My outcome is an ordinal variable having 4 levels. I did an ordinal regression and get one universal beta-coefficient describing each level change.

If I do 3 logistic regressions on each level change, I would have an alpha-error of 3 * 5% (multiple testing)

My question: Is there such a cumulation of alpha error in ordinal regression models (proportional odds or continuation ratio), too?


If you are using the ordinary parallel forms of proportion odds or CR models, the restrictions imposed on those models (equal slopes assumptions) concentrates the effects into a single parameter if the predictor is linear. There is no extra type I error. This is a form of borrowing information across $Y$ levels.

  • $\begingroup$ thx for your answer. is this still true in "partial proportional models", where the equal slopes assumption does not hold for one predictor, and where the model gives for that predictor a coefficient for each level change (while giving universal coefficients for any other predictor)? $\endgroup$ – Produnis Aug 4 '13 at 18:35
  • 2
    $\begingroup$ No, then all bets are off. It is best for those models to do joint (composite; chunk) tests grouping all the parameters that go with each predictor. The degrees of freedom in such tests is equal to the number of unconstrained slopes, which gives a perfect multiplicity adjustment. And if you estimate cutoff-specific effects of variables or make graphical judgments doing same, you'll need to estimate the effective degrees of freedom to do the multiplicity adjustment. $\endgroup$ – Frank Harrell Aug 4 '13 at 22:23

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