model{
for(i in 1:N){
    r1[i] ~ dbin(phi1[i], n[i])
    r2[i] ~ dbin(phi2[i], n[i])
    logit(phi2[i])<-alpha0[i]+beta*(logit(phi1[i])-logit(phi1.bar))
    alpha0[i]~dnorm(mu.alpha0, tau.alpha)
    alpha[i]<-alpha0[i]-beta*logit(phi1.bar)
}
tau.alpha<-1/ss.alpha
ss.alpha<-s.alpha*s.alpha
phi1.bar<-mean(phi1[])
mu.alpha <- mu.alpha0 - beta*logit(phi1.bar)


#predicted ACR to find plug in residuals
for(i in 1:N){
#    pred[i]<-1/(1+exp(-(alpha[i]+beta*logit(phi1[i])))) #model fit

    pred[i] <- 1/(1+exp(-(mu.alpha+beta*logit((r1[i]+0.5)/(n[i]+1))))) #simple prediction

    alpha.pred[i]~dnorm(mu.alpha, tau.alpha) #MCMC prediction
    logit.phi2.pred[i] <- alpha.pred[i]+beta*logit(phi1[i])
    phi2.pred[i] <- 1/(1+exp(-(logit.phi2.pred[i])))
    r2.pred[i] ~ dbin(phi2.pred[i],n[i])
    pred.res[i]<- r2[i]/n[i] - r2.pred[i]/n[i] #non-standardized predictive residuals
   
}

#Predicted probability of achieving ACR at six months
for(i in 1:Nr){
    r1.new[i] ~ dbin(phi1.new[i], n1.new[i])
    alpha.new[i] ~ dnorm(mu.alpha, tau.alpha)
    logit.phi2.new[i] <- alpha.new[i]+beta*logit(phi1.new[i])
    phi2.new[i] <- 1/(1+exp(-(logit.phi2.new[i])))
}

#priors
for(i in 1:N){phi1[i]~dbeta(1, 1)}
for(i in 1:Nr){phi1.new[i]~dbeta(1, 1)}
beta~dnorm(0,1.0E-3)
mu.alpha0~dnorm(0,1.0E-3)
s.alpha~dunif(0,3)

#extra variables
dur.bar<-mean(dur[])
haq.b.bar<-mean(haq.b[])
type.dum<-mean(type[])


}