Bayesian Multinomial Regression using rjags package - r

Question

I am trying to fit a multinomial logistic regression model using rjags for the outcome is a categorical (nominal) variable (Outcome) with 3 levels, and the explanatory variables are Age (continuous) and Group (categorical with 3 levels). In doing so, I would like to obtain the Posterior means and 95% quantile-based regions for Age and Group.
I am not really great at for loop which I think is the reason why my written code for the model isn't working working properly.
My beta priors follow a Normal distribution, βj ∼ Normal(0,100) for j ∈ {0, 1, 2}.
Reproducible R code
library(rjags)
set.seed(1)
data <- data.frame(Age = round(runif(119, min = 1, max = 18)),
Group = c(rep("pink", 20), rep("blue", 18), rep("yellow", 81)),
Outcome = c(rep("A", 45), rep("B", 19), rep("C", 55)))
X <- as.matrix(data[,c("Age", "Group")])
J <- ncol(X)
N <- nrow(X)
## Step 1: Specify model
cat("
model {
for (i in 1:N){
##Sampling model
yvec[i] ~ dmulti(p[i,1:J], 1)
#yvec[i] ~ dcat(p[i, 1:J]) # alternative
for (j in 1:J){
log(q[i,j]) <- beta0 + beta1*X[i,1] + beta2*X[i,2]
p[i,j] <- q[i,j]/sum(q[i,1:J])
}
##Priors
beta0 ~ dnorm(0, 0.001)
beta1 ~ dnorm(0, 0.001)
beta2 ~ dnorm(0, 0.001)
}
}",
file="model.txt")
##Step 2: Specify data list
dat.list <- list(yvec = data$Outcome, X=X, J=J, N=N)
## Step 3: Compile and adapt model in JAGS
jagsModel<-jags.model(file = "model.txt",
data = dat.list,
n.chains = 3,
n.adapt = 3000
)
Error message:
Sources I have been looking at for help:
http://people.bu.edu/dietze/Bayes2018/Lesson21_GLM.pdf
Dirichlet Multinomial model in JAGS with categorical X
Reference from http://www.stats.ox.ac.uk/~nicholls/MScMCMC15/jags_user_manual.pdf, page 31
I have just started to learn how to use the rjags package so any hint/explanation and link to relevant sources would be greatly appreciated!

Answer 1

I will include an approach to your issue. I have taken the same priors you defined for coefficients. I only need to mention that as you have a factor in Group I will use one of its levels as reference (in this case pink) so its effect will be taken into account by the constant in the model. Next the code:
library(rjags)
#Data
set.seed(1)
data <- data.frame(Age = round(runif(119, min = 1, max = 18)),
Group = c(rep("pink", 20), rep("blue", 18), rep("yellow", 81)),
Outcome = c(rep("A", 45), rep("B", 19), rep("C", 55)))
#Input Values we will avoid pink because it is used as reference level
#so constant absorbs the effect of that level
r1 <- as.numeric(data$Group=='pink')
r2 <- as.numeric(data$Group=='blue')
r3 <- as.numeric(data$Group=='yellow')
age <- data$Age
#Output 2 and 3
o1 <- as.numeric(data$Outcome=='A')
o2 <- as.numeric(data$Outcome=='B')
o3 <- as.numeric(data$Outcome=='C')
#Dim, all have the same length
N <- length(r2)
## Step 1: Specify model
model.string <- "
model{
for (i in 1:N){
## outcome levels B, C
o1[i] ~ dbern(pi1[i])
o2[i] ~ dbern(pi2[i])
o3[i] ~ dbern(pi3[i])
## predictors
logit(pi1[i]) <- b1+b2*age[i]+b3*r2[i]+b4*r3[i]
logit(pi2[i]) <- b1+b2*age[i]+b3*r2[i]+b4*r3[i]
logit(pi3[i]) <- b1+b2*age[i]+b3*r2[i]+b4*r3[i]
}
## priors
b1 ~ dnorm(0, 0.001)
b2 ~ dnorm(0, 0.001)
b3 ~ dnorm(0, 0.001)
b4 ~ dnorm(0, 0.001)
}
"
#Model
model.spec<-textConnection(model.string)
## fit model w JAGS
jags <- jags.model(model.spec,
data = list('r2'=r2,'r3'=r3,
'o1'=o1,'o2'=o2,'o3'=o3,
'age'=age,'N'=N),
n.chains=3,
n.adapt=3000)
#Update the model
#Update
update(jags, n.iter=1000,progress.bar = 'none')
#Sampling
results <- coda.samples(jags,variable.names=c("b1","b2","b3","b4"),n.iter=1000,
progress.bar = 'none')
#Results
Res <- do.call(rbind.data.frame, results)
With the results of chains for parameters saved in Res, you can compute posterior media and credible intervals using next code:
#Posterior means
apply(Res,2,mean)
b1 b2 b3 b4
-0.79447801 0.00168827 0.07240954 0.08650250
#Lower CI limit
apply(Res,2,quantile,prob=0.05)
b1 b2 b3 b4
-1.45918662 -0.03960765 -0.61027923 -0.42674155
#Upper CI limit
apply(Res,2,quantile,prob=0.95)
b1 b2 b3 b4
-0.13005617 0.04013478 0.72852243 0.61216838
The b parameters belong to the each of the variables considered (age and the levels of Group). Final values could change because of the mixed chains!