# cumulative odds ratios - additive or exponential?

#### Marvelli

##### New Member
I have run some regression models that examine the effect of variable X (a 15 point continuous scale) on Y (a binary variable - didn't perform/did perform a particular behaviour) using logistic regression.

For the sake of this example, let’s say that the OR is 1.08. I can argue that for each extra exposure on scale X, the respondents are 8% more likely to do Y. So far, so good.

The average score on the X scale is 7. I originally considered that somebody with an average score on the X scale (7) was 56% more likely to do Y (7 x 8%) than somebody with a 0 score on the X scale. However, I have been told that this is incorrect – that the correct calculation is 1.08 to the power of 7 (= 1.71), or in other words that they are 71% more likely to do Y if they have an average score on X compared to somebody who has a 0 score on X.

Cam anybody confirm (1) that this is correct and (2) provide a good reference for this?

Thanks!

#### hlsmith

##### Less is more. Stay pure. Stay poor.
X is continous from 1-15. Just curious if they only get an integer value or can someone get 2.7 points?

P.S., I have not heard of this process.

#### Marvelli

##### New Member
X is continous from 1-15. Just curious if they only get an integer value or can someone get 2.7 points?
No, only an integer value. It was a scale of exposure to an environmental influence.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Well, I have not heard of doing the proposed approach.

I would posit that you can plug values into your model (using the beta coefficients) and get the probabilities, then easily convert this over into odds. In particular, when you do this, you just multiply the terms by the value of interest (e.g., 7) and do not take it to a power per se, but convert using a type of log transformation (generally speaking).

You can also usually calculate select odds (e.g., 7) using estimate statements in your software as well. For good measure you can also compare that value to the hand calculations.