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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.

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    $\begingroup$ 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. $\endgroup$ – Noah Mar 2 at 1:17
  • $\begingroup$ 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. $\endgroup$ – badmax Mar 2 at 1:19

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