I am new to stats, I am working on a problem and I need some direction.
I have a binary dataset and I have three explanatory variables x,y, and z that I want to analyze. There is no guarantee of independence between any of them. I would like to perform a test to compare the explanatory power of two of them e.g x,y. I think that if for example, I do logistic regression with x,z, and another y,z and compare the goodness of fit or I compare coefficients in one logistic regression with all variables, it wouldn't work because none of the variables are independent.
So I am not sure how to proceed.
Please let me know if the post needs more information/clarity.
You can add an interaction term. So if your response is w, your formula would be $w \sim x + y + x*y$ if you just wanted to use x and y as predictors, or $w \sim x + y + z + x*y + y*z + x*z + x*y*z$. Usually three factors interactions aren’t common so you could omit the last term.