zip.bymCAR <- function(formula, formula.omega, data=NULL, W, burnin, n.sample, thin=1, prior.mean.beta=NULL, prior.var.beta=NULL, prior.tau2=NULL, prior.sigma2=NULL, prior.mean.delta=NULL, prior.var.delta=NULL, MALA=TRUE, verbose=TRUE)
{
##############################################
#### Format the arguments and check for errors
##############################################
#### Verbose
a <- common.verbose(verbose)
    

#### Frame object
frame.results <- common.frame(formula, data, "poisson")
K <- frame.results$n
p <- frame.results$p
X <- frame.results$X
X.standardised <- frame.results$X.standardised
X.sd <- frame.results$X.sd
X.mean <- frame.results$X.mean
X.indicator <- frame.results$X.indicator 
offset <- frame.results$offset
Y <- frame.results$Y
which.miss <- frame.results$which.miss
n.miss <- frame.results$n.miss  
Y.DA <- Y   


#### Frame object for the omega model
## Create the matrix
frame.omega <- try(suppressWarnings(model.frame(formula.omega, data=data, na.action=na.pass)), silent=TRUE)
    if(class(frame.omega)=="try-error") stop("the formula.omega inputted contains an error.", call.=FALSE)
V <- try(suppressWarnings(model.matrix(object=attr(frame.omega, "terms"), data=frame.omega)), silent=TRUE)
    if(class(V)=="try-error") stop("the covariate matrix for the zero probabilities contains inappropriate values.", call.=FALSE)
    if(sum(is.na(V))>0) stop("the covariate matrix for the zero probabilities contains missing 'NA' values.", call.=FALSE)
    if(nrow(V)!=nrow(X)) stop("the two matrices of covariates don't have the same length.", call.=FALSE)
q <- ncol(V)

## Check for linearly related columns
cor.V <- suppressWarnings(cor(V))
diag(cor.V) <- 0
    if(max(cor.V, na.rm=TRUE)==1) stop("the covariate matrix for the zero probabilities has two exactly linearly related columns.", call.=FALSE)
    if(min(cor.V, na.rm=TRUE)==-1) stop("the covariate matrix for the zero probabilities has two exactly linearly related columns.", call.=FALSE)
    if(q>1)
    {
        if(sort(apply(V, 2, sd))[2]==0) stop("the covariate matrix for the zero probabilities has two intercept terms.", call.=FALSE)
    }else
    {}

## Standardise the matrix
V.standardised <- V
V.sd <- apply(V, 2, sd)
V.mean <- apply(V, 2, mean)
V.indicator <- rep(NA, q)       # To determine which parameter estimates to transform back

    for(j in 1:q)
    {
        if(length(table(V[ ,j]))>2)
        {
        V.indicator[j] <- 1
        V.standardised[ ,j] <- (V[ ,j] - mean(V[ ,j])) / sd(V[ ,j])
        }else if(length(table(V[ ,j]))==1)
        {
        V.indicator[j] <- 2
        }else
        {
        V.indicator[j] <- 0
        }
    }

## Check for an offset term
offset.omega <- try(model.offset(frame.omega), silent=TRUE)
    if(class(offset.omega)=="try-error")   stop("the offset for the probability of being a zero is not numeric.", call.=FALSE)
    if(is.null(offset.omega))  offset.omega <- rep(0,K)
    if(sum(is.na(offset.omega))>0) stop("the offset for the probability of being a zero has missing 'NA' values.", call.=FALSE)
    if(!is.numeric(offset.omega)) stop("the offset for the probability of being a zero variable has non-numeric values.", call.=FALSE)


#### Set up which elements are zero
which.zero <- which(Y==0)
n.zero <- length(which.zero)


#### Check on MALA argument
    if(length(MALA)!=1) stop("MALA is not length 1.", call.=FALSE)
    if(!is.logical(MALA)) stop("MALA is not logical.", call.=FALSE)  


#### Priors
    if(is.null(prior.mean.beta)) prior.mean.beta <- rep(0, p)
    if(is.null(prior.var.beta)) prior.var.beta <- rep(100000, p)
    if(is.null(prior.tau2)) prior.tau2 <- c(1, 0.01)
    if(is.null(prior.sigma2)) prior.sigma2 <- c(1, 0.01)
    if(is.null(prior.mean.delta)) prior.mean.delta <- rep(0, q)
    if(is.null(prior.var.delta)) prior.var.delta <- rep(100000, q)
common.prior.beta.check(prior.mean.beta, prior.var.beta, p)
common.prior.var.check(prior.tau2)
common.prior.var.check(prior.sigma2)
common.prior.beta.check(prior.mean.delta, prior.var.delta, q)


#### Compute the blocking structure for beta     
block.temp <- common.betablock(p)
beta.beg  <- block.temp[[1]]
beta.fin <- block.temp[[2]]
n.beta.block <- block.temp[[3]]
list.block <- as.list(rep(NA, n.beta.block*2))
    for(r in 1:n.beta.block)
    {
    list.block[[r]] <- beta.beg[r]:beta.fin[r]-1
    list.block[[r+n.beta.block]] <- length(list.block[[r]])
    }


## Compute the blocking structure for delta     
block.temp <- common.betablock(q)
delta.beg  <- block.temp[[1]]
delta.fin <- block.temp[[2]]
n.delta.block <- block.temp[[3]]
list.block.delta <- as.list(rep(NA, n.delta.block*2))
    for(r in 1:n.delta.block)
    {
    list.block.delta[[r]] <- delta.beg[r]:delta.fin[r]-1
    list.block.delta[[r+n.delta.block]] <- length(list.block.delta[[r]])
    }    



#### MCMC quantities - burnin, n.sample, thin
common.burnin.nsample.thin.check(burnin, n.sample, thin)



#############################
#### Initial parameter values
#############################
mod.glm <- glm(Y~X.standardised-1, offset=offset, family="quasipoisson")
beta.mean <- mod.glm$coefficients
beta.sd <- sqrt(diag(summary(mod.glm)$cov.scaled))
beta <- rnorm(n=length(beta.mean), mean=beta.mean, sd=beta.sd)

log.Y <- log(Y)
log.Y[Y==0] <- -0.1  
res.temp <- log.Y - X.standardised %*% beta.mean - offset
res.sd <- sd(res.temp, na.rm=TRUE)/5
phi <- rnorm(n=K, mean=rep(0,K), sd=res.sd)
tau2 <- var(phi) / 10
theta <- rnorm(n=K, mean=rep(0,K), sd=res.sd)
sigma2 <- var(theta) / 10
fitted <- exp(as.numeric(X.standardised %*% beta) + phi + theta + offset)

Y.zero <- rep(0,K)
Y.zero[which.zero] <- 1
mod.glm2 <- glm(Y.zero~V.standardised-1, offset=offset.omega, family="binomial")
delta.mean <- mod.glm2$coefficients
delta.sd <- sqrt(diag(summary(mod.glm2)$cov.scaled))
delta <- rnorm(n=length(delta.mean), mean=delta.mean, sd=delta.sd)

omega <- exp(V.standardised %*% delta+offset.omega) / (1+exp(V.standardised %*% delta+offset.omega))
prob.pointmass <- omega[which.zero] / (omega[which.zero]+(1-omega[which.zero])*exp(-exp(X.standardised[which.zero, ] %*% beta + offset[which.zero])))
Z <-  rep(0, K)
Z[which.zero] <- rbinom(n=n.zero, size=1, prob=prob.pointmass)   



###############################    
#### Set up the MCMC quantities    
###############################
#### Matrices to store samples
n.keep <- floor((n.sample - burnin)/thin)
samples.beta <- array(NA, c(n.keep, p))
samples.re <- array(NA, c(n.keep, K))
samples.tau2 <- array(NA, c(n.keep, 1))
samples.sigma2 <- array(NA, c(n.keep, 1))
samples.delta <- array(NA, c(n.keep, q))    
samples.Z <- array(NA, c(n.keep, K))    
samples.like <- array(NA, c(n.keep, K))
samples.fitted <- array(NA, c(n.keep, K))
    if(n.miss>0) samples.Y <- array(NA, c(n.keep, n.miss))


## Metropolis quantities
accept.all <- rep(0,8)
accept <- accept.all
proposal.sd.beta <- 0.01
proposal.sd.phi <- 0.1
proposal.sd.theta <- 0.1
proposal.sd.delta <- 0.01
sigma2.posterior.shape <- prior.sigma2[1] + 0.5 * K



##################################
#### Set up the spatial quantities
##################################
#### CAR quantities
W.quants <- common.Wcheckformat(W, K)
W <- W.quants$W
W.triplet <- W.quants$W.triplet
n.triplet <- W.quants$n.triplet
W.triplet.sum <- W.quants$W.triplet.sum
n.neighbours <- W.quants$n.neighbours 
W.begfin <- W.quants$W.begfin


#### Check for islands
W.list<- mat2listw(W)
W.nb <- W.list$neighbours
W.islands <- n.comp.nb(W.nb)
islands <- W.islands$comp.id
n.islands <- max(W.islands$nc)
tau2.posterior.shape <- prior.tau2[1] + 0.5 * (K-n.islands)   



###########################
#### Run the Bayesian model
###########################
## Start timer
    if(verbose)
    {
    cat("Generating", n.keep, "post burnin and thinned (if requested) samples\n", sep = " ")
    progressBar <- txtProgressBar(style = 3)
    percentage.points<-round((1:100/100)*n.sample)
    }else
    {
    percentage.points<-round((1:100/100)*n.sample)     
    }
     

#### Create the MCMC samples     
    for(j in 1:n.sample)
    {
    ####################################
    ## Sample from Y - data augmentation
    ####################################
        if(n.miss>0)
        {
        Y.DA[which.miss==0] <- rpois(n=n.miss, lambda=fitted[which.miss==0]) * (1-Z[which.miss==0]) 
        }else
        {}
    which.zero <- which(Y.DA==0)
    n.zero <- length(which.zero)           
        

        
    ###################################
    #### Update Z via data augmentation
    ###################################
    prob.pointmass <- omega[which.zero] / (omega[which.zero] + (1 - omega[which.zero]) * exp(-exp(X.standardised[which.zero, ] %*% beta + offset[which.zero] + phi[which.zero] + theta[which.zero])))
    Z <-  rep(0, K)
    Z[which.zero] <- rbinom(n=n.zero, size=1, prob=prob.pointmass)    
    
    

    ####################
    ## Sample from beta
    ####################
    Z.zero <- which(Z==0)
    offset.temp <- phi[Z.zero] + offset[Z.zero] + theta[Z.zero]
        if(p>2)
        {
        temp <- poissonbetaupdateMALA(X.standardised[Z.zero, ], length(Z.zero), p, beta, offset.temp, Y.DA[Z.zero], prior.mean.beta, prior.var.beta, n.beta.block, proposal.sd.beta, list.block)
        }else
        {
        temp <- poissonbetaupdateRW(X.standardised[Z.zero, ], length(Z.zero), p, beta, offset.temp, Y.DA[Z.zero], prior.mean.beta, prior.var.beta, proposal.sd.beta)
        }
    beta <- temp[[1]]
    accept[1] <- accept[1] + temp[[2]]
    accept[2] <- accept[2] + n.beta.block  

    
    
    ####################
    ## Sample from phi
    ####################
    beta.offset <- X.standardised %*% beta + theta + offset
        if(MALA)
        {
        temp1 <- zipcarupdateMALA(Wtriplet=W.triplet, Wbegfin=W.begfin, W.triplet.sum, nsites=K, phi=phi, tau2=tau2, y=Y.DA, phi_tune=proposal.sd.phi, rho=1, offset=beta.offset, 1-Z)
        }else
        {
        temp1 <- zipcarupdateRW(Wtriplet=W.triplet, Wbegfin=W.begfin, W.triplet.sum, nsites=K, phi=phi, tau2=tau2, y=Y.DA, phi_tune=proposal.sd.phi, rho=1, offset=beta.offset, 1-Z)
        }
    phi <- temp1[[1]]
    phi[which(islands==1)] <- phi[which(islands==1)] - mean(phi[which(islands==1)])
    accept[3] <- accept[3] + temp1[[2]]
    accept[4] <- accept[4] + sum(Z==0)    
    
    

    ####################
    ## Sample from theta
    ####################
    beta.offset <- as.numeric(X.standardised %*% beta) + phi + offset
        if(MALA)
        {
        temp2 <- zipindepupdateMALA(nsites=K, theta=theta, sigma2=sigma2, y=Y.DA, theta_tune=proposal.sd.theta, offset=beta.offset, 1-Z) 
        }else
        {
        temp2 <- zipindepupdateRW(nsites=K, theta=theta, sigma2=sigma2, y=Y.DA, theta_tune=proposal.sd.theta, offset=beta.offset, 1-Z) 
        }
    theta <- temp2[[1]]
    theta <- theta - mean(theta)    
    accept[5] <- accept[5] + temp2[[2]]
    accept[6] <- accept[6] + sum(Z==0) 

  

    ###################
    ## Sample from tau2
    ###################
    temp2 <- quadform(W.triplet, W.triplet.sum, n.triplet, K, phi, phi, 1)
    tau2.posterior.scale <- temp2 + prior.tau2[2] 
    tau2 <- 1 / rgamma(1, tau2.posterior.shape, scale=(1/tau2.posterior.scale))
    
    
    
    #####################
    ## Sample from sigma2
    #####################
    sigma2.posterior.scale <- prior.sigma2[2] + 0.5*sum(theta^2)
    sigma2 <- 1 / rgamma(1, sigma2.posterior.shape, scale=(1/sigma2.posterior.scale))    
    
    
    
    ######################    
    #### Sample from delta
    ######################
    offset.temp <- offset.omega
        if(q>2)
        {
        temp <- binomialbetaupdateMALA(V.standardised, K, q, delta, offset.temp, Z, 1-Z, rep(1,K), prior.mean.delta, prior.var.delta, n.delta.block, proposal.sd.delta, list.block.delta)
        }else
        {
        temp <- binomialbetaupdateRW(V.standardised, K, q, delta, offset.temp, Z, 1-Z, prior.mean.delta, prior.var.delta, proposal.sd.delta)
        }
    delta <- temp[[1]]
    accept[7] <- accept[7] + temp[[2]]
    accept[8] <- accept[8] + n.delta.block  
    omega <- exp(V.standardised %*% delta+offset.omega) / (1+exp(V.standardised %*% delta+offset.omega))
    
    
    
    #########################
    ## Calculate the deviance
    #########################
    lp <- as.numeric(X.standardised %*% beta) + phi + theta + offset
    fitted <- exp(lp)
    fitted.zip <- fitted * (1-omega)    
    temp <- rep(0,K)
    temp[Z==1] <- log(omega[Z==1])
    deviance.all <- temp + (1-Z) * (log(1-omega) + dpois(x=as.numeric(Y), lambda=fitted, log=T))
    like <- exp(deviance.all)
    deviance <- -2 * sum(deviance.all, na.rm=TRUE)  
    

        
    ###################
    ## Save the results
    ###################
        if(j > burnin & (j-burnin)%%thin==0)
        {
        ele <- (j - burnin) / thin
        samples.beta[ele, ] <- beta
        samples.re[ele, ] <- phi + theta
        samples.tau2[ele, ] <- tau2
        samples.sigma2[ele, ] <- sigma2
        samples.delta[ele, ] <- delta
        samples.Z[ele, ] <- Z
        samples.like[ele, ] <- like
        samples.fitted[ele, ] <- fitted.zip
            if(n.miss>0) samples.Y[ele, ] <- Y.DA[which.miss==0]
        }else
        {
        }


    ########################################
    ## Self tune the acceptance probabilties
    ########################################
    k <- j/100
        if(ceiling(k)==floor(k))
        {
        #### Update the proposal sds
            if(p>2)
            {
            proposal.sd.beta <- common.accceptrates1(accept[1:2], proposal.sd.beta, 40, 50)
            }else
            {
            proposal.sd.beta <- common.accceptrates1(accept[1:2], proposal.sd.beta, 30, 40)    
            }

            if(q>2)
            {
            proposal.sd.delta <- common.accceptrates1(accept[7:8], proposal.sd.delta, 40, 50)
            }else
            {
            proposal.sd.delta <- common.accceptrates1(accept[7:8], proposal.sd.delta, 30, 40)    
            }
            
        proposal.sd.phi <- common.accceptrates1(accept[3:4], proposal.sd.phi, 40, 50)
        proposal.sd.theta <- common.accceptrates1(accept[5:6], proposal.sd.theta, 40, 50)
        accept.all <- accept.all + accept
        accept <- c(0,0,0,0,0,0,0,0)
        }else
        {   
        }

    
    
    ################################       
    ## print progress to the console
    ################################
        if(j %in% percentage.points & verbose)
        {
        setTxtProgressBar(progressBar, j/n.sample)
        }
    }


#### end timer
    if(verbose)
    {
    cat("\nSummarising results")
    close(progressBar)
    }else
    {}
   

  
###################################
#### Summarise and save the results 
###################################
#### Compute the acceptance rates
accept.beta <- 100 * accept.all[1] / accept.all[2]
accept.phi <- 100 * accept.all[3] / accept.all[4]
accept.theta <- 100 * accept.all[5] / accept.all[6]
accept.delta <- 100 * accept.all[7] / accept.all[8]
accept.tau2 <- 100
accept.sigma2 <- 100
accept.final <- c(accept.beta, accept.phi, accept.theta, accept.tau2, accept.sigma2, accept.delta)
names(accept.final) <- c("beta", "phi", "theta", "tau2", "sigma2", "delta")

     
#### Compute the fitted deviance
mean.beta <- apply(samples.beta, 2, mean)
mean.re <- apply(samples.re, 2, mean)
mean.lp <- X.standardised %*% mean.beta  + mean.re + offset
mean.fitted <- exp(mean.lp)
mean.Z <- round(apply(samples.Z,2,mean))
mean.delta <- apply(samples.delta, 2, mean)
mean.omega <- exp(V.standardised %*% mean.delta + offset.omega) / (1+exp(V.standardised %*% mean.delta + offset.omega))
temp <- rep(0,K)
temp[mean.Z==1] <- log(mean.omega[mean.Z==1])
mean.deviance.all <- temp + (1-mean.Z) * (log(1-mean.omega) + dpois(x=as.numeric(Y), lambda=mean.fitted, log=T))
deviance.fitted <- -2 * sum(mean.deviance.all, na.rm=TRUE)  


#### Model fit criteria
modelfit <- common.modelfit(samples.like, deviance.fitted)


#### transform the parameters back to the origianl covariate scale.
samples.beta.orig <- common.betatransform(samples.beta, X.indicator, X.mean, X.sd, p, FALSE)
samples.delta.orig <- common.betatransform(samples.delta, V.indicator, V.mean, V.sd, q, FALSE)


#### Create a summary object
samples.beta.orig <- mcmc(samples.beta.orig)
summary.beta <- t(apply(samples.beta.orig, 2, quantile, c(0.5, 0.025, 0.975))) 
summary.beta <- cbind(summary.beta, rep(n.keep, p), rep(accept.beta,p), effectiveSize(samples.beta.orig), geweke.diag(samples.beta.orig)$z)
rownames(summary.beta) <- colnames(X)
colnames(summary.beta) <- c("Median", "2.5%", "97.5%", "n.sample", "% accept", "n.effective", "Geweke.diag")

samples.delta.orig <- mcmc(samples.delta.orig)
summary.delta <- t(apply(samples.delta.orig, 2, quantile, c(0.5, 0.025, 0.975))) 
summary.delta <- cbind(summary.delta, rep(n.keep, q), rep(accept.delta,q), effectiveSize(samples.delta.orig), geweke.diag(samples.delta.orig)$z)
    for(i in 1:q)
    {
    rownames(summary.delta)[i] <- paste("omega - ", colnames(V)[i])    
    }
colnames(summary.delta) <- c("Median", "2.5%", "97.5%", "n.sample", "% accept", "n.effective", "Geweke.diag")

summary.hyper <- array(NA, c(2,7))
summary.hyper[1, 1:3] <- quantile(samples.tau2, c(0.5, 0.025, 0.975))
summary.hyper[1, 4:7] <- c(n.keep, accept.tau2, effectiveSize(samples.tau2), geweke.diag(samples.tau2)$z)
summary.hyper[2, 1:3] <- quantile(samples.sigma2, c(0.5, 0.025, 0.975))
summary.hyper[2, 4:7] <- c(n.keep, accept.sigma2, effectiveSize(samples.sigma2), geweke.diag(samples.sigma2)$z)

summary.results <- rbind(summary.beta, summary.delta, summary.hyper)
rownames(summary.results)[(nrow(summary.results)-1):(nrow(summary.results))] <- c("tau2", "sigma2")
summary.results[ , 1:3] <- round(summary.results[ , 1:3], 4)
summary.results[ , 4:7] <- round(summary.results[ , 4:7], 1)


#### Create the fitted values and residuals
fitted.values <- apply(samples.fitted, 2, mean)
response.residuals <- as.numeric(Y) - fitted.values
var.y <- fitted.values + (1 - mean.omega) * mean.omega * mean.fitted^2
pearson.residuals <- response.residuals /sqrt(var.y)
residuals <- data.frame(response=response.residuals, pearson=pearson.residuals)


#### Compile and return the results
model.string <- c("Likelihood model - Zero-Inflated Poisson (log link function)", "\nRandom effects model - BYM CAR\n")
if(n.miss==0) samples.Y = NA

samples <- list(beta=samples.beta.orig, psi=mcmc(samples.re), tau2=mcmc(samples.tau2), sigma2=mcmc(samples.sigma2), delta=mcmc(samples.delta), Z=mcmc(samples.Z), fitted=mcmc(samples.fitted), Y=mcmc(samples.Y))
results <- list(summary.results=summary.results, samples=samples, fitted.values=fitted.values, residuals=residuals, modelfit=modelfit, accept=accept.final, localised.structure=NULL,  formula=formula, model=model.string, X=X)
class(results) <- "CARBayes"


#### Finish by stating the time taken    
if(verbose)
{
    b<-proc.time()
    cat(" finished in ", round(b[3]-a[3], 1), "seconds")
}else
{}
return(results)
}