Help with bayesian regression modeling (beginner)

[Ara_Winter]

As for question 1 there is a lot of great discussion here which has folks tackling this question in different ways

Bayesian credible intervals: Significant compared to what?

Thank you, but I’m still unsure as to whether the variables are compared to the pooled intercept or to each of the alpha-numerically lowest values of each variable? Put another way using my example: Is the significance of “Nike” compared only to that of Adidas (the alpha-numerically lowest value of the variable “Shoes”) or to the whole intercept (“Adidas”, “Beginner”, “Old”, pooled)?

particularly jscolar comments.

@jsocolar

The latter. An important clue is the fact that there is no coefficient estimated for Adidas.

Again, I’d encourage you to think more broadly than what the “significance” is in reference to. The fundamental question is not about the significance of the coefficient, but rather about the meaning of the coefficient, irrespective of what its posterior distribution is and whether or not that distribution includes substantial probability mass on both sides of zero.

In your model, the parameter for Nike means the expected difference between Nike and Adidas with all other covariates held constant. And the 95% credible interval for this parameter that brms has constructed for you doesn’t overlap zero.

Priors can get difficult quickly. However I tend to view them as just additional data you are adding into your model. So if you know some about how all your parameters interact you can code that up.

Like in my area fire is bad for wetland plants in arid system. If my model increase something for fire I might have a prior normal(-0.5, 0.5).

As for default best pracites priors we would need to get help from some other folks. There is this
Prior Choice Recommendations · stan-dev/stan Wiki · GitHub but it was last updated 2023.