I ran this ordinal logistic regression in R:
mtcars_ordinal <- polr(as.factor(carb) ~ mpg, mtcars)
I got this summary of the model:
summary(mtcars_ordinal)
Re-fitting to get Hessian
Call:
polr(formula = as.factor(carb) ~ mpg, data = mtcars)
Coefficients:
Value Std. Error t value
mpg -0.2335 0.06855 -3.406
Intercepts:
Value Std. Error t value
1|2 -6.4706 1.6443 -3.9352
2|3 -4.4158 1.3634 -3.2388
3|4 -3.8508 1.3087 -2.9425
4|6 -1.2829 1.3254 -0.9679
6|8 -0.5544 1.5018 -0.3692
Residual Deviance: 81.36633
AIC: 93.36633
I can get the log odds of the coefficient for mpg
like this:
exp(coef(mtcars_ordinal))
mpg
0.7917679
And the the log odds of the thresholds like:
exp(mtcars_ordinal$zeta)
1|2 2|3 3|4 4|6 6|8
0.001548286 0.012084834 0.021262900 0.277242397 0.574406353
Could someone tell me if my interpretation of this model is correct:
As
mpg
increases by one unit, the odds of moving from category 1 ofcarb
into any of the other 5 categories, decreases by -0.23. If the log odds crosses the threshold of 0.0015, then the predicted value for a car will be category 2 ofcarb
. If the log odds crosses the threshold of 0.0121, then the predicted value for a car will be category 3 ofcarb
, and so on.
Best Answer
You have perfectly confused odds and log odds. Log odds are the coefficients; odds are exponentiated coefficients. Besides, the odds interpretation goes the other way round. (I grew up with econometrics thinking about the limited dependent variables, and the odds interpretation of the ordinal regression is... uhm... amusing to me.) So your first statement should read, "As
mpg
increases by one unit, the odds of observing category 1 ofcarb
vs. other 5 categories increase by 21%."As far as the interpretation of the thresholds goes, you really have to plot all of the predicted curves to be able to say what the modal prediction is:
The blue curve for the 3rd category never picked up, and neither did the purple curve for the 6th category. So if anything I would say that for values of
mpg
above 27 have, the most likely category is 1; between 18 and 27, category 2; between 4 and 18, category 4; and below 4, category 8. (I wonder what it is that you are studying -- commercial trucks? Most passenger cars these days should have mpg > 25). You may want to try to determine the intersection points more accurately.I also noticed that you have these weird categories that go 1, 2, 3, 4, then 6 (skipping 5), then 8 (skipping 7). If 5 and 7 were missing by design, that's fine. If these are valid categories that
carb
just does not fall into, this is not good.