Assessing Proportionality in the Proportional Odds Model for Ordinal Logistic Regression

(1990) - Rollin Brant

Journal: Biometrics
Link::
DOI:: 10.2307/2532457
Links::
Tags:: #paper #Methods #ProportionalOddsModel #OrdinalLogit
Cite Key:: [@Brant1990]

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.

Notes

"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." (Brant 1990:1172)

"Suppose that one has N sets of independent observations on a response variable y taking ordinal values 1 to k and x a p-vector of explanatory variables. The proportional odds model (McCullagh, 1980) is based on consideration of the cumulative distribution probabilities 'yJ = Pr{ y - j } and takes the form logit(-yj) = log[Lyj/(l - yA)] = Oj-,Btx where the p-vector , and 01 < 02 < ... < Ok-I represent unknown parameters. The mod" (Brant 1990:1172)