Hi,

I want to add an additional prior to my brms model. So for example if this is my model:

```
fit1 <- brm(out_fvc ~ days_from_baseline * diagnosis + gender +
cohort + (days_from_baseline | uin), data = df2, chains=4, iter = 100)
```

I want to add a prior that constrains the sum of the population + random intercept, or the population + random slope. I know I can do things like this with stanvars → for example:

```
svars <- stanvar(scode = "sd_1 + Intercept ~ normal(0, 0.1);\n",
block = "model")
```

I *think* this constrains the sum of the population + random intercept - but my question is which variables in the stancode correspond to the population + random slope ? Looking at the code below I think the population slope (i.e days_from_baseline) is represented by so element of `b`

, but I’m not sure which variable represents the random slope specified by `(days_from_baseline | uin)`

? Can any decipher the brms code in this respect? Many thanks.

```
// generated with brms 2.16.3
functions {
/* compute correlated group-level effects
* Args:
* z: matrix of unscaled group-level effects
* SD: vector of standard deviation parameters
* L: cholesky factor correlation matrix
* Returns:
* matrix of scaled group-level effects
*/
matrix scale_r_cor(matrix z, vector SD, matrix L) {
// r is stored in another dimension order than z
return transpose(diag_pre_multiply(SD, L) * z);
}
}
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
// data for group-level effects of ID 1
int<lower=1> N_1; // number of grouping levels
int<lower=1> M_1; // number of coefficients per level
int<lower=1> J_1[N]; // grouping indicator per observation
// group-level predictor values
vector[N] Z_1_1;
vector[N] Z_1_2;
int<lower=1> NC_1; // number of group-level correlations
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
vector<lower=0>[M_1] sd_1; // group-level standard deviations
matrix[M_1, N_1] z_1; // standardized group-level effects
cholesky_factor_corr[M_1] L_1; // cholesky factor of correlation matrix
}
transformed parameters {
matrix[N_1, M_1] r_1; // actual group-level effects
// using vectors speeds up indexing in loops
vector[N_1] r_1_1;
vector[N_1] r_1_2;
// compute actual group-level effects
r_1 = scale_r_cor(z_1, sd_1, L_1);
r_1_1 = r_1[, 1];
r_1_2 = r_1[, 2];
}
model {
// likelihood including constants
if (!prior_only) {
// initialize linear predictor term
vector[N] mu = Intercept + rep_vector(0.0, N);
for (n in 1:N) {
// add more terms to the linear predictor
mu[n] += r_1_1[J_1[n]] * Z_1_1[n] + r_1_2[J_1[n]] * Z_1_2[n];
}
target += normal_id_glm_lpdf(Y | Xc, mu, b, sigma);
}
// priors including constants
target += student_t_lpdf(Intercept | 3, 3.1, 2.5);
target += student_t_lpdf(sigma | 3, 0, 2.5)
- 1 * student_t_lccdf(0 | 3, 0, 2.5);
target += student_t_lpdf(sd_1 | 3, 0, 2.5)
- 2 * student_t_lccdf(0 | 3, 0, 2.5);
target += std_normal_lpdf(to_vector(z_1));
target += lkj_corr_cholesky_lpdf(L_1 | 1);
}
generated quantities {
// actual population-level intercept
real b_Intercept = Intercept - dot_product(means_X, b);
// compute group-level correlations
corr_matrix[M_1] Cor_1 = multiply_lower_tri_self_transpose(L_1);
vector<lower=-1,upper=1>[NC_1] cor_1;
// extract upper diagonal of correlation matrix
for (k in 1:M_1) {
for (j in 1:(k - 1)) {
cor_1[choose(k - 1, 2) + j] = Cor_1[j, k];
}
}
}
```