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I am wondering about the relationship and interpretation of the regression coefficient and odds ratio (OR) of an ordered logistic regression.

I know the OR will always be positive given the computation. But how does one interpret the outcome if the coefficient is negative?

For example, a DV has 5 levels (very unlikely, somewhat unlikely, neither likely nor unlikely, somewhat likely, very likely). The purpose would be to observe the likelihood between groups (A, B, C). So, it might be that the odds of being very unlikely to attend college for group B are X time the odds of group A.

I would be assuming that very unlikely and group A are treated as the 'base' levels for the regression. If group B had a negative coefficient (some example: coef = -0.550 and thus the OR would be 0.5769), would the interpretation be:

  1. For group B, the odds of being very unlikely to attend college are 0.5769 times more than the odds of group A.

OR

    1. For group B, the odds of being very unlikely to attend college are 0.5769 times less than the odds of group A.

When observing it from the perspective of the OR, I am always coming out with greater odds for the non-base group (i.e. group B has 'greater' odds than group A based on the OR). But this seems illogical.

I would just like to clarify my understanding of this for future use. Can anyone provide clarification on this interpretation?

Note: I did not see another post that provided an explicit explanation with regards to this relationship. If I missed it, please direct me to it, and my sincere apologies for the duplicated post.

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Human languages are imprecise.

For your example, the odds of group B are 0.5769 the odds of group A, whatever the odds of group A might be (which might depend on other predictors). So, the odds of the group B are always lower than A's.

If the odds of A are 1, the odds of B are 0.5769. If the odds of A are 5, the odds of B are 2.8847, etc.

How to write this in English is a question for a different Stack Exchange site, maybe English Language & Usage.

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  • $\begingroup$ so this would have no influence from the coefficient, then? $\endgroup$
    – anelson
    Commented Jan 31, 2021 at 14:31
  • $\begingroup$ I'm not sure I understand. Of course the coefficient determines the odds ratio. It's just a different way of expressing it. $\endgroup$
    – Igor F.
    Commented Jan 31, 2021 at 14:46
  • $\begingroup$ Apologies. I meant so the sign of the coefficient is relevant for expressing it in words? If the coefficient has a negative sign, this does not mean the odds (per the odds ratio) are less likely? $\endgroup$
    – anelson
    Commented Feb 1, 2021 at 10:06
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    $\begingroup$ Negative coefficient translates into odds ratio < 1. Positive coefficient translates into odds ratio > 1. A coefficient which is exactly zero translates into odds ratio = 1, meaning that the odds of the two outcomes are equal. $\endgroup$
    – Igor F.
    Commented Feb 1, 2021 at 12:20

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