Dear community,

I have a hierarchical DDM model with the following parameters:

- One drift rate per stimulus, subject and exp condition
- One boundary separation per subject and exp condition
- One starting point per subject and exp condition
- One non-decision time per subject and exp condition

This is the only version of this model that doesn’t give any convergency problems and that has a good parameter recovery.

I wanted to do cross-validation to ensure the model was not overfit, and used the LOO package, however, I’m not completely sure what to make of the output:

My questions are:

- Does that one high value for one observation indicate I can’t trust my posteriors?
- Where do I go from here
- Are there other better ways to run cross validation in rStan taking into account I can’t do PPC because wiener_rng is not implemented yet?
- Is there anything in the code that shows a gross mistake?

Here’s the model:

```
data {
int<lower=1> N; // Number of Trials
int<lower=1> S; // Number of Subjects
vector[N] RT; // response times
int<lower=0,upper=1> response[N]; // choice made in that trial (1 for high reward)
int<lower=1> K; // Number of Stimuli
int<lower=1> C; // number of conditions
matrix[C, S] min_rt; // upper bound for tau
int<lower=1> subject[N]; // Subject in that trial
int<lower=1> stimulus[N]; // Stimulus in that trial
int<lower=1> condition [N]; // Condition in that trial
}
transformed data{ //to allow group comparison
int CONDITION_VEHICLE = 1;
int CONDITION_DRUG = 2;
}
parameters {
array[C, S, K] real delta; // Drift rate per condition, subject, and stimulus
matrix[C, K] d_mu; // group level mean drift rate
matrix<lower=0>[C, K] d_sig; // variation of drift rates on the group level
matrix<lower=0>[C, S] alpha; // Distance betwen boundaries, per condition and subject
vector<lower=0>[C] a_mu; // group level mean distance between boundaries
vector<lower=0>[C] a_sig; // variation of distance between boundaries on the group level
matrix<lower=0, upper=1>[C, S] beta; // Starting bias
vector<lower=0>[C] b_mu; // group level mean starting bias
vector<lower=0>[C] b_sig; // variation of starting bias on the group level
matrix<lower=0, upper=1>[C, S] tau_raw; // non decision time
}
transformed parameters{
matrix[C, S] tau = tau_raw .* min_rt; //transformation of tau into range
}
model {
for (c in 1:C){
for(s in 1:S){
tau_raw[c, s] ~ beta(1, 1); //tau prior
}}
for (c in 1:C) {
for(s in 1:S){
for(k in 1:K){
delta[c, s, k] ~ normal(d_mu[c,k],d_sig[c,k]); //delta prior
}
}}
for (c in 1:C){
for(s in 1:S){
alpha[c, s] ~ normal(a_mu[c],a_sig[c])T[0,]; //alpha prior
}}
for (c in 1:C){
for(s in 1:S){
beta[c, s] ~ normal(b_mu[c],b_sig[c])T[0, 1]; //beta prior
}}
for (c in 1:C){ //delta mean and variation priors
for(k in 1:K){
d_mu[c, k] ~ normal(0, 1);
d_sig[c, k] ~ inv_gamma(4, 3);
}}
for (c in 1:C) { //alpha mean and variation priors
a_mu[c] ~ inv_gamma(4, 3);
a_sig[c] ~ inv_gamma(4, 3);
}
for (c in 1:C) { //beta mean and variation priors
b_mu[c] ~ inv_gamma(4, 3);
b_sig[c] ~ inv_gamma(4, 3);
}
for (t in 1:N) {
int c = condition[t]; //condition in that trial
int s = subject[t]; //subject in that trial
int k = stimulus [t]; //stimulus in that trial
if(response[t]==1){
RT[t] ~ wiener(
alpha[c, s],
tau[c, s],
beta[c, s],
delta[c, s, k]
);
}else{
RT[t] ~ wiener(
alpha[c, s],
tau[c, s],
1-beta[c, s],
-delta[c, s, k]
);
}
}
}
generated quantities{
array[C, K] real group_condition_delta;
for (c in 1:C) {
for (k in 1:K) {
group_condition_delta[c, k] = d_mu[c, k];
}
}
array[K] real drug_delta_effect;
for (k in 1:K){
drug_delta_effect[k] = group_condition_delta[CONDITION_VEHICLE, k]- group_condition_delta[CONDITION_DRUG, k];
}
//Log likelihood calculation
vector[N] log_lik;
for (n in 1:N) {
int c= condition[n];
int s = subject[n];
int k = stimulus[n];
if(response[n]==1){
log_lik[n] = wiener_lpdf(RT[n] | alpha[c, s], tau[c, s], beta[c, s], delta[c, s, k]);
} else {
log_lik[n] = wiener_lpdf(RT[n] | alpha[c, s], tau[c, s], 1-beta[c, s], -delta[c, s, k]);
}
}
}
```

I am aware that truncated distributions and matrices aren’t exactly best practice, but as said before, this is the only version of the model that doesn’t give any convergence problems.

Thank you for your help!!