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
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.