See question in title. Here is the code:

**Data for stan model (as lists):**

```
> head(data.frame(stan_data_participant1),10)
N Source1 Source2 y
1 150 0.999 0.750 1
2 150 0.625 0.250 0
3 150 0.625 0.875 1
4 150 0.500 0.125 0
5 150 0.750 0.750 1
6 150 0.999 0.999 1
7 150 0.375 0.375 0
8 150 0.625 0.375 0
9 150 0.750 0.500 1
10 150 0.999 0.999 1
```

**Model compilation:**

```
WB_mod <- cmdstan_model(file, cpp_options = list(stan_threads = TRUE), stanc_options = list("O1"), pedantic = TRUE)
```

**Model fit:**

```
WB_fit <- WB_mod$sample(
data = stan_data_participant1,
seed = 123,
chains = 2,
parallel_chains = 2,
threads_per_chain = 2,
iter_warmup = 1500,
iter_sampling = 3000,
refresh = 500
)
```

**Model specification:**

```
data {
int<lower=0> N; // number of trials
array[N] int<lower=0,upper=1> y; // discrete choice
array[N] real <lower = 0, upper = 1> Source1; // own source
array[N] real <lower = 0, upper = 1> Source2; // other source
}
transformed data {
array[N] real l_Source1; // array of len N with logit of Source1
array[N] real l_Source2; // array of len N with logit of Source2
l_Source1 = logit(Source1); // logit of Source1
l_Source2 = logit(Source2); // logit of Source2
}
parameters {
real bias; // bias param
// meaningful weights are btw 0.5 and 1 (theory reasons)
real<lower = 0.5, upper = 1> w1; // weight for own source real number between 0.5 and 1
real<lower = 0.5, upper = 1> w2; // weight for other source real number between 0.5 and 1
}
transformed parameters {
real<lower = 0, upper = 1> weight1; // weight for own source
real<lower = 0, upper = 1> weight2; // weight for other source
// weight parameters are rescaled to be on a 0-1 scale (0 -> no effects; 1 -> face value)
weight1 = (w1 - 0.5) * 2; // rescale weight1
weight2 = (w2 - 0.5) * 2; // rescale weight2
}
model {
target += normal_lpdf(bias | 0, 1); // prior for bias
target += beta_lpdf(weight1 | 1, 1); // prior for weight1 -> uniform prior
target += beta_lpdf(weight2 | 1, 1); // prior for weight2 -> uniform prior
for (n in 1:N)
target += bernoulli_logit_lpmf(y[n] | bias + weight1 * l_Source1[n] + weight2 * l_Source2[n]);
}
generated quantities{
array[N] real log_lik; // array of len N with log likelihood
real bias_prior; // prior for bias
real w1_prior; // prior for weight1
real w2_prior; // prior for weight2
bias_prior = normal_rng(0, 1) ; // sample from prior for bias
w1_prior = 0.5 + inv_logit(normal_rng(0, 1))/2 ; // sample from prior for weight1
w2_prior = 0.5 + inv_logit(normal_rng(0, 1))/2 ; // sample from prior for weight2
for (n in 1:N)
log_lik[n]= bernoulli_logit_lpmf(y[n] | bias + weight1 * l_Source1[n] + weight2 * l_Source2[n]);
}
```

**The markov chains**