Start with a short summary of your inquiry.

Hi, I just ran a Bayesian multilevel logistic regression model with varying intercepts for participants. Of course the brms output includes the Population-level effects (e.g., here in my data a factor ‘condition’ which has 4 levels) and the Group-level effects (e.g., the class ‘sd’ for participants). But I am confused. Does the estimation for the population-level effects already incorporate information from the varying/random effects or NOT?

Let me give you a concrete example, I attached a screenshot from Richard McElreath’s book “statistical rethinking”. This screenshot includes the mathematical model for a multilevel logistic regression with varying intercepts only. There are two parameters to be estimated: the alpha bar and the sigma. My question is: Does the Population-level effect from the brms output mean the estimation only for the alpha bar without incorporating any information

from the varying effect?```
format_code(like_this, if_applicable)
```

If you need to use math formula, use Latex syntax:

Don’t forget to attach tags (top right of this form) for application area/class of models or other general subject areas your topic touches on.