# Writing an ordinal (proportion odds model) as function of binary regression

I wonder if it is possible to write a proportional odds model as some function of binary logistic models.

Indeed I have data on an ordinal response scale (mild, moderate, poor). There are options to dichotomous the data because, we will only need to apply two treatments. But of-course an ordinal model can be use for the classification, then the choice of the two treatments can be applied accordingly.

The question is which model does well on the data? How do we quantify "do well"?

Available solutions are: 1) Build the models and look at the AUC for binary and VUS for ordinal and compare them. 2)Look at the Brier score for ordinal and binary model.

But I still think the fundamental solutions lie on the effects we are modelling ($\beta$) how do they relate for the two models.

• You will get better responses if your question is more specific. What are the models you have in mind and what do you want to achieve with this approach? What are your initial ideas to approach this problem? – Andy May 12 '14 at 9:39