// generated with brms 2.22.8
functions {
}
data {
   int<lower=1> N;  // total number of observations
   vector[N] Y;  // response variable
   int<lower=1> K;  // number of population-level effects
   matrix[N, K] X;  // population-level design matrix
   int<lower=1> Kc;  // number of population-level effects after centering
   int prior_only;  // should the likelihood be ignored?
 }
 transformed data {
   matrix[N, Kc] Xc;  // centered version of X without an intercept
   vector[Kc] means_X;  // column means of X before centering
   for (i in 2:K) {
     means_X[i - 1] = mean(X[, i]);
     Xc[, i - 1] = X[, i] - means_X[i - 1];
   }
 }
 parameters {
   vector[Kc] b;  // regression coefficients
   real Intercept;  // temporary intercept for centered predictors
   real<lower=0> sigma;  // dispersion parameter
 }
 transformed parameters {
   real lprior = 0;  // prior contributions to the log posterior
   real lprior_covariates = 0;
   real lprior_treatment = 0;
   real lprior_Intercept = 0;
   real lprior_sigma = 0;
   lprior += normal_lpdf(b[1] | 0, 1);
   lprior_treatment += normal_lpdf(b[1] | 0, 1);
   lprior += normal_lpdf(b[2] | 0, 5);
   lprior_covariates += normal_lpdf(b[2] | 0, 5);
   lprior += normal_lpdf(Intercept | 0, 100);
   lprior += normal_lpdf(sigma | 0, 10)
     - 1 * normal_lccdf(0 | 0, 10);
 }
 model {
   // likelihood including constants
   if (!prior_only) {
     target += normal_id_glm_lpdf(Y | Xc, Intercept, b, sigma);
   }
   // priors including constants
   target += lprior;
 }
generated quantities {
   // actual population-level intercept
   real b_Intercept = Intercept - dot_product(means_X, b);
 }