poisson.localisedCAR <- function(formula, data=NULL, G, W, burnin, n.sample, thin=1, prior.mean.beta=NULL, prior.var.beta=NULL, prior.tau2=NULL, prior.delta = NULL, MALA=FALSE, verbose=TRUE)
{
##############################################
#### Format the arguments and check for errors
##############################################
#### Verbose
a <- common.verbose(verbose)
#### Frame object
frame.results <- common.frame.localised(formula, data, "poisson", trials=NA)
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$Y
log.Y <- log(Y)
log.Y[Y==0] <- -0.1
regression.vec <- frame.results$regression.vec
beta <- frame.results$beta
#### Check on MALA argument
if(length(MALA)!=1) stop("MALA is not length 1.", call.=FALSE)
if(!is.logical(MALA)) stop("MALA is not logical.", call.=FALSE)
#### Format and check the number of clusters G
if(length(G)!=1) stop("G is the wrong length.", call.=FALSE)
if(!is.numeric(G)) stop("G is not numeric.", call.=FALSE)
if(G<=1) stop("G is less than 2.", call.=FALSE)
if(G!=round(G)) stop("G is not an integer.", call.=FALSE)
if(floor(G/2)==ceiling(G/2))
{
Gstar <- G/2
}else
{
Gstar <- (G+1)/2
}
#### Priors
if(!is.null(X))
{
if(is.null(prior.mean.beta)) prior.mean.beta <- rep(0, p)
if(is.null(prior.var.beta)) prior.var.beta <- rep(100000, p)
common.prior.beta.check(prior.mean.beta, prior.var.beta, p)
}else
{}
if(is.null(prior.tau2)) prior.tau2 <- c(1, 0.01)
common.prior.var.check(prior.tau2)
if(is.null(prior.delta)) prior.delta <- 10
if(length(prior.delta)!=1) stop("the prior value for delta is the wrong length.", call.=FALSE)
if(!is.numeric(prior.delta)) stop("the prior value for delta is not numeric.", call.=FALSE)
if(sum(is.na(prior.delta))!=0) stop("the prior value for delta has missing values.", call.=FALSE)
if(prior.delta<=0) stop("the prior value for delta is not positive.", call.=FALSE)
#### Compute the blocking structure for beta
if(!is.null(X))
{
## Compute the blocking structure for beta
block.temp <- common.betablock(p)
beta.beg <- block.temp[[1]]
beta.fin <- block.temp[[2]]
n.beta.block <- block.temp[[3]]
list.block <- as.list(rep(NA, n.beta.block*2))
for(r in 1:n.beta.block)
{
list.block[[r]] <- beta.beg[r]:beta.fin[r]-1
list.block[[r+n.beta.block]] <- length(list.block[[r]])
}
}else
{}
#### MCMC quantities - burnin, n.sample, thin
common.burnin.nsample.thin.check(burnin, n.sample, thin)
#############################
#### Initial parameter values
#############################
res.temp <- log.Y - regression.vec - offset
clust <- kmeans(res.temp,G)
lambda <- clust$centers[order(clust$centers)]
Z <- rep(1, K)
for(j in 2:G)
{
Z[clust$cluster==order(clust$centers)[j]] <- j
}
delta <- runif(1,1, min(2, prior.delta))
res.sd <- sd(res.temp, na.rm=TRUE)/5
phi <- rnorm(n=K, mean=rep(0,K), sd = res.sd)
for(i in 1:G)
{
phi[which(Z==i)] <- phi[which(Z==i)] - mean(phi[which(Z==i)])
}
tau2 <- var(phi) / 10
###############################
#### Set up the MCMC quantities
###############################
#### Matrices to store samples
n.keep <- floor((n.sample - burnin)/thin)
samples.phi <- array(NA, c(n.keep, K))
samples.tau2 <- array(NA, c(n.keep, 1))
samples.Z <- array(NA, c(n.keep, K))
samples.lambda <- array(NA, c(n.keep, G))
samples.delta <- array(NA, c(n.keep, 1))
samples.loglike <- array(NA, c(n.keep, K))
samples.fitted <- array(NA, c(n.keep, K))
#### Metropolis quantities
if(!is.null(X))
{
samples.beta <- array(NA, c(n.keep, p))
accept <- rep(0,8)
proposal.sd.beta <- 0.01
}else
{
accept <- rep(0,6)
}
proposal.sd.phi <- 0.1
proposal.sd.delta <- 0.1
proposal.sd.lambda <- 0.01
tau2.posterior.shape <- prior.tau2[1] + 0.5 * K
##################################
#### Set up the spatial quantities
##################################
#### CAR quantities
W.quants <- common.Wcheckformat(W)
W <- W.quants$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
###########################
#### 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 beta
###################
if(!is.null(X))
{
offset.temp <- phi + offset + lambda[Z]
if(MALA)
{
temp <- poissonbetaupdateMALA(X.standardised, K, p, beta, offset.temp, Y, prior.mean.beta, prior.var.beta, n.beta.block, proposal.sd.beta, list.block)
}else
{
temp <- poissonbetaupdateRW(X.standardised, K, p, beta, offset.temp, Y, prior.mean.beta, prior.var.beta, n.beta.block, proposal.sd.beta, list.block)
}
beta <- temp[[1]]
accept[7] <- accept[7] + temp[[2]]
accept[8] <- accept[8] + n.beta.block
regression.vec <- X.standardised %*% beta
}else
{}
##################
## Sample from phi
##################
phi.offset <- regression.vec + offset + lambda[Z]
if(MALA)
{
temp1 <- poissoncarupdateMALA(Wtriplet=W.triplet, Wbegfin=W.begfin, W.triplet.sum, nsites=K, phi=phi, tau2=tau2, y=Y, phi_tune=proposal.sd.phi, rho=1, offset=phi.offset)
}else
{
temp1 <- poissoncarupdateRW(Wtriplet=W.triplet, Wbegfin=W.begfin, W.triplet.sum, nsites=K, phi=phi, tau2=tau2, y=Y, phi_tune=proposal.sd.phi, rho=1, offset=phi.offset)
}
phi <- temp1[[1]]
for(i in 1:G)
{
phi[which(Z==i)] <- phi[which(Z==i)] - mean(phi[which(Z==i)])
}
accept[1] <- accept[1] + temp1[[2]]
accept[2] <- accept[2] + K
###################
## 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 lambda
#####################
proposal.extend <- c(-1000, lambda, 1000)
lambda.extend <- c(-1000, lambda, 1000)
for(i in 1:G)
{
proposal.extend[(i+1)] <- rtruncnorm(n=1, a=proposal.extend[i], b=proposal.extend[(i+2)], mean=lambda[i], sd=proposal.sd.lambda)
}
proposal <- proposal.extend[2:(G+1)]
lp.current <- lambda[Z] + phi + regression.vec + offset
lp.proposal <- proposal[Z] + phi + regression.vec + offset
prob1 <- sum((exp(lp.current) - exp(lp.proposal)))
prob2 <- sum(Y * (lp.proposal - lp.current))
prob <- exp(prob1 + prob2)
if(prob > runif(1))
{
lambda <- proposal
accept[3] <- accept[3] + 1
}else
{
}
accept[4] <- accept[4] + 1
################
## Sample from Z
################
Z.offset <- phi + offset + regression.vec
Z.proposal <- sample(1:G, size=K, replace=TRUE)
prior <- delta * ((Z - Gstar)^2 - (Z.proposal-Gstar)^2)
like <- exp(Z.offset) * (exp(lambda[Z]) - exp(lambda[Z.proposal])) + Y * (lambda[Z.proposal] - lambda[Z])
prob <- exp(like + prior)
test <- prob> runif(K)
Z[test] <- Z.proposal[test]
####################
## Sample from delta
####################
proposal.delta <- rtruncnorm(n=1, a=1, b=prior.delta, mean=delta, sd=proposal.sd.delta)
prob1 <- sum((Z-Gstar)^2) * (delta - proposal.delta)
prob2 <- K * log(sum(exp(-delta *(1:G - Gstar)^2))) - K * log(sum(exp(-proposal.delta *(1:G - Gstar)^2)))
hastings <- log(dtruncnorm(x=delta, a=1, b=prior.delta, mean=proposal.delta, sd=proposal.sd.delta)) - log(dtruncnorm(x=proposal.delta, a=1, b=prior.delta, mean=delta, sd=proposal.sd.delta))
prob <- exp(prob1 + prob2 + hastings)
if(prob > runif(1))
{
delta <- proposal.delta
accept[5] <- accept[5] + 1
}else
{
}
accept[6] <- accept[6] + 1
#########################
## Calculate the deviance
#########################
lp <- lambda[Z] + phi + regression.vec + offset
fitted <- exp(lp)
loglike <- dpois(x=as.numeric(Y), lambda=fitted, log=TRUE)
###################
## Save the results
###################
if(j > burnin & (j-burnin)%%thin==0)
{
ele <- (j - burnin) / thin
samples.phi[ele, ] <- phi
samples.lambda[ele, ] <- lambda
samples.tau2[ele, ] <- tau2
samples.Z[ele, ] <- Z
samples.delta[ele, ] <- delta
samples.loglike[ele, ] <- loglike
samples.fitted[ele, ] <- fitted
if(!is.null(X)) samples.beta[ele, ] <- beta
}else
{
}
########################################
## Self tune the acceptance probabilties
########################################
if(ceiling(j/100)==floor(j/100) & j < burnin)
{
if(!is.null(X))
{
if(p>2)
{
proposal.sd.beta <- common.accceptrates1(accept[7:8], proposal.sd.beta, 40, 50)
}else
{
proposal.sd.beta <- common.accceptrates1(accept[7:8], proposal.sd.beta, 30, 40)
}
proposal.sd.phi <- common.accceptrates1(accept[1:2], proposal.sd.phi, 40, 50)
proposal.sd.lambda <- common.accceptrates1(accept[3:4], proposal.sd.lambda, 20, 40)
proposal.sd.delta <- common.accceptrates2(accept[5:6], proposal.sd.delta, 40, 50, prior.delta/6)
accept <- rep(0,8)
}else
{
proposal.sd.phi <- common.accceptrates1(accept[1:2], proposal.sd.phi, 40, 50)
proposal.sd.lambda <- common.accceptrates1(accept[3:4], proposal.sd.lambda, 20, 40)
proposal.sd.delta <- common.accceptrates2(accept[5:6], proposal.sd.delta, 40, 50, prior.delta/6)
accept <- rep(0,6)
}
}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.phi <- 100 * accept[1] / accept[2]
accept.lambda <- 100 * accept[3] / accept[4]
accept.delta <- 100 * accept[5] / accept[6]
accept.tau2 <- 100
if(!is.null(X))
{
accept.beta <- 100 * accept[7] / accept[8]
accept.final <- c(accept.beta, accept.lambda, accept.delta, accept.phi, accept.tau2)
names(accept.final) <- c("beta", "lambda", "delta", "phi", "tau2")
}else
{
accept.final <- c(accept.lambda, accept.delta, accept.phi, accept.tau2)
names(accept.final) <- c("lambda", "delta", "phi", "tau2")
}
#### Compute the fitted deviance
mean.phi <- apply(samples.phi, 2, mean)
mean.Z <- round(apply(samples.Z,2,mean),0)
mean.lambda <- apply(samples.lambda,2,mean)
if(!is.null(X))
{
mean.beta <- apply(samples.beta,2,mean)
regression.vec <- as.numeric(X.standardised %*% mean.beta)
}else
{
regression.vec <- rep(0,K)
}
fitted.mean <- exp(regression.vec + mean.lambda[mean.Z] + mean.phi + offset)
deviance.fitted <- -2 * sum(dpois(x=Y, lambda=fitted.mean, log=TRUE))
#### Model fit criteria
modelfit <- common.modelfit(samples.loglike, deviance.fitted)
#### transform the parameters back to the origianl covariate scale.
if(!is.null(X))
{
samples.beta.orig <- common.betatransform(samples.beta, X.indicator, X.mean, X.sd, p, TRUE)
}else
{}
#### Create a summary object
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.delta, c(0.5, 0.025, 0.975))
summary.hyper[2, 4:7] <- c(n.keep, accept.delta, effectiveSize(samples.delta), geweke.diag(samples.delta)$z)
samples.lambda <- mcmc(samples.lambda)
summary.lambda <- t(apply(samples.lambda, 2, quantile, c(0.5, 0.025, 0.975)))
summary.lambda <- cbind(summary.lambda, rep(n.keep, G), rep(accept.lambda, G), effectiveSize(samples.lambda), geweke.diag(samples.lambda)$z)
Z.used <- as.numeric(names(table(samples.Z)))
summary.lambda <- summary.lambda[Z.used, ]
if(!is.null(X))
{
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)
summary.results <- rbind(summary.beta, summary.lambda, summary.hyper)
row.names(summary.results)[(p+1):nrow(summary.results)] <- c(paste("lambda", Z.used, sep=""), "tau2", "delta")
colnames(summary.results) <- c("Median", "2.5%", "97.5%", "n.sample", "% accept", "n.effective", "Geweke.diag")
summary.results[ , 1:3] <- round(summary.results[ , 1:3], 4)
summary.results[ , 4:7] <- round(summary.results[ , 4:7], 1)
}else
{
summary.results <- rbind(summary.lambda, summary.hyper)
row.names(summary.results) <- c(paste("lambda", Z.used, sep=""), "tau2", "delta")
colnames(summary.results) <- c("Median", "2.5%", "97.5%", "n.sample", "% accept", "n.effective", "Geweke.diag")
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
pearson.residuals <- response.residuals /sqrt(fitted.values)
residuals <- data.frame(response=response.residuals, pearson=pearson.residuals)
## Compile and return the results
model.string <- c("Likelihood model - Poisson (log link function)", "\nRandom effects model - Localised CAR model\n")
if(is.null(X)) samples.beta.orig = NA
samples <- list(beta=mcmc(samples.beta.orig), phi=mcmc(samples.phi), lambda=mcmc(samples.lambda), Z=mcmc(samples.Z), tau2=mcmc(samples.tau2), delta=mcmc(samples.delta), fitted=mcmc(samples.fitted), Y=NA)
results <- list(summary.results=summary.results, samples=samples, fitted.values=fitted.values, residuals=residuals, modelfit=modelfit, accept=accept.final, localised.structure=mean.Z, 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.\n")
}else
{}
return(results)
}
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