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I am trying to report the results of an odds ratio from a cumulative link model (ordinal regression) in a way that is comprehensible to statistically naive readers (and myself). As far is it is possible I would like to get a balance between accuracy and comprehensibility.

In the paper showcasing the clm package in R see here on p.15 the authors analyse and report data from a wine tasting study where ratings of bitterness of wine (ordered factor with five levels, higher being more bitter) is regressed on two predictors: exposure to cold (categorical no/yes) and contact between juice and skins (categorical no/yes).

The regression coefficients from this model are as follows

Coefficients:
         Estimate Std. Error z value  Pr(>|z|)
tempwarm   2.5031     0.5287   4.735  2.19e-06 ***
contactyes 1.5278     0.4766   3.205  0.00135 **

Focusing on the contact predictor the authors exponentiate the coefficient of 1.53 (yielding 4.61) and interpret it as follows.

"The odds ratio of bitterness being rated in category j or above (OR(Y>=j)) is ...4.61"

Now I admire their precision but such an interpretation does not give me much of a sense of what's happening and what the value of 4.61 means in this context. In this CV post the OP interprets their odds ratios from an cumulative link model where a three-level ordinal outcome indicating exam performance (below average, average, above average) is regressed on a binary attendance predictor (did not attend, attend) as follows

"the odds of achieving average or above average performance is 18.64 times more if the participant attended than if they did not"

Is this an acceptable way to interpret the odds ratio from a cumulative link model? The interpretation to me reads more like seems like something from a logistic regression with a bernoulli outcome where they have collapsed average and above average into one category and compared that to below average. Moreover I am not clear how one would transpose the interpretation from the second example I gave to the first example where there is a five- (rather than three-) level outcome.

For the first example could you say

"The odds of the wine being rated in a higher category of bitterness are an estimated 4.61 times greater if the skins and juice had contact with one another than if they did not."

??

Any advice much appreciated.

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I would interpret the contact coefficient as:

Wines fermented in contact with grape skins had an odds ratio of 4.61 for being reported in a higher category of bitterness.

My problem with the authors' interpretation is two fold:

  1. The use of jargon (OR(Y >= j)). The point of interpreting results is to get away from jargon.
  2. It's a bit ambiguous verging on wrong. By referring to a specific category $j$ it's not clear they mean all categories. The strength (and limitation) of the proportional odds model is that the resulting effect is averaged up over every possible threshold, and that's why we can use vague event description of "reporting a higher category" to describe exactly what the cumulative odds ratio considers to be an event.

Having said that, when I've written papers employing cumulative link models, I've usually had to provide model predictions to make the results completely understandable to the lay audience. Sometimes the correct answer is to treat an ordinal outcome like a continuous response for the sake of easily understanding the output.

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  • $\begingroup$ Fantastic thank you @AdamO. Great answer $\endgroup$
    – llewmills
    Oct 20, 2021 at 3:19

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