I have a logistic regression:
ln(p/(1-p)) = a + b * Age + c * Balance + d * Tenure
Let's say that:
b = 1.4
c = 2.5
d = -0.7
We can compare signs of the coefficients. I.e. right away we can say that an increase in Tenure will cause a decrease in probability of the dependent variable.
My question is: can we compare magnitudes of the coefficients to each other?
I know that we can take the exp() of any coefficient and get the odds ratio and make conclusions then. But what I am referring to is different – without taking the exp() can we simply say the following:
Since c > b then the impact from a 1 unit change in Balance on the DV's probability is greater than the impact from a 1 unit change in Age. (without saying how much greater. Just simply greater)
I did quite a lot of search and only found this thread: Comparing coefficients in logistic regression
Where this approach seems to be implied. However, I would like to confirm that you can interpret coefficients like this.
I look forward to your thoughts,
Thank you,
Kirill
Best Answer
The marginal effects from a logistic regression is the following:
The partial derivative essentially tells you the effect of a unit change in some variable x
The first part of the equation,[1-%5CLambda(x'%5Cbeta)]))
, is always positive and would look like the curve below:
First thing to notice is that the marginal effect will depend on X. So normally we would evaluate the marginal effects at the mean. Having said that, regardless of where you evaluate the marginal effects
c > b implies that the balance has a higher effect on the probability of event than the age. (bcos the first part of that marginal effects equation is always positive)