Ologit: percentage likelihood (odds ratio)

[Sarah Aspen]

Hello,

I am currently using ordered logit to test my hypotheses. Could someone explain me what is meant by the percentage change in the odds ratios? For instance the odds ratio for one of my independent variables is 1.41. Firstly, because it is above 1 it has a positive effect, right? Furthermore, there is a 41% increase in the likelihood of going up by 1 level on the dependent variable - with each increase of my independent variable. What does the estimate of the percentage likelihood of going up (or down) by one category actually tell me? I am not sure if I understand it correctly. If you are able to use a practical example, that would be great.

Thank you in advance!

[Clyde Schechter]

Firstly, because it is above 1 it has a positive effect, right?

If by positive effect you mean that the higher value of the predictor is associated with higher probabilities of being in high numbered outcome probabilities, yes this is right.

Furthermore, there is a 41% increase in the likelihood of going up by 1 level on the dependent variable - with each increase of my independent variable.

No, that's wrong. There is nothing about "going up one level" in the interpretation of ordinal logistic regression. Here's a different way to think about it. Let's say for concreteness that your outcome variable has 4 levels, call them 1, 2, 3, and 4. If you wanted, you could do a simple logistic regression of outcome 1 (base category) vs outcomes 2, 3, and 4 combined (non-base category). You could also do a logistic regression of outcomes 1 and 2 combined (base category) vs outcomes 3 and 4 combined (non-base category). And you could also do a logistic regression of outcomes 1, 2, and 3 combined (base category) vs outcome 4 (non-base category). Now suppose you did all of these logistic regressions and then estimated under an imposed constraint (known as the proportional odds assumption) that the odds ratio had to be the same in all of them. That is what ordinal logistic regression does. So the odds ratio says nothing about going up 1 category. It refers to the odds of being in a higher vs lower category, where higher and lower are separated by any of the outcome categories. So, concretely, in your example, among those with a 1 unit higher value of the independent variable, the odds (not likelihood) are 41% greater, compared to an entity with the lower value of the independent variable, of being in categories 2, 3, or 4 as opposed to 1. Or of being in categories 3 or 4 as opposed to 1 or2. Or of being in category 4 as opposed to 1, 2, or 3.

What does the estimate of the percentage likelihood of going up (or down) by one category actually tell me?

In light of the answer to the preceding question, this is moot.

I hope this helps.

[Sarah Aspen]

This was very helpful indeed! Thank you very much:-)