13.3 [Excursion:] Inspecting the underlying Stan code

Under the hood, the brms package automatically creates Stan code, runs it and computes useful additional information for regression modeling around the stan_fit object. Here’s how we can inspect the precise model that brms set up for us and ran:

brms::stancode(fit_temperature)

## // generated with brms 2.18.0
## 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 prior_only;  // should the likelihood be ignored?
## }
## transformed data {
##   int Kc = K - 1;
##   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;  // population-level effects
##   real Intercept;  // temporary intercept for centered predictors
##   real<lower=0> sigma;  // dispersion parameter
## }
## transformed parameters {
##   real lprior = 0;  // prior contributions to the log posterior
##   lprior += student_t_lpdf(Intercept | 3, 8.3, 2.5);
##   lprior += student_t_lpdf(sigma | 3, 0, 2.5)
##     - 1 * student_t_lccdf(0 | 3, 0, 2.5);
## }
## 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);
## }

Even if the Stan code itself is not entirely transparent, a few interesting observations to be glimpsed are:

brms automatically centralizes the predictor values, but returns fits for the non-centralized coefficients
by default, the prior for slope coefficients is a completely uninformative one (every value is equally likely)