Help converting IRT model from JAGS

Modeling
1

Hello all,

I have a model in JAGS that I am willing to convert in Stan.
Basically, it adapts the IRT framework to measure policy mood using aggregate survey response data. It models the proportion of left-wing responses in each given year y giving response to question q which are repeated at different points over time.

The full model graph looks like this :

Screen Shot 2022-01-10 at 11.08.04
Screen Shot 2022-01-10 at 11.08.041336×838 94.2 KB

A detailed description of the IRT model can be found in this paper by McGann (2014).

Do you think it is possible to convert this JAGS code (below) in Stan?
Thank you in advance for your help. I have no idea where to start to build the model in Stan, so any tips will be helpful.

JAGS Model

data{
for (i in 1:len){
leftr[i]<-round(leftp[i]*n[i]/100)
}
secondyear<-startyear+1
}

model{

##loop over the data
for (i in 1:len){
sqresid[i]<-(leftp[i]-leftp.rep[i])^2
leftp.exp[i]<-m[i]*100
leftp.rep[i]<-leftr.rep[i]/n[i]*100
leftr.rep[i]~dbin(p[i], n[i])
p.rep[i]~dbeta(a[i], b)

leftr[i]~dbin(p[i], n[i])
p[i]~dbeta(a[i], b)
a[i]<--b*m[i]/(m[i]-1)
m[i]<-phi(x[i])
x[i]<-(mu[year[i]] - lambda[q[i]]) / sqrt((alpha[q[i]])^2+(sigma[year[i]])^2)
}

##priors for this model
##mu[endyear]<-0
##mu[3]<- -1

b~dunif(0, 100)
##lambda[1]<-0
##alpha[1]<-0.25

for (i in 1:nquest){
lambda[i]~dunif(-10,10)
alpha[i]~dunif(0,10)
}

for (i in 1947:1978){
mu[i]~dunif(-10, 10)
}

for (i in 1980:1996){
mu[i]~dunif(-10, 10)
}

for (i in 1998:2005){
mu[i]~dunif(-10, 10)
}

for (i in startyear:(endyear)){
sigma[i]~dunif(0,10)
}

mu[1979]<--1
mu[1997]<-1
}
2

Something about your model that’s confused me a little, your main likelihood involves a loop from 1:len over mu[year[i]]:

for (i in 1:len){
  x[i]<-(mu[year[i]] - lambda[q[i]]) / sqrt((alpha[q[i]])^2+(sigma[year[i]])^2)
}

Then when constructing mu, you’re setting priors by looping over years:

for (i in 1998:2005){
  mu[i]~dunif(-10, 10)
}

This implies that mu contains at least 2005 elements, but you’re not setting priors/values for any elements below 1946. Is that right? Can you post any more information about the dimensions of your input/data?