Consider an ordered logistic (i.e., ordinal) regression, where a binary predictor variable increases a response variable that measured on a 4-point scale:

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.

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    $\begingroup$ Perhaps 1.48 times as likely to be in a higher category? Incidentally I think there is a typo in your third bullet point. $\endgroup$ – mdewey Feb 19 '18 at 16:00
  • $\begingroup$ @mdewey the only thing I don’t like with saying “in a higher category” is that the comparative language raises the question: higher than what? $\endgroup$ – Mark White Feb 19 '18 at 16:24
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    $\begingroup$ One important thing is that you need to be very clear on how your software defines the relationship between the data & the fitted parameter, see: Negative coefficient in ordered logistic regression. $\endgroup$ – gung - Reinstate Monica Feb 19 '18 at 16:34

I think you need either all three bullet points or the sentence immediately after the bullet points. Using only one of the three bullet points wouldn't be a full explanation.

You might use some variation of the sentence plus one bullet point as an example of what you mean in the sentence.

I think both of those options are fairly intuitive.


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