- Operating System: OSX Catalina
- brms Version: 2.13

I’m trying to understand how brms implements hierarchical models by writing similar models in Stan. From the documentation, `prior_summary`

, and the generated stan code from brms, I understand that the following brms model…

```
library(brms)
library(tidyverse)
baseline_prior<-set_prior('normal(0.61, 0.12)', class = 'Intercept')
variant_prior<-set_prior('normal(0,1)', class = 'b', coef = 'variantB')
brms_model = brm(y|trials(n) ~ variant + (1|member_id),
data = ab_data,
prior = baseline_prior + variant_prior,
family = binomial())
```

should be equivalent to the following Stan model

```
stan_code="
data{
int N;
int n[N];
int y[N];
vector[N] variant;
}
parameters{
real Intercept;
real variantB;
vector[N] z;
real<lower=0> sigma;
}
model{
Intercept~normal(0.61, 0.12);
variantB~normal(0,1);
z~normal(0,1);
sigma~student_t(3,0,2.5);
y~binomial_logit(n,Intercept + z*sigma + variantB*variant);
}
"
```

However, running these two models yields different results for the coefficient of `variant`

(code to run models found here

```
# My Stan Code
ab_data = read_csv('ab_data.csv')
data = list(N = nrow(ab_data),
y = ab_data$y,
n = ab_data$n,
variant = if_else(ab_data$variant=='A',0,1))
model = stan_model(model_code = stan_code)
fit=sampling(model, data = data, pars = c('Intercept','variantB'))
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
Intercept 0.75 0.00 0.08 0.60 0.70 0.75 0.80 0.90 2376 1
variantB 0.24 0.00 0.13 -0.02 0.15 0.24 0.32 0.50 2124 1
lp__ -1735.62 1.97 46.89 -1826.75 -1767.32 -1736.25 -1704.76 -1643.39 567 1
# brms model
brms_model$fit
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
b_Intercept 0.77 0.00 0.09 0.59 0.70 0.77 0.83 0.96 2131 1.00
b_variantB 0.13 0.00 0.14 -0.14 0.04 0.13 0.23 0.41 2386 1.00
```

It is entirely possible that I have a) misunderstood the documentation for brms default priors/`prior_summary`

, and/or b) have not properly coded up the model I want in Stan. Which of these happens to be the case?