Fitting values between 0 to 1

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Hello, I’m new to this kind of modeling.

say i have y variables, and its values are between 0 and 1 (not including 0 and 1),
and my predictor is a categorical variable, with 4 levels: animals, people, items, insects.

I read that a fitted DGP for this type of y values can be Beta() distribution.

so if i have a beta(alpha, beta) DGP,
how do I model each parameter?

eventually i want to see if there are differences between those catagories in the y values

As a start, I think Andrew’s post summarizes things nicely:

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