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 1:52){
for(j in 1:732){
logit(hl1[i,j])<-tumvar[i]*(tummean[i]-pathX[j])
logit(hl2[i,j])<-tumvar[i]*(tummean[i]-pathY[j])
hp[i,j,1]<-1-hl1[i,j]
hp[i,j,2]<-hl1[i,j]-hl2[i,j]
hp[i,j,3]<-hl2[i,j]
hg[i,j]~dcat(hp[i,j,1:3])
hg1[i,j]<-equals(hg[i,j],1)
hg2[i,j]<-equals(hg[i,j],2)
hg3[i,j]<-equals(hg[i,j],3)
}
nohg1[i]<-sum(hg1[i,1:732])
nohg2[i]<-sum(hg2[i,1:732])
nohg3[i]<-sum(hg3[i,1:732])
mode[i]<-1+step(nohg2[i]-max(nohg1[i],nohg3[i]))+2*step(nohg3[i]-max(nohg1[i],nohg2[i]))
for(j in 550:732){
prop[i,j]<-equals(hg[i,j],mode[i])
}

}


}