So the trick i was taught when making regression models is to write your syntax systematically so as you include additional factors, you can check which coefficients change. That can give you a sense of what’s going on, and you can ultimately refine it to demonstrate your findings in a series of models (which is ultimately a way of looking at mediators) although at some point you’re just making structural equation modeling.

This doesn’t stop at just additional variables, though, you can see if your model improves with exponents, play with splines, and more. I’m personally fond of checking moderators-- factors that interact. And I guess it you’re feeling a bit bayesian you could look at the BIC or something.

Edit: oh right, btw polical polsters have literally no concept of good research, so all this is just woooosh.