p2 <- function (Nsim=1000){

x<- c(0.301,0,-0.301,-0.602,-0.903,-1.208, -1.309,-1.807,-2.108,-2.71) # logdose
n<-c(19,20,19,21,19,20,16,19,40,81) # total subject in dose-response experiment
y<-c(19,18,19,14,15,4,0,0,0,2) # success in each trials
dta<-cbind(x,n,y)
dta<-as.data.frame(dta) # creating data frame

proposal.b0 = current.b0 = ratio0 = double(Nsim) # blank vector
proposal.b1 = current.b1 = ratio1 = double(Nsim) # blank vector
index <- 1:Nsim # creating index
a0 <- 10 # initial value (assumed) for tau
b0 <- (.01) # initial value (assumed) for tau
fit <- glm((y/n)~x,family=binomial, weight = n, data=dta) # initial value for beta

parameters <- c("Beta0", "Beta1", "Tau")
parameter.matrix <- array(NA,c(Nsim,3)) # blank array
parameter.matrix <- as.data.frame(parameter.matrix) # creating data frame
parameter.matrix[1,] <- c(fit$coef[1],fit$coef[2],rgamma(1, shape=a0, scale = b0)) # putting initial values

for (i in 2:Nsim){
# generating Gibbs sampler
parameter.matrix[i,]<- c(rnorm(1, 0, (1/parameter.matrix[i-1,3])), rnorm(1, 0, (1/parameter.matrix[i-1,3])), rgamma(1, shape=(a0+1), rate=(1/b0+(parameter.matrix[i-1,1]^2+parameter.matrix[i-1,2]^2)/2)))
# implementing Metropolis-Hastings within Gibbs to get estimates of beta0 and beta1      
proposal.b0[i]<-sum(log( ((exp(parameter.matrix[i,1])^y)/((1+exp(parameter.matrix[i,1])^n))*exp(-parameter.matrix[i-1,3]*(parameter.matrix[i,1]^2)/2))))
proposal.b1[i]<-sum(log( ((exp(parameter.matrix[i,2]*x)^y) / ((1+exp(parameter.matrix[i,2]*x))^n) * exp(-parameter.matrix[i-1,3]*(parameter.matrix[i,2]^2)/2) )))
 
current.b0[i]<-sum(log( (( exp(parameter.matrix[i-1,1])^y)/((1+exp(parameter.matrix[i-1,1])^n))*exp(-parameter.matrix[i-1,3]*(parameter.matrix[i-1,1]^2)/2))))
current.b1[i]<-sum(log( (( exp(parameter.matrix[i-1,2]*x)^y) / ((1+exp(parameter.matrix[i-1,2]*x))^n) * exp(-parameter.matrix[i-1,3]*(parameter.matrix[i-1,2]^2)/2))))

# ratio0 id for beta0
if(current.b0[i]==0) {ratio0[i]=1} else {ratio0[i] <- proposal.b0[i]-current.b0[i]}
if (ratio0[i] < log(runif(1))) {parameter.matrix[i,1] <- parameter.matrix[i-1,1]}
# for beta0
# ratio1 id for beta1
if(current.b1[i]==0) {ratio1[i]=1} else {ratio1[i]=proposal.b1[i]-current.b1[i]}
if (ratio1[i] < log(runif(1))) {parameter.matrix[i,2] <- parameter.matrix[i-1,2]}
# for beta1
cat("At Iteration ", i, "ratio0 and ratio1 are", ratio0[i], ratio1[i], "\n" )
}

x11()
plot(parameter.matrix[,1], parameter.matrix[,2], type="b", xlab="beta.0", ylab="beta.1")
write.table(parameter.matrix, file="z:\\paramaters.txt", quote = F, sep = " ")
x11()

par(mfrow=c(3,1))
plot(index, parameter.matrix[index,1], type="l", xlab="Index", ylab="beta0")
plot(index, parameter.matrix[index,2], type="l", xlab="Index", ylab="beta1")
plot(index, parameter.matrix[index,3], type="l", xlab="Index", ylab="tau")
}

p2(Nsim=1000)