Odds ratio for ordinal regression

Interfaces brms
1

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.

image
image986×466 15.9 KB

image
image883×820 35.7 KB

Cheers!

2

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?

3

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?

4

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

5

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