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.

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    $\begingroup$ 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? $\endgroup$ – Andy May 12 '14 at 9:39

You can get close, and this approximation is behind the Brant test and the Wolfe-Gould test of the proportional odds assumption. However, a proportional odds model will include the constraint that the predicted probabilities for the different outcomes categories add up to 1, while the separate logit models obviously have no way of enforcing that constraint.

  • $\begingroup$ Indeed thanks a lot. I am looking at the Brant test paper. My ultimate goal is to assess the performances of these two models on prediction. Assessment measures I have in mind so far are the AUC(VUS) and the Brier . But if I can also write these models in an equivalent way it will be useful. $\endgroup$ – Chamberlain Foncha May 12 '14 at 9:56
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    $\begingroup$ @ChamberlainFoncha : Which two models do you want to compare? It is probably best if you edit your question to clarify which models you want to compare and why you want to do that. $\endgroup$ – Maarten Buis May 12 '14 at 10:07
  • $\begingroup$ I have edited my question. I hope it is explicit enough. Meanwhile your answer seems like a useful start to the tackle to this problem with the cited paper. $\endgroup$ – Chamberlain Foncha May 12 '14 at 11:40

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