Can Relative Risk mislead us when choosing predictors for a logistic model?

Question

My friend taught me to use Relative Risk as a guide to check if my coefficients make sense. For example, I have a propensity to default model, where the variable fl_default is equal to 1 if the individual defaulted and equal to zero if he didn't default. I also have the region where individuals belong: A, B, C, D and E - and other variables. In the figure below, I have the number of people that defaulted in each region and their relative risk, and what I understand is that people in region A, B and D are good customers, they have more propensity to pay.

However, if I run a logistic regression and the coefficient for the predictor REGION is the opposite of this Relative Risk, should I treat this variable (make some modification) or it is possible that the coefficient gives a different direction than the relative risk? What could be happening with my model?

Answer 1

This is not a direct answer to your question but I suspect it might solve some issues for you.

A relative risk compares two groups so in your situation you could compare the risk of defaulting in group A versus group D. The risk in group A is $\frac{86}{86 + 179}$ and in group D is $\frac{240}{240 + 268}$. The risk ratio is thus the ratio of these two quantities $$\frac{\frac{86}{86 + 179}}{\frac{240}{240 + 268}}$$ If when you work them out correctly you still get an issue then perhaps better to post a new question.