model{

for(i in 1:52){
tummean[i]~dnorm(tummmu,tummtau)
tumvar[i]~dnorm(0,tumvtau) I(0,)
}



for(i in 1:732){
pathcent[i]~dnorm(0,centtau)
pathspread[i]~dnorm(2,spreadtau)I(0,)
pathX[i]<-pathcent[i]-pathspread[i]
pathY[i]<-pathcent[i]+pathspread[i]
}


for(i in 1:24177){

logit(Q[i,1])<-tumvar[caseID[i]]*(tummean[caseID[i]]-pathX[pathID[i]])
logit(Q[i,2])<-tumvar[caseID[i]]*(tummean[caseID[i]]-pathY[pathID[i]])
p[i,1]<-1-Q[i,1]
p[i,2]<-Q[i,1]-Q[i,2]
p[i,3]<-Q[i,2]
grade[i]~dcat(p[i,1:3])
}


centtau~dnorm(0,1)I(0,)

spreadtau~dnorm(0,1)I(0,)
tummtau~dnorm(0,1)I(0,)
tumvtau~dnorm(0,1)I(0,)
tummmu~dnorm(0,4)


for(i in 1:24177){

logit(hl1[i])<-tumvar[caseID[i]]*(tummean[caseID[i]]-pathX[pathID[i]])
logit(hl2[i])<-tumvar[caseID[i]]*(tummean[caseID[i]]-pathY[pathID[i]])
hp[i,1]<-1-hl1[i]
hp[i,2]<-hl1[i]-hl2[i]
hp[i,3]<-hl2[i]

hg[i]~dcat(hp[i,1:3])
hg2[i]<-equals(hg[i],2)
}

hgs<-sum(hg2[1:24177])

}