Hello,

I would like to define the values of the distribution parameters in a hierarchical Bayesian model of Reaction times. I am using the brms package.

I don’t understand how to set values for the parameters of the priors. The online guide Prior Choice Recommendations suggest using a normal(0,10), but the range of the values for reaction times in this study goes from 200 to 750 ms.

- How do I formalise this information in the prior, given that I want a very weakly informative prior?
- If I understood correctly, I need to define priors on the parameters defining the outcome variable distribution (here, an ex-Gaussian). How do I define the values for the different parameters outcome distribution?
- Another measure is accuracy, for which the model is the same, but I am using a different family (family = bernoulli(link = “logit”)). How does the prior parameter estimation changes in this case?

Thank you very much!

Here is the model I am using:

```
RTs1.bmodel = brm(RTs ~ conditionStimuli * sequenceTrials + (conditionStimuli * sequenceTrials | Num_part)
, data = data_RTs_go
, family = exgaussian(link = "identity")
, warmup = 500
, iter = 2000
, chains = 3
, inits = "random"
, cores = 2
, seed = 123
, save_pars = save_pars(all = TRUE)
, prior = prior1_rt
, sample_prior = "only" #for prior predictive checks
)
```

```
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;
vector[N] Z_1_3;
vector[N] Z_1_4;
vector[N] Z_1_5;
vector[N] Z_1_6;
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<lower=250,upper=750>[Kc] b; // population-level effects
real Intercept; // temporary intercept for centered predictors
real<lower=0> sigma; // residual SD
real<lower=0> beta; // scale 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;
vector[N_1] r_1_3;
vector[N_1] r_1_4;
vector[N_1] r_1_5;
vector[N_1] r_1_6;
// 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];
r_1_3 = r_1[, 3];
r_1_4 = r_1[, 4];
r_1_5 = r_1[, 5];
r_1_6 = r_1[, 6];
}
model {
// likelihood including constants
if (!prior_only) {
// initialize linear predictor term
vector[N] mu = Intercept + Xc * b;
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] + r_1_3[J_1[n]] * Z_1_3[n] + r_1_4[J_1[n]] * Z_1_4[n] + r_1_5[J_1[n]] * Z_1_5[n] + r_1_6[J_1[n]] * Z_1_6[n];
}
target += exp_mod_normal_lpdf(Y | mu - beta, sigma, inv(beta));
}
// priors including constants
target += normal_lpdf(b | 0, 3)
- 5 * log_diff_exp(normal_lcdf(750 | 0, 3), normal_lcdf(250 | 0, 3));
target += normal_lpdf(Intercept | 0, 3);
target += student_t_lpdf(sigma | 3, 0, 118.6)
- 1 * student_t_lccdf(0 | 3, 0, 118.6);
target += gamma_lpdf(beta | 1, 0.1);
target += normal_lpdf(sd_1 | 0, 3)
- 6 * normal_lccdf(0 | 0, 3);
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];
}
}
}
```

Here is an example of the data:

```
Num_part trial_type Go_type conditionStimuli ITI_ms response RTs correctResponse order_pres sequenceTrials sdt
2 1 Go Bent leaves 819 1 301 1 1 NGG 1
3 1 Go Bent leaves 771 1 237 1 1 GG 1
4 1 Go Bent leaves 1086 1 393 1 1 GG 1
5 1 Go Straight leaves 652 1 331 1 1 GG 1
7 1 Go Bent leaves 919 1 372 1 1 NGG 1
9 1 Go Straight leaves 802 1 359 1 1 NGG 1
```