# Odds ratio for ordinal regression

Hi everyone,

I am new to brms package and ordinal regression, so my question might be kind of obvious, but I couldn’t find an answer for it. I’m analyzing Likert (9 points) data from a study about the influence of verbal labeling on perceived pleasantness of odors. Overall, the models I’ve made look good. I did cumulative and adjacent category models trying to understand this data set from different perspectives. It’s clear that depending on the verbal label participants chose mostly either 9 over 1 or in the second condition this disproportion is smaller. If I understand correctly, in an adjacent category model I can calculate odds ratio for choosing 1 over 2, or 3 over 4, etc… Is there a way to calculate odds ratio of choosing X point on the scale over point Y [where Y is not adjacent to X], i.e. 9 over 1? Below I paste my summary table and marginal effects plot, I hope it helps.

Cheers!

Hi and welcome to the community. I’m not really sure this is what you’re after but the estimates you get are on the log-cumulative-odds scale if I remember correctly. If you want the cumulative probabilities then you simply do:

``````> library(brms)
> inv_logit(c(0.8, 0.02,-0.31,-0.64,-0.34,-0.36, -0.12,-1.04))
[1] 0.6899745 0.5049998 0.4231147 0.3452465 0.4158095 0.4109596 0.4700359 0.2611500
``````

of course, you can simply do (hmm, one of these at least): `inv_logit(fixef(mod_2_pine))` or `inv_logit(coef(mod_2_pine))`, I guess?

Thank you for your reply! I wasn’t thinking about getting cumulative probabilities, although it helped me understand something else. I was wandering about somehow quantifying the ‘difference’ between the probability of choosing point 9 over point 1. I thought about odds ratio, but right now I’m not sure if that makes sense in terms of ordinal regression. I know it’s visible on the plot, that in the ‘nice’ condition there is a much higher probability of observing point 9 than point 1, and in ‘bad’ condition this difference in probabilities is smaller. Maybe this plot is enough and I’m overthinking this?

Hmm, hard question to answer but the plot together with cumulative probabilities seems good to me :)

I have the same question. I would be curious to hear how you calculated the odds ratio after all (if you even did it).