What's the difference between specifying prior for general intercept vs using family =?

Interfaces brms
1

What’s the difference between specifying prior for general intercept vs using family =?

In the documentation they read almost like specifying the same thing (the prior of the response)?

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Those are two very different things - family describes how the whole linear predictor (including intercept) gives raise to observed data (transformations, whether those are count or real valued, the noise model).

You might benefit from reviewing some introduction to generalized linear models, R. McElreath course is IMHO particularly fun and useful: GitHub - rmcelreath/statrethinking_winter2019: Statistical Rethinking course at MPI-EVA from Dec 2018 through Feb 2019

Best of luck with your modelling!

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