# How do I choose between regression methods for inference?

Suppose my goal is to understand the relationship between variable $$y$$ and covariates $$X$$. Let's say $$y$$ is a rate, the number of success in $$n$$ trials, therefore bounded between $$0$$ and $$1$$.

Now I have (at least) 2 approaches. Take the log of $$y$$ and use a linear model, or use logistic regression. Logistic regression is the more theoretically appropriate model but estimation can lead to problems (example) that the linear method doesn't have.

How do I choose between them when the goal is understanding, not predicting? I thought of using AIC or a similar criterion but the target is not the same so I don't think that will work.

• You actually probably want s quasi-Poisson model with an offset, not logistic or linear regression. The QP model is appropriate for counts and rates. – Noah Mar 2 at 1:17
• That's 3 models on the table now. I'm still not sure how I can balance the theoretical appropriateness of them vs. accurate estimation and stability. – badmax Mar 2 at 1:19