Consider an ordered logistic (i.e., ordinal) regression, where a binary predictor variable increases a response variable that measured on a 4-point scale:
library(ordinal) set.seed(1839) n <- 500 x <- rbinom(n, 1, .5) y <- cut(0.4 * x + rnorm(n), 5) exp(coef(clm(y ~ x))[["x"]])
where the responses are "not at all", "sometimes", "often", and "frequently."
This last line returns the odds ratio, which is 1.48 in this case. Given that this model assumes proportional odds, we could say that people in group 1 (i.e.,
x == 1) are 1.48 times as likely to...
- Respond with sometimes, often, or frequently rather than not at all
- Respond with often or frequently rather than not at all or sometimes
- Respond with frequently rather than not at all, sometimes, or often
Another way I've heard of this odds ratio being explained is that it is the "odds of moving up one level" in the response.
What is an intuitive—but statistically accurate—way to explain this odds ratio to someone who is not familiar with ordered logistic regression? In an article, I suppose one could simply use one of those three bullet points above to explain the phenomenon, but I wouldn't want to lay out all of them.