptotic goodness‑of‑fit statistics, supplemented by bootstrap simulation, is proposed. The authors discuss and illustrate several proposals, including bootstrap simulation, using a data example.

Abstract

The proportional odds model for ordinal logistic regression provides a useful extension of the binary logistic model to situations where the response variable takes on values in a set of ordered categories. The model may be represented by a series of logistic regressions for dependent binary variables, with common regression parameters reflecting the proportional odds assumption. Key to the valid application of the model is the assessment of the proportionality assumption. An approach is described arising from comparisons of the separate (correlated) fits to the binary logistic models underlying the overall model. Based on asymptotic distributional results, formal goodness-of-fit measures are constructed to supplement informal comparisons of the different fits. A number of proposals, including application of bootstrap simulation, are discussed and illustrated with a data example.