Dear Stan experts,

I’m now trying to apply the classical diffusion drift model (ddm) to my data (a binary-choice task; accept or reject), by using the hierarchical Bayesian estimation via rstan.

My model is based on the existent ddm examples (e.g., hBayesDM toolbox; and the wiener distribution doc, see: https://github.com/stan-dev/stan/issues/1576). The only modification I did here is that the drift rate (v) is modulated by trial-wise values (i.e., v = alpha*P_S + beta*P_O; see the model below for details).

Unfortunately, the estimation is quite poor (i.e., the rhat of the estimated parameters is much larger than 1; with n_sample = 3000, n_warmup = 2000, n_chain = 4). Also, there are always warnings about rejecting initial values at the beginning of the sampling.

Please find my Stan model code below:

```
data {
int <lower=1> S; // number of subjects
int <lower=1> T; // number of maxtrials among all sbjs
int <lower=1, upper=T> Tsbj[S]; // numbers of valid trials per sbj
int <lower=0> P_S[S,T]; // trial-wise payoff for S
int <lower=0> P_O[S,T]; // trial-wise payoff for O
int <lower=0,upper=1> IsAccept[S,T]; // 1 for accept, 0 for reject
real <lower=0> DT[S,T]; // trial-wise decision time (in seconds)
real minDT[S]; // minimum RT for each subject of the observed data
}
parameters {
// Declare all parameters as vectors for vectorizing
// Hyper(group)-parameters
vector[5] mu_p;
vector<lower=0>[5] sigma;
// Subject-level raw parameters (for Mathematics trick)
vector[S] alpha_pr;
vector[S] beta_pr;
vector[S] bound_pr; // boundary for acceptance
vector[S] nonDT_pr; // non-decision time (in s)
vector[S] SP_pr; // starting point or initial bias
}
transformed parameters {
// Transform subject-level raw parameters
vector<lower=-20,upper=20>[S] alpha; // weights on the payoff for S [-20,20]
vector<lower=-20,upper=20>[S] beta; // weights on the payoff for O [-20,20]
vector<lower=0,upper=100>[S] bound; // boundary [0,20]
vector<lower=0.1,upper=max(minDT)>[S] nonDT; // non-decision time [0.1,max(minRT)]; 0.1 s as the bilogical wall
vector<lower=0,upper=1>[S] SP; // starting point or initial bias [0,1]
for (i in 1:S) {
alpha[i] = -20 + Phi_approx( mu_p[1] + sigma[1] * alpha_pr[i] )*40;
beta[i] = -20 + Phi_approx( mu_p[2] + sigma[2] * beta_pr[i] )*40;
bound[i] = Phi_approx( mu_p[3] + sigma[3] * bound_pr[i] )*100;
nonDT[i] = Phi_approx( mu_p[4] + sigma[4] * nonDT_pr[i] )*(minDT[i]-0.1) + 0.1;
SP[i] = Phi_approx( mu_p[5] + sigma[5] * SP_pr[i] );
}
}
model {
// Hyperparameters
mu_p ~ normal(0, 1);
sigma ~ cauchy(0, 5);
// individual parameters
alpha_pr ~ normal(0, 1);
beta_pr ~ normal(0, 1);
bound_pr ~ normal(0, 1);
nonDT_pr ~ normal(0, 1);
SP_pr ~ normal(0, 1);
for (i in 1:S) {
// Define values
real U_Accept; // U_Accept is the utility for the accept option
real U_Reject; // U_Reject is the utility for the reject option
for (t in 1:(Tsbj[i])) {
// Calculating utility (served as drift rate)
U_Accept = alpha[i]*P_S[i,t] + beta[i]*P_O[i,t];
U_Reject = 0;
if (IsAccept[i,t] == 1) {
DT[i,t] ~ wiener(bound[i], nonDT[i], SP[i], (U_Accept - U_Reject));
} else {
DT[i,t] ~ wiener(bound[i], nonDT[i], 1 - SP[i], -1*(U_Accept - U_Reject));
}
} // end of trial
} //end of subjects
} // end of model section
```

**

I would like to make sure whether my code is correct (esp., the new drift rate). Thanks a lot for your help!

Best,

Yang