How to specify nested model - r

Question

I am using runjags to model some hierarchical data. I can model one level of the hierarchy but I do not know how to extend it to more levels. I am trying to do this using method 3 from page 24 of "Bayesian Hierarchical Modelling using WinBUGS", by Nicky Best et al which uses a nested loop (as opposed to nested indexing).
For one level I can model
filestring <-
"model{
for(j in 1:Ninner){
for(i in 1:N){
y[j,i] ~ dnorm(beta + alpha[j], py)
}
alpha[j] ~ dnorm(0, taua)
}
beta ~ dnorm(0, 0.001)
taua ~ dgamma(0.01, 0.01)
py ~ dgamma(0.01, 0.1)
}"
INITS <- list(list(.RNG.seed=1, .RNG.name="base::Wichmann-Hill"),
list(.RNG.seed=2, .RNG.name="base::Wichmann-Hill"))
results <- run.jags(filestring, monitor=c("py", "beta", "alpha"), data=jags_data, sample=1e3,
n.chains=2, inits=INITS, summarise=FALSE)
I then tried to add another level using
for(k in 1:Nouter){
for(j in 1:Ninner){
for(i in 1:N){
y[j,i] ~ dnorm(beta + alpha_in[j] + alpha_out[k], py)
} } }
but receive the error
Compilation error on line 5.
Attempt to redefine node y[1,1]
How do I extend this to model another level of which the first one is nested? Thank you.
Below is some reproducible data which shows the structure of the data. I wish to estimate random estimates for both outer_grp and the inner_grp.
library(data.table)
library(runjags)
set.seed(12345)
dat <- data.table(outer_grp=rep(1:5, each=10), inner_grp=rep(1:10, each=5), y=rnorm(50), x=rnorm(50), time=1:5)
wdat = dcast(dat, inner_grp + outer_grp ~ time, value.var=c("y", "x"))
jags_data = c(setNames(
lapply(split.default(wdat, substr(names(wdat), 1, 1)),as.matrix),
c("inner_grp", "outer_grp","x", "y")),
N=5, Nouter=5, Ninner=10)
EDIT
Perhaps it is enough to model like??
filestring <-
"model{
for(j in 1:Ninner){
for(i in 1:N){
y[j,i] ~ dnorm(beta + alpha_in[j] + alpha_out[outer_grp[j]], py)
}
}
for(i in 1:Ninner){ alpha_in[i] ~ dnorm(0, taua) }
for(i in 1:Nouter){ alpha_out[i] ~ dnorm(0, taub) }
beta ~ dnorm(0, 0.001)
taua ~ dgamma(0.01, 0.01)
taub ~ dgamma(0.01, 0.01)
py ~ dgamma(0.01, 0.1)
}"

Answer 1

It is possible to add the outer group intercept by using nested indexing while still using the loop format. I'll use the Pastes dataset from lme4 for comparison.
filestring <-
"model{
for(j in 1:Ninner){
for(i in 1:N){
y[j,i] ~ dnorm(beta + alpha_in[j] + alpha_out[batch[j]], py)
}
}
for(i in 1:Ninner){ alpha_in[i] ~ dnorm(0, taua) }
for(i in 1:Nouter){ alpha_out[i] ~ dnorm(0, taub) }
beta ~ dnorm(0, 0.001)
taua <- 1/(sa*sa)
sa ~ dunif(0,100)
taub <- 1/(sb*sb)
sb ~dunif(0,100)
py ~ dgamma(0.001, 0.001)
}"
INITS <- list(list(.RNG.seed=1, .RNG.name="base::Wichmann-Hill"),
list(.RNG.seed=2, .RNG.name="base::Wichmann-Hill"))
results <- run.jags(filestring, monitor=c("py", "beta", "alpha_in", "alpha_out", "sa", "sb"),
data=jags_data, burnin=1e4, sample=1e4, n.chains=2,
inits=INITS, summarise=0)
summary(results, vars=c("py", "beta", "sa", "sb"))
Compare to lme4
fm1 <- lmer(strength ~ (1|batch) + (1|sample), Pastes)
print(summary(fm1), corr=FALSE)
Data used
library(lme4); library(data.table); library(runjags)
data(Pastes); setDT(Pastes)
Pastes[,time := sequence(.N), by=sample]
# Change format to match question
wdat = dcast(Pastes, batch + sample ~ time, value.var="strength")
jags_data = list(y=as.matrix(wdat[,3:4]), batch=wdat$batch, N=2, Ninner=length(unique(wdat$sample)), Nouter=length(unique(wdat$batch)))