Hi all,

I am a very new user to stan and rStan and have been trying to model choice using linear ballistic accumulator modelling using rstan. The stan code was written by Annis et al (2016) and seems to behave fine with sample data and real world data. When I use the code with several sets of different data from the lab I receive the following warning -

I have also noticed that the Rhat values are also not ideal nor are the plots of the posterior predictive.

I have also produced a plot of the pairs for pred[1], pred[2], tau, v[1] and v[2]. Not sure how to plot all the parameters as the graph gets very messy with all the parameters included.

My mathematical knowledge of stan and linear ballistic modelling is extremely limited. I have tried adjusting the adapt_delta value from 0.8 up to 0.99 but that had little impact. I have also tried increasing the number of chains (from 3 to 4) and iterations (from 2000 to 3000) to no avail. I have been reading the forums and guides for ideas but most of the suggestions are above my current skillset.

I would greatly appreciate any advice on fixing these issues. I have included the stan code below. Please let me know if any more information is required.

Thanks !

```
functions{
real lba_pdf(real t, real b, real A, real v, real s){
//PDF of the LBA model
real b_A_tv_ts;
real b_tv_ts;
real term_1;
real term_2;
real term_3;
real term_4;
real pdf;
b_A_tv_ts <- (b - A - t*v)/(t*s);
b_tv_ts <- (b - t*v)/(t*s);
term_1 <- v*Phi(b_A_tv_ts);
term_2 <- s*exp(normal_log(b_A_tv_ts,0,1));
term_3 <- v*Phi(b_tv_ts);
term_4 <- s*exp(normal_log(b_tv_ts,0,1));
pdf <- (1/A)*(-term_1 + term_2 + term_3 - term_4);
return pdf;
}
real lba_cdf(real t, real b, real A, real v, real s){
//CDF of the LBA model
real b_A_tv;
real b_tv;
real ts;
real term_1;
real term_2;
real term_3;
real term_4;
real cdf;
b_A_tv <- b - A - t*v;
b_tv <- b - t*v;
ts <- t*s;
term_1 <- b_A_tv/A * Phi(b_A_tv/ts);
term_2 <- b_tv/A * Phi(b_tv/ts);
term_3 <- ts/A * exp(normal_log(b_A_tv/ts,0,1));
term_4 <- ts/A * exp(normal_log(b_tv/ts,0,1));
cdf <- 1 + term_1 - term_2 + term_3 - term_4;
return cdf;
}
real lba_log(matrix RT, real k, real A, vector v, real s, real tau){
real t;
real b;
real cdf;
real pdf;
vector[rows(RT)] prob;
real out;
real prob_neg;
b <- A + k;
for (i in 1:rows(RT)){
t <- RT[i,1] - tau;
if(t > 0){
cdf <- 1;
for(j in 1:num_elements(v)){
if(RT[i,2] == j){
pdf <- lba_pdf(t, b, A, v[j], s);
}else{
cdf <- (1-lba_cdf(t, b, A, v[j], s)) * cdf;
}
}
prob_neg <- 1;
for(j in 1:num_elements(v)){
prob_neg <- Phi(-v[j]/s) * prob_neg;
}
prob[i] <- pdf*cdf;
prob[i] <- prob[i]/(1-prob_neg);
if(prob[i] < 1e-10){
prob[i] <- 1e-10;
}
}else{
prob[i] <- 1e-10;
}
}
out <- sum(log(prob));
return out;
}
vector lba_rng(real k, real A, vector v, real s, real tau){
int get_pos_drift;
int no_pos_drift;
int get_first_pos;
vector[num_elements(v)] drift;
int max_iter;
int iter;
real start[num_elements(v)];
real ttf[num_elements(v)];
int resp[num_elements(v)];
real rt;
vector[2] pred;
real b;
//try to get a positive drift rate
get_pos_drift <- 1;
no_pos_drift <- 0;
max_iter <- 1000;
iter <- 0;
while(get_pos_drift){
for(j in 1:num_elements(v)){
drift[j] <- normal_rng(v[j],s);
if(drift[j] > 0){
get_pos_drift <- 0;
}
}
iter <- iter + 1;
if(iter > max_iter){
get_pos_drift <- 0;
no_pos_drift <- 1;
}
}
//if both drift rates are <= 0
//return an infinite response time
if(no_pos_drift){
pred[1] <- -1;
pred[2] <- -1;
}else{
b <- A + k;
for(i in 1:num_elements(v)){
//start time of each accumulator
start[i] <- uniform_rng(0,A);
//finish times
ttf[i] <- (b-start[i])/drift[i];
}
//rt is the fastest accumulator finish time
//if one is negative get the positive drift
resp <- sort_indices_asc(ttf);
ttf <- sort_asc(ttf);
get_first_pos <- 1;
iter <- 1;
while(get_first_pos){
if(ttf[iter] > 0){
pred[1] <- ttf[iter] + tau;
pred[2] <- resp[iter];
get_first_pos <- 0;
}
iter <- iter + 1;
}
}
return pred;
}
}
data{
int LENGTH;
matrix[LENGTH,2] RT;
int NUM_CHOICES;
}
parameters {
real<lower=0> k;
real<lower=0> A;
real<lower=0> tau;
vector<lower=0>[NUM_CHOICES] v;
}
transformed parameters {
real s;
s <- 1;
}
model {
k ~ normal(.5,1)T[0,];
A ~ normal(.5,1)T[0,];
tau ~ normal(.5,.5)T[0,];
for(n in 1:NUM_CHOICES){
v[n] ~ normal(2,1)T[0,];
}
RT ~ lba(k,A,v,s,tau);
}
generated quantities {
vector[2] pred;
pred <- lba_rng(k,A,v,s,tau);
}
```