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I have ordinal data (4 levels) which I have fit with:

a) 1 proportional-odds logistic regression model

and also

b) 3 separate binary logistic regression models fit to values >= levels 2, 3, and 4.

The binary model curves and coefficients are 'very close' to those of the ordinal model, which has substantive implications. My question is whether there is a formal way to describe 'very close', other than looking at a plot of the curves and looking at the coefficients.

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  • $\begingroup$ Not sure how to develop this in a formal way, but I'd suggest comparing the odds ratio of the ordinal model with the respective binary ones. $\endgroup$
    – Lucas Farias
    Commented Nov 16, 2018 at 11:04
  • $\begingroup$ Your option b looks very like the continuation ratio model but it is not clear to me exactly what you did. $\endgroup$
    – mdewey
    Commented Nov 16, 2018 at 21:32

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b) is not recommended method. You can fit one model called generalized logit model to replace 3 models in b. You already have proportional-odds logit model. Then you are ready to perform likelihood ratio test. No significant means no difference between two models. Therefore we will select the simple one: proportional-odds logit model. If significant, maybe you can try partial proportional-odds logit model. if you have more than one covariate.

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