Bayesian Weighted Proportional-Odds Cumulative Logit model in JAGS - r

Question

I am creating multilevel/mixed ordinal models in JAGS code, which are run through the “runjags” package interface in [R].
The dataset that I am analysing also includes a set of survey weights. These are important to include, in order to make the data representative of the population surveyed.
For a glm regression this can be achieved with the following code, which seeks to reduce the variance of extreme responses, bringing values closer to the expected distribution ("bias-variance tradeoff"):
y[i] ~ dnorm(fitted[i], (precision/weights[i]))
I would like to know the most appropriate way to include survey weights in a Proportional-Odds Cumulative Logit model.
Please see the JAGS code beneath for an example of the unweighted models that I have constructed so far. A working application for the displayed code and/or reference to a relevant citation would be most appreciated.
polr_model <- model{
## N = Number of observations
## ConditionCat = y-varaiable measured as 5-point Likert scale
## Categories = Number of y-variable categories (5)
## variable1 = numeric x-variable
## variable2 = numeric x-variable
## Geography = level-2 hierachical struture, in which observations are nested
## weights = survey weights (NOT CURRENTLY USED)
for(i in 1:N){
## Calculate categorical likelihood of the outcome:
ConditionCat[i] ~ dcat(prob[i,1:Categories])
## The odds is fixed between observation categories
## This is the same as any LR except that the intercept isnt included here:
odds[i] <- b1 * variable1[i] + b2 * variable2[i] +
randomeffect[Geography[i]]
## Each observation category is associated with a cumualtive probability called theta:
for(k in 1:(Categories-1)){
## Each observation category has its own intercept - note the minus sign here NOT plus:
logit(theta[i,k]) <- intercept[k] - odds[i]
}
## With the cumulative probability of the highest category equal to 1:
theta[i, Categories] <- 1
## Then calculate the non-cumulative probabilities from theta:
prob[i,1] <- theta[i,1]
for(k in 2:(Categories-1)){
prob[i,k] <- theta[i,k] - theta[i,(k-1)]
}
prob[i, Categories] <- 1 - theta[i,(Categories-1)]
}
## These lines give the prior distributions for the numeric fixed parameters to be estimated:
b1 ~ dnorm(0, 10^-6)
b2 ~ dnorm(0, 10^-6)
## Calculate the Categories-1 independent intercepts::
for(k in 1:(Categories-1)){
intercept[k] ~ dnorm(0, 10^-6)
}
## These lines give the prior distributions for the 'random' (hierachical/nested) parameters to be estimated:
for(iterator in 1:Nest1){
randomeffect[iterator] ~ dnorm(0, Geography_precision)}
Geography_precision ~ dgamma(0.001, 0.001)
#data# N, Nest1, Categories, ConditionCat, variable1, variable2, Geography
#monitor# intercept, b1, b2, randomeffect
#inits# Geography_precision, intercept, b1, b2
#modules# glm on, lecuyer on
}