Dear Stan users:

I’m a student and Stan’s beginner.

Recently, I try to use stan to estimate the Response Times IRT Model (RT-IRTM), and the formula for this model is as follows:

As we can see, the

**tij**in this model is response time, so it is a given fixed variable that obtained during test, just like the response data.

**I have two matrix data with equal ranks, which are Y[n_participant,n_item] and RT[n_participant,n_item], and I want to use these two data to estimate the model parameter in rstan.**

I wrote some code to estimate the item parameters for the model, Here is my Stan code:

data{

int<lower=0> n_participant;

int<lower=0> n_item;

int<lower=0, upper=1> Y[n_participant,n_item]; //the response of each student to answer each item

real RT[n_participant,n_item]; //theresponse timesof each student to answer each item

}

parameters{

vector<lower=-3,upper=3> [n_participant] theta;

vector<lower=0,upper=2> [n_participant] rho;

vector<lower=0,upper=2.5> [n_item] alpha;

vector<lower=-3,upper=3>[n_item] beta;

vector<lower=0,upper=10> [n_item] delta;

}

model {

theta ~ normal(0,1);

rho ~ uniform(0,2);

beta ~ normal(0,1);

alpha ~ lognormal(0,1);

delta ~ uniform(0,10);

for(i in 1:n_participant){

for(j in 1:n_item){

real p;

p=inv_logit(-1.7alpha[j](theta[i]-((rho[i]*delta[j])/RT[i,j])-beta[j]));

Y[i,j] ~ bernoulli§;

}}}

However, I get some errors when I try to run the model:

SAMPLING FOR MODEL ‘4PL’ NOW (CHAIN 1).

Chain 1: Rejecting initial value:

Chain 1: Log probability evaluates to log(0), i.e. negative infinity.

Chain 1: Stan can’t start sampling from this initial value.

…

And the R code are as follows:

library(“rstan”)

rstan_options(auto_write=TRUE)

options(mc.cores=parallel::detectCores())

#data

data<-read.csv(“C:/Users/Y.Luis/Desktop/4PL.csv”,header=T)

I<-nrow(data)

J<-ncol(data)

RT<-read.csv(“C:/Users/Y.Luis/Desktop/4PLRT.csv”,header=T)

data_4pl<-list(n_participant=I,n_item=J,RT=RT,Y=data)

irt_4pl<-stan(file=“4PL.stan”,data=data_4pl,iter=1000,chains=1)

4/25

Today, I try to change the RT[i,j] term to a constant 10, of course I deleted the code related to response time, and I found the model could be fit. So I think it might be a code problem with the response time data.

p=inv_logit(-1.7

alpha[j](theta[i]-((rho[i]delta[j])/alpha[j]*(theta[i]-((rho[i]*delta[j])/RT[i,j])-beta[j]));

p=inv_logit(-1.710)-beta[j]));

**But, I still can not solve this problem. so upset… : (**

**This problem has been bothering me for a long time.**

5/15

**So I am wondering if the way I put the response time matrix into the rstan parameter estimated code is correct**

**If you have any suggestions for using two matrices to evaluate model parameters in a model, then please give me some guidance and I’ll be very grateful.**