Nothing
R/binomial.CARlinear.R
In CARBayesST: Spatio-Temporal Generalised Linear Mixed Models for Areal Unit Data
Defines functions
binomial.CARlinear
binomial.CARlinear <- function(formula, data=NULL, trials, W, burnin, n.sample, thin=1, n.chains=1, n.cores=1, prior.mean.beta=NULL, prior.var.beta=NULL, prior.mean.alpha=NULL, prior.var.alpha=NULL, prior.tau2=NULL, rho.slo=NULL, rho.int=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, "binomial")
N.all <- 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$n.miss
#### Determine the number of spatial and temporal units
W.quants <- common.Wcheckformat.leroux(W)
K <- W.quants$n
N <- N.all / K
offset.mat <- matrix(offset, nrow=K, ncol=N, byrow=FALSE)
time <-(1:N - mean(1:N))/N
time.mat <- matrix(rep(time, K), byrow=TRUE, nrow=K)
#### 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)
#### Check the trials argument
if(sum(is.na(trials))>0) stop("the numbers of trials has missing 'NA' values.", call.=FALSE)
if(!is.numeric(trials)) stop("the numbers of trials has non-numeric values.", call.=FALSE)
int.check <- N.all-sum(ceiling(trials)==floor(trials))
if(int.check > 0) stop("the numbers of trials has non-integer values.", call.=FALSE)
if(min(trials)<=0) stop("the numbers of trials has zero or negative values.", call.=FALSE)
if(sum(Y>trials, na.rm=TRUE)>0) stop("the response variable has larger values that the numbers of trials.", call.=FALSE)
failures <- trials - Y
#### Check on the rho arguments
if(is.null(rho.int))
{
rho <- runif(1)
fix.rho.int <- FALSE
}else
{
rho <- rho.int
fix.rho.int <- TRUE
}
if(!is.numeric(rho)) stop("rho.int is fixed but is not numeric.", call.=FALSE)
if(rho<0 ) stop("rho.int is outside the range [0, 1].", call.=FALSE)
if(rho>1 ) stop("rho.int is outside the range [0, 1].", call.=FALSE)
if(is.null(rho.slo))
{
lambda <- runif(1)
fix.rho.slo <- FALSE
}else
{
lambda <- rho.slo
fix.rho.slo <- TRUE
}
if(!is.numeric(lambda)) stop("rho.slo is fixed but is not numeric.", call.=FALSE)
if(lambda<0 ) stop("rho.slo is outside the range [0, 1].", call.=FALSE)
if(lambda>1 ) stop("rho.slo is outside the range [0, 1].", 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.mean.alpha)) prior.mean.alpha <- rep(0, 1)
if(is.null(prior.var.alpha)) prior.var.alpha <- rep(100000, 1)
prior.beta.check(prior.mean.beta, prior.var.beta, p)
prior.var.check(prior.tau2)
if(length(prior.mean.alpha)!=1) stop("the prior mean for alpha is the wrong length.", call.=FALSE)
if(!is.numeric(prior.mean.alpha)) stop("the prior mean for alpha is not numeric.", call.=FALSE)
if(sum(is.na(prior.mean.alpha))!=0) stop("the prior mean for alpha has missing values.", call.=FALSE)
if(length(prior.var.alpha)!=1) stop("the prior variance for alpha is the wrong length.", call.=FALSE)
if(!is.numeric(prior.var.alpha)) stop("the prior variance for alpha is not numeric.", call.=FALSE)
if(sum(is.na(prior.var.alpha))!=0) stop("the prior variance for alpha has missing values.", call.=FALSE)
if(min(prior.var.alpha) <=0) stop("the prior variance for alpha has elements less than zero", call.=FALSE)
#### 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]])
}
#### MCMC quantities - burnin, n.sample, thin
common.burnin.nsample.thin.check(burnin, n.sample, thin)
########################
#### Run the MCMC chains
########################
if(n.chains==1)
{
#### Only 1 chain
results <- binomial.CARlinearMCMC(Y=Y, failures=failures, trials=trials, offset=offset, X.standardised=X.standardised, W=W, rho=rho, lambda=lambda, fix.rho.int=fix.rho.int, fix.rho.slo=fix.rho.slo, K=K, N=N, N.all=N.all, p=p, which.miss=which.miss, n.miss=n.miss, burnin=burnin, n.sample=n.sample, thin=thin, MALA=MALA, n.beta.block=n.beta.block, list.block=list.block, prior.mean.beta=prior.mean.beta, prior.var.beta=prior.var.beta, prior.mean.alpha=prior.mean.alpha, prior.var.alpha=prior.var.alpha, prior.tau2=prior.tau2, verbose=verbose, chain=1)
}else if(n.chains > 1 & ceiling(n.chains)==floor(n.chains) & n.cores==1)
{
#### Multiple chains in series
results <- as.list(rep(NA, n.chains))
for(i in 1:n.chains)
{
results[[i]] <- binomial.CARlinearMCMC(Y=Y, failures=failures, trials=trials, offset=offset, X.standardised=X.standardised, W=W, rho=rho, lambda=lambda, fix.rho.int=fix.rho.int, fix.rho.slo=fix.rho.slo, K=K, N=N, N.all=N.all, p=p, which.miss=which.miss, n.miss=n.miss, burnin=burnin, n.sample=n.sample, thin=thin, MALA=MALA, n.beta.block=n.beta.block, list.block=list.block, prior.mean.beta=prior.mean.beta, prior.var.beta=prior.var.beta, prior.mean.alpha=prior.mean.alpha, prior.var.alpha=prior.var.alpha, prior.tau2=prior.tau2, verbose=verbose, chain=i)
}
}else if(n.chains > 1 & ceiling(n.chains)==floor(n.chains) & n.cores>1 & ceiling(n.cores)==floor(n.cores))
{
#### Multiple chains in parallel
results <- as.list(rep(NA, n.chains))
if(verbose)
{
compclust <- makeCluster(n.cores, outfile="CARBayesSTprogress.txt")
cat("The current progress of the model fitting algorithm has been output to CARBayesSTprogress.txt in the working directory")
}else
{
compclust <- makeCluster(n.cores)
}
results <- clusterCall(compclust, fun=binomial.CARlinearMCMC, Y=Y, failures=failures, trials=trials, offset=offset, X.standardised=X.standardised, W=W, rho=rho, lambda=lambda, fix.rho.int=fix.rho.int, fix.rho.slo=fix.rho.slo, K=K, N=N, N.all=N.all, p=p, which.miss=which.miss, n.miss=n.miss, burnin=burnin, n.sample=n.sample, thin=thin, MALA=MALA, n.beta.block=n.beta.block, list.block=list.block, prior.mean.beta=prior.mean.beta, prior.var.beta=prior.var.beta, prior.mean.alpha=prior.mean.alpha, prior.var.alpha=prior.var.alpha, prior.tau2=prior.tau2, verbose=verbose, chain="all")
stopCluster(compclust)
}else
{
stop("n.chains or n.cores are not positive integers.", call.=FALSE)
}
#### end timer
if(verbose)
{
cat("\nSummarising results.\n")
}else
{}
###################################
#### Summarise and save the results
###################################
if(n.chains==1)
{
#### If n.chains==1
## Compute the acceptance rates
accept.final <- rep(NA, 6)
names(accept.final) <- c("beta", "alpha", "phi", "delta", "rho.int", "rho.slo")
accept.final[1] <- 100 * results$accept[1] / results$accept[2]
accept.final[2] <- 100 * results$accept[3] / results$accept[4]
accept.final[3] <- 100 * results$accept[5] / results$accept[6]
accept.final[4] <- 100 * results$accept[7] / results$accept[8]
if(!fix.rho.int) accept.final[5] <- 100 * results$accept[9] / results$accept[10]
if(!fix.rho.slo) accept.final[6] <- 100 * results$accept[11] / results$accept[12]
## Compute the fitted deviance
mean.phi <- apply(results$samples.phi, 2, mean)
mean.delta <- apply(results$samples.delta, 2, mean)
mean.phi.mat <- matrix(rep(mean.phi, N), byrow=F, nrow=K)
delta.time.mat <- apply(time.mat, 2, "*", mean.delta)
mean.alpha <- mean(results$samples.alpha)
mean.beta <- apply(results$samples.beta,2,mean)
regression.mat <- matrix(X.standardised %*% mean.beta, nrow=K, ncol=N, byrow=FALSE)
lp.mean <- as.numeric(offset.mat + regression.mat + mean.phi.mat + delta.time.mat + mean.alpha * time.mat)
mean.prob <- exp(lp.mean) / (1 + exp(lp.mean))
fitted.mean <- trials * mean.prob
deviance.fitted <- -2 * sum(dbinom(x=Y, size=trials, prob=mean.prob, log=TRUE), na.rm=TRUE)
modelfit <- common.modelfit(results$samples.loglike, deviance.fitted)
## Create the fitted values and residuals
fitted.values <- apply(results$samples.fitted, 2, mean)
response.residuals <- as.numeric(Y) - fitted.values
pearson.residuals <- response.residuals /sqrt(fitted.values * (1 - mean.prob))
residuals <- data.frame(response=response.residuals, pearson=pearson.residuals)
## Transform the parameters back to the origianl covariate scale.
samples.beta.orig <- common.betatransform(results$samples.beta, X.indicator, X.mean, X.sd, p, FALSE)
## Create the samples object
if(fix.rho.int & fix.rho.slo)
{
samples.rhoext <- NA
}else if(fix.rho.int & !fix.rho.slo)
{
samples.rhoext <- results$samples.lambda
names(samples.rhoext) <- "rho.slo"
}else if(!fix.rho.int & fix.rho.slo)
{
samples.rhoext <- results$samples.rho
names(samples.rhoext) <- "rho.int"
}else
{
samples.rhoext <- cbind(results$samples.rho, results$samples.lambda)
colnames(samples.rhoext) <- c("rho.int", "rho.slo")
}
colnames(results$samples.tau2) <- c("tau2.int", "tau2.slo")
samples <- list(beta=mcmc(samples.beta.orig), alpha=mcmc(results$samples.alpha), phi=mcmc(results$samples.phi), delta=mcmc(results$samples.delta), tau2=mcmc(results$samples.tau2), rho=mcmc(samples.rhoext), fitted=mcmc(results$samples.fitted), Y=mcmc(results$samples.Y))
## Create a summary object
n.keep <- floor((n.sample - burnin)/thin)
summary.beta <- t(rbind(apply(samples$beta, 2, mean), apply(samples$beta, 2, quantile, c(0.025, 0.975))))
summary.beta <- cbind(summary.beta, rep(n.keep, p), rep(accept.final[names(accept.final)=="beta"],p), effectiveSize(samples$beta), geweke.diag(samples$beta)$z)
rownames(summary.beta) <- colnames(X)
colnames(summary.beta) <- c("Mean", "2.5%", "97.5%", "n.sample", "% accept", "n.effective", "Geweke.diag")
summary.tau2 <- cbind(apply(results$samples.tau2, 2, mean), t(apply(results$samples.tau2, 2, quantile, c(0.025, 0.975))), rep(n.keep, 2), rep(100, 2),
effectiveSize(samples$tau2), geweke.diag(samples$tau2)$z)
summary.alpha <- c(mean(results$samples.alpha), quantile(results$samples.alpha, c(0.025, 0.975)), n.keep, accept.final[names(accept.final)=="alpha"],
effectiveSize(samples$alpha), geweke.diag(samples$alpha)$z)
summary.combine <- rbind(summary.alpha, summary.tau2)
rownames(summary.combine)[1] <- "alpha"
summary.rho <- array(NA, c(2,7))
row.names(summary.rho) <- c("rho.int", "rho.slo")
if(!fix.rho.int)
{
summary.rho[1, 1:3] <- c(mean(results$samples.rho), quantile(results$samples.rho, c(0.025, 0.975)))
summary.rho[1, 4:7] <- c(n.keep, accept.final[names(accept.final)=="rho.int"], effectiveSize(results$samples.rho), geweke.diag(results$samples.rho)$z)
}else
{
summary.rho[1, 1:3] <- c(rho, rho, rho)
summary.rho[1, 4:7] <- rep(NA, 4)
}
if(!fix.rho.slo)
{
summary.rho[2, 1:3] <- c(mean(results$samples.lambda), quantile(results$samples.lambda, c(0.025, 0.975)))
summary.rho[2, 4:7] <- c(n.keep, accept.final[names(accept.final)=="rho.slo"], effectiveSize(results$samples.lambda), geweke.diag(results$samples.lambda)$z)
}else
{
summary.rho[2, 1:3] <- c(lambda, lambda, lambda)
summary.rho[2, 4:7] <- rep(NA, 4)
}
summary.results <- rbind(summary.beta, summary.combine, summary.rho)
summary.results[ , 1:3] <- round(summary.results[ , 1:3], 4)
summary.results[ , 4:7] <- round(summary.results[ , 4:7], 1)
}else
{
#### If n.chains > 1
## Compute the acceptance rates
accept.final <- rep(NA, 6)
names(accept.final) <- c("beta", "alpha", "phi", "delta", "rho.int", "rho.slo")
accept.temp <- lapply(results, function(l) l[["accept"]])
accept.temp2 <- do.call(what=rbind, args=accept.temp)
accept.final[1] <- 100 * sum(accept.temp2[ ,1]) / sum(accept.temp2[ ,2])
accept.final[2] <- 100 * sum(accept.temp2[ ,3]) / sum(accept.temp2[ ,4])
accept.final[3] <- 100 * sum(accept.temp2[ ,5]) / sum(accept.temp2[ ,6])
accept.final[4] <- 100 * sum(accept.temp2[ ,7]) / sum(accept.temp2[ ,8])
if(!fix.rho.int) accept.final[5] <- 100 * sum(accept.temp2[ ,9]) / sum(accept.temp2[ ,10])
if(!fix.rho.slo) accept.final[6] <- 100 * sum(accept.temp2[ ,11]) / sum(accept.temp2[ ,12])
## Extract the samples into separate matrix and list objects
samples.beta.list <- lapply(results, function(l) l[["samples.beta"]])
samples.beta.matrix <- do.call(what=rbind, args=samples.beta.list)
samples.phi.list <- lapply(results, function(l) l[["samples.phi"]])
samples.phi.matrix <- do.call(what=rbind, args=samples.phi.list)
samples.delta.list <- lapply(results, function(l) l[["samples.delta"]])
samples.delta.matrix <- do.call(what=rbind, args=samples.delta.list)
samples.alpha.list <- lapply(results, function(l) l[["samples.alpha"]])
samples.alpha.matrix <- do.call(what=rbind, args=samples.alpha.list)
if(!fix.rho.int)
{
samples.rho.list <- lapply(results, function(l) l[["samples.rho"]])
samples.rho.matrix <- do.call(what=rbind, args=samples.rho.list)
}
if(!fix.rho.slo)
{
samples.lambda.list <- lapply(results, function(l) l[["samples.lambda"]])
samples.lambda.matrix <- do.call(what=rbind, args=samples.lambda.list)
}
samples.tau2.list <- lapply(results, function(l) l[["samples.tau2"]])
samples.tau2.matrix <- do.call(what=rbind, args=samples.tau2.list)
samples.loglike.list <- lapply(results, function(l) l[["samples.loglike"]])
samples.loglike.matrix <- do.call(what=rbind, args=samples.loglike.list)
samples.fitted.list <- lapply(results, function(l) l[["samples.fitted"]])
samples.fitted.matrix <- do.call(what=rbind, args=samples.fitted.list)
if(n.miss>0) samples.Y.list <- lapply(results, function(l) l[["samples.Y"]])
## Compute the fitted deviance
mean.phi <- apply(samples.phi.matrix, 2, mean)
mean.delta <- apply(samples.delta.matrix, 2, mean)
mean.phi.mat <- matrix(rep(mean.phi, N), byrow=F, nrow=K)
delta.time.mat <- apply(time.mat, 2, "*", mean.delta)
mean.alpha <- mean(samples.alpha.matrix)
mean.beta <- apply(samples.beta.matrix,2,mean)
regression.mat <- matrix(X.standardised %*% mean.beta, nrow=K, ncol=N, byrow=FALSE)
lp.mean <- as.numeric(offset.mat + regression.mat + mean.phi.mat + delta.time.mat + mean.alpha * time.mat)
mean.prob <- exp(lp.mean) / (1 + exp(lp.mean))
fitted.mean <- trials * mean.prob
deviance.fitted <- -2 * sum(dbinom(x=Y, size=trials, prob=mean.prob, log=TRUE), na.rm=TRUE)
modelfit <- common.modelfit(samples.loglike.matrix, deviance.fitted)
## Create the fitted values and residuals
fitted.values <- apply(samples.fitted.matrix, 2, mean)
response.residuals <- as.numeric(Y) - fitted.values
pearson.residuals <- response.residuals /sqrt(fitted.values * (1 - mean.prob))
residuals <- data.frame(response=response.residuals, pearson=pearson.residuals)
## Transform the parameters back to the original covariate scale.
samples.beta.list <- samples.beta.list
for(j in 1:n.chains)
{
samples.beta.list[[j]] <- common.betatransform(samples.beta.list[[j]], X.indicator, X.mean, X.sd, p, FALSE)
}
samples.beta.matrix <- do.call(what=rbind, args=samples.beta.list)
## Create MCMC objects
beta.mcmc <- mcmc.list(lapply(samples.beta.list, mcmc))
alpha.mcmc <- mcmc.list(lapply(samples.alpha.list, mcmc))
phi.mcmc <- mcmc.list(lapply(samples.phi.list, mcmc))
delta.mcmc <- mcmc.list(lapply(samples.delta.list, mcmc))
fitted.mcmc <- mcmc.list(lapply(samples.fitted.list, mcmc))
for(j in 1:n.chains)
{
colnames(samples.tau2.list[[j]]) <- c("tau2.int", "tau2.slo")
}
tau2.mcmc <- mcmc.list(lapply(samples.tau2.list, mcmc))
if(n.miss>0)
{
Y.mcmc <- mcmc.list(lapply(samples.Y.list, mcmc))
}else
{
Y.mcmc <- NA
}
if(fix.rho.int & fix.rho.slo)
{
rhoext.mcmc <- NA
}else if(fix.rho.int & !fix.rho.slo)
{
for(j in 1:n.chains)
{
colnames(samples.lambda.list[[j]]) <- c("rho.slo")
}
rhoext.mcmc <- mcmc.list(lapply(samples.lambda.list, mcmc))
}else if(!fix.rho.int & fix.rho.slo)
{
for(j in 1:n.chains)
{
colnames(samples.rho.list[[j]]) <- c("rho.int")
}
rhoext.mcmc <- mcmc.list(lapply(samples.rho.list, mcmc))
}else
{
rho.temp <- as.list(rep(NA, n.chains))
for(j in 1:n.chains)
{
rho.temp[[j]] <- cbind(samples.rho.list[[j]], samples.lambda.list[[j]])
colnames(rho.temp[[j]]) <- c("rho.int", "rho.slo")
}
rhoext.mcmc <- mcmc.list(lapply(rho.temp, mcmc))
}
samples <- list(beta=beta.mcmc, alpha=alpha.mcmc, phi=phi.mcmc, delta=delta.mcmc, rho=rhoext.mcmc, tau2=tau2.mcmc, fitted=fitted.mcmc, Y=Y.mcmc)
## create a summary object
n.keep <- floor((n.sample - burnin)/thin) * n.chains
summary.beta <- t(rbind(apply(samples.beta.matrix, 2, mean), apply(samples.beta.matrix, 2, quantile, c(0.025, 0.975))))
summary.beta <- cbind(summary.beta, rep(n.keep, p), rep(accept.final[names(accept.final)=="beta"],p), effectiveSize(beta.mcmc), gelman.diag(beta.mcmc)$psrf[ ,2])
rownames(summary.beta) <- colnames(X)
colnames(summary.beta) <- c("Mean", "2.5%", "97.5%", "n.sample", "% accept", "n.effective", "PSRF (upper 95% CI)")
summary.tau2 <- cbind(apply(samples.tau2.matrix, 2, mean), t(apply(samples.tau2.matrix, 2, quantile, c(0.025, 0.975))), rep(n.keep, 2), rep(100, 2),
effectiveSize(tau2.mcmc), gelman.diag(tau2.mcmc)$psrf[ ,2])
summary.alpha <- c(mean(samples.alpha.matrix), quantile(samples.alpha.matrix, c(0.025, 0.975)), n.keep, accept.final[names(accept.final)=="alpha"],
effectiveSize(alpha.mcmc), gelman.diag(alpha.mcmc)$psrf[ ,2])
summary.combine <- rbind(summary.alpha, summary.tau2)
rownames(summary.combine)[1] <- "alpha"
summary.rho <- array(NA, c(2,7))
row.names(summary.rho) <- c("rho.int", "rho.slo")
if(!fix.rho.int)
{
temp <- mcmc.list(lapply(samples.rho.list, mcmc))
summary.rho[1, 1:3] <- c(mean(samples.rho.matrix), quantile(samples.rho.matrix, c(0.025, 0.975)))
summary.rho[1, 4:7] <- c(n.keep, accept.final[names(accept.final)=="rho.int"], effectiveSize(temp), gelman.diag(temp)$psrf[ ,2])
}else
{
summary.rho[1, 1:3] <- c(rho, rho, rho)
summary.rho[1, 4:7] <- rep(NA, 4)
}
if(!fix.rho.slo)
{
temp <- mcmc.list(lapply(samples.lambda.list, mcmc))
summary.rho[2, 1:3] <- c(mean(samples.lambda.matrix), quantile(samples.lambda.matrix, c(0.025, 0.975)))
summary.rho[2, 4:7] <- c(n.keep, accept.final[names(accept.final)=="rho.slo"], effectiveSize(temp), gelman.diag(temp)$psrf[ ,2])
}else
{
summary.rho[2, 1:3] <- c(lambda, lambda, lambda)
summary.rho[2, 4:7] <- rep(NA, 4)
}
summary.results <- rbind(summary.beta, summary.combine, summary.rho)
summary.results[ , 1:3] <- round(summary.results[ , 1:3], 4)
summary.results[ , 4:7] <- round(summary.results[ , 4:7], 1)
}
###################################
#### Compile and return the results
###################################
model.string <- c("Likelihood model - binomial (logit link function)", "\nLatent structure model - Spatially autocorrelated linear time trends\n")
n.total <- floor((n.sample - burnin) / thin) * n.chains
mcmc.info <- c(n.total, n.sample, burnin, thin, n.chains)
names(mcmc.info) <- c("Total samples", "n.sample", "burnin", "thin", "n.chains")
results.final <- 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, mcmc.info=mcmc.info, X=X)
class(results.final) <- "CARBayesST"
if(verbose)
{
b<-proc.time()
cat("Finished in ", round(b[3]-a[3], 1), "seconds.\n")
}else
{}
return(results.final)
}
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Defines functions binomial.CARlinear
binomial.CARlinear <- function(formula, data=NULL, trials, W, burnin, n.sample, thin=1, n.chains=1, n.cores=1, prior.mean.beta=NULL, prior.var.beta=NULL, prior.mean.alpha=NULL, prior.var.alpha=NULL, prior.tau2=NULL, rho.slo=NULL, rho.int=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, "binomial")
N.all <- 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$n.miss
#### Determine the number of spatial and temporal units
W.quants <- common.Wcheckformat.leroux(W)
K <- W.quants$n
N <- N.all / K
offset.mat <- matrix(offset, nrow=K, ncol=N, byrow=FALSE)
time <-(1:N - mean(1:N))/N
time.mat <- matrix(rep(time, K), byrow=TRUE, nrow=K)
#### 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)
#### Check the trials argument
if(sum(is.na(trials))>0) stop("the numbers of trials has missing 'NA' values.", call.=FALSE)
if(!is.numeric(trials)) stop("the numbers of trials has non-numeric values.", call.=FALSE)
int.check <- N.all-sum(ceiling(trials)==floor(trials))
if(int.check > 0) stop("the numbers of trials has non-integer values.", call.=FALSE)
if(min(trials)<=0) stop("the numbers of trials has zero or negative values.", call.=FALSE)
if(sum(Y>trials, na.rm=TRUE)>0) stop("the response variable has larger values that the numbers of trials.", call.=FALSE)
failures <- trials - Y
#### Check on the rho arguments
if(is.null(rho.int))
{
rho <- runif(1)
fix.rho.int <- FALSE
}else
{
rho <- rho.int
fix.rho.int <- TRUE
}
if(!is.numeric(rho)) stop("rho.int is fixed but is not numeric.", call.=FALSE)
if(rho<0 ) stop("rho.int is outside the range [0, 1].", call.=FALSE)
if(rho>1 ) stop("rho.int is outside the range [0, 1].", call.=FALSE)
if(is.null(rho.slo))
{
lambda <- runif(1)
fix.rho.slo <- FALSE
}else
{
lambda <- rho.slo
fix.rho.slo <- TRUE
}
if(!is.numeric(lambda)) stop("rho.slo is fixed but is not numeric.", call.=FALSE)
if(lambda<0 ) stop("rho.slo is outside the range [0, 1].", call.=FALSE)
if(lambda>1 ) stop("rho.slo is outside the range [0, 1].", 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.mean.alpha)) prior.mean.alpha <- rep(0, 1)
if(is.null(prior.var.alpha)) prior.var.alpha <- rep(100000, 1)
prior.beta.check(prior.mean.beta, prior.var.beta, p)
prior.var.check(prior.tau2)
if(length(prior.mean.alpha)!=1) stop("the prior mean for alpha is the wrong length.", call.=FALSE)
if(!is.numeric(prior.mean.alpha)) stop("the prior mean for alpha is not numeric.", call.=FALSE)
if(sum(is.na(prior.mean.alpha))!=0) stop("the prior mean for alpha has missing values.", call.=FALSE)
if(length(prior.var.alpha)!=1) stop("the prior variance for alpha is the wrong length.", call.=FALSE)
if(!is.numeric(prior.var.alpha)) stop("the prior variance for alpha is not numeric.", call.=FALSE)
if(sum(is.na(prior.var.alpha))!=0) stop("the prior variance for alpha has missing values.", call.=FALSE)
if(min(prior.var.alpha) <=0) stop("the prior variance for alpha has elements less than zero", call.=FALSE)
#### 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]])
}
#### MCMC quantities - burnin, n.sample, thin
common.burnin.nsample.thin.check(burnin, n.sample, thin)
########################
#### Run the MCMC chains
########################
if(n.chains==1)
{
#### Only 1 chain
results <- binomial.CARlinearMCMC(Y=Y, failures=failures, trials=trials, offset=offset, X.standardised=X.standardised, W=W, rho=rho, lambda=lambda, fix.rho.int=fix.rho.int, fix.rho.slo=fix.rho.slo, K=K, N=N, N.all=N.all, p=p, which.miss=which.miss, n.miss=n.miss, burnin=burnin, n.sample=n.sample, thin=thin, MALA=MALA, n.beta.block=n.beta.block, list.block=list.block, prior.mean.beta=prior.mean.beta, prior.var.beta=prior.var.beta, prior.mean.alpha=prior.mean.alpha, prior.var.alpha=prior.var.alpha, prior.tau2=prior.tau2, verbose=verbose, chain=1)
}else if(n.chains > 1 & ceiling(n.chains)==floor(n.chains) & n.cores==1)
{
#### Multiple chains in series
results <- as.list(rep(NA, n.chains))
for(i in 1:n.chains)
{
results[[i]] <- binomial.CARlinearMCMC(Y=Y, failures=failures, trials=trials, offset=offset, X.standardised=X.standardised, W=W, rho=rho, lambda=lambda, fix.rho.int=fix.rho.int, fix.rho.slo=fix.rho.slo, K=K, N=N, N.all=N.all, p=p, which.miss=which.miss, n.miss=n.miss, burnin=burnin, n.sample=n.sample, thin=thin, MALA=MALA, n.beta.block=n.beta.block, list.block=list.block, prior.mean.beta=prior.mean.beta, prior.var.beta=prior.var.beta, prior.mean.alpha=prior.mean.alpha, prior.var.alpha=prior.var.alpha, prior.tau2=prior.tau2, verbose=verbose, chain=i)
}
}else if(n.chains > 1 & ceiling(n.chains)==floor(n.chains) & n.cores>1 & ceiling(n.cores)==floor(n.cores))
{
#### Multiple chains in parallel
results <- as.list(rep(NA, n.chains))
if(verbose)
{
compclust <- makeCluster(n.cores, outfile="CARBayesSTprogress.txt")
cat("The current progress of the model fitting algorithm has been output to CARBayesSTprogress.txt in the working directory")
}else
{
compclust <- makeCluster(n.cores)
}
results <- clusterCall(compclust, fun=binomial.CARlinearMCMC, Y=Y, failures=failures, trials=trials, offset=offset, X.standardised=X.standardised, W=W, rho=rho, lambda=lambda, fix.rho.int=fix.rho.int, fix.rho.slo=fix.rho.slo, K=K, N=N, N.all=N.all, p=p, which.miss=which.miss, n.miss=n.miss, burnin=burnin, n.sample=n.sample, thin=thin, MALA=MALA, n.beta.block=n.beta.block, list.block=list.block, prior.mean.beta=prior.mean.beta, prior.var.beta=prior.var.beta, prior.mean.alpha=prior.mean.alpha, prior.var.alpha=prior.var.alpha, prior.tau2=prior.tau2, verbose=verbose, chain="all")
stopCluster(compclust)
}else
{
stop("n.chains or n.cores are not positive integers.", call.=FALSE)
}
#### end timer
if(verbose)
{
cat("\nSummarising results.\n")
}else
{}
###################################
#### Summarise and save the results
###################################
if(n.chains==1)
{
#### If n.chains==1
## Compute the acceptance rates
accept.final <- rep(NA, 6)
names(accept.final) <- c("beta", "alpha", "phi", "delta", "rho.int", "rho.slo")
accept.final[1] <- 100 * results$accept[1] / results$accept[2]
accept.final[2] <- 100 * results$accept[3] / results$accept[4]
accept.final[3] <- 100 * results$accept[5] / results$accept[6]
accept.final[4] <- 100 * results$accept[7] / results$accept[8]
if(!fix.rho.int) accept.final[5] <- 100 * results$accept[9] / results$accept[10]
if(!fix.rho.slo) accept.final[6] <- 100 * results$accept[11] / results$accept[12]
## Compute the fitted deviance
mean.phi <- apply(results$samples.phi, 2, mean)
mean.delta <- apply(results$samples.delta, 2, mean)
mean.phi.mat <- matrix(rep(mean.phi, N), byrow=F, nrow=K)
delta.time.mat <- apply(time.mat, 2, "*", mean.delta)
mean.alpha <- mean(results$samples.alpha)
mean.beta <- apply(results$samples.beta,2,mean)
regression.mat <- matrix(X.standardised %*% mean.beta, nrow=K, ncol=N, byrow=FALSE)
lp.mean <- as.numeric(offset.mat + regression.mat + mean.phi.mat + delta.time.mat + mean.alpha * time.mat)
mean.prob <- exp(lp.mean) / (1 + exp(lp.mean))
fitted.mean <- trials * mean.prob
deviance.fitted <- -2 * sum(dbinom(x=Y, size=trials, prob=mean.prob, log=TRUE), na.rm=TRUE)
modelfit <- common.modelfit(results$samples.loglike, deviance.fitted)
## Create the fitted values and residuals
fitted.values <- apply(results$samples.fitted, 2, mean)
response.residuals <- as.numeric(Y) - fitted.values
pearson.residuals <- response.residuals /sqrt(fitted.values * (1 - mean.prob))
residuals <- data.frame(response=response.residuals, pearson=pearson.residuals)
## Transform the parameters back to the origianl covariate scale.
samples.beta.orig <- common.betatransform(results$samples.beta, X.indicator, X.mean, X.sd, p, FALSE)
## Create the samples object
if(fix.rho.int & fix.rho.slo)
{
samples.rhoext <- NA
}else if(fix.rho.int & !fix.rho.slo)
{
samples.rhoext <- results$samples.lambda
names(samples.rhoext) <- "rho.slo"
}else if(!fix.rho.int & fix.rho.slo)
{
samples.rhoext <- results$samples.rho
names(samples.rhoext) <- "rho.int"
}else
{
samples.rhoext <- cbind(results$samples.rho, results$samples.lambda)
colnames(samples.rhoext) <- c("rho.int", "rho.slo")
}
colnames(results$samples.tau2) <- c("tau2.int", "tau2.slo")
samples <- list(beta=mcmc(samples.beta.orig), alpha=mcmc(results$samples.alpha), phi=mcmc(results$samples.phi), delta=mcmc(results$samples.delta), tau2=mcmc(results$samples.tau2), rho=mcmc(samples.rhoext), fitted=mcmc(results$samples.fitted), Y=mcmc(results$samples.Y))
## Create a summary object
n.keep <- floor((n.sample - burnin)/thin)
summary.beta <- t(rbind(apply(samples$beta, 2, mean), apply(samples$beta, 2, quantile, c(0.025, 0.975))))
summary.beta <- cbind(summary.beta, rep(n.keep, p), rep(accept.final[names(accept.final)=="beta"],p), effectiveSize(samples$beta), geweke.diag(samples$beta)$z)
rownames(summary.beta) <- colnames(X)
colnames(summary.beta) <- c("Mean", "2.5%", "97.5%", "n.sample", "% accept", "n.effective", "Geweke.diag")
summary.tau2 <- cbind(apply(results$samples.tau2, 2, mean), t(apply(results$samples.tau2, 2, quantile, c(0.025, 0.975))), rep(n.keep, 2), rep(100, 2),
effectiveSize(samples$tau2), geweke.diag(samples$tau2)$z)
summary.alpha <- c(mean(results$samples.alpha), quantile(results$samples.alpha, c(0.025, 0.975)), n.keep, accept.final[names(accept.final)=="alpha"],
effectiveSize(samples$alpha), geweke.diag(samples$alpha)$z)
summary.combine <- rbind(summary.alpha, summary.tau2)
rownames(summary.combine)[1] <- "alpha"
summary.rho <- array(NA, c(2,7))
row.names(summary.rho) <- c("rho.int", "rho.slo")
if(!fix.rho.int)
{
summary.rho[1, 1:3] <- c(mean(results$samples.rho), quantile(results$samples.rho, c(0.025, 0.975)))
summary.rho[1, 4:7] <- c(n.keep, accept.final[names(accept.final)=="rho.int"], effectiveSize(results$samples.rho), geweke.diag(results$samples.rho)$z)
}else
{
summary.rho[1, 1:3] <- c(rho, rho, rho)
summary.rho[1, 4:7] <- rep(NA, 4)
}
if(!fix.rho.slo)
{
summary.rho[2, 1:3] <- c(mean(results$samples.lambda), quantile(results$samples.lambda, c(0.025, 0.975)))
summary.rho[2, 4:7] <- c(n.keep, accept.final[names(accept.final)=="rho.slo"], effectiveSize(results$samples.lambda), geweke.diag(results$samples.lambda)$z)
}else
{
summary.rho[2, 1:3] <- c(lambda, lambda, lambda)
summary.rho[2, 4:7] <- rep(NA, 4)
}
summary.results <- rbind(summary.beta, summary.combine, summary.rho)
summary.results[ , 1:3] <- round(summary.results[ , 1:3], 4)
summary.results[ , 4:7] <- round(summary.results[ , 4:7], 1)
}else
{
#### If n.chains > 1
## Compute the acceptance rates
accept.final <- rep(NA, 6)
names(accept.final) <- c("beta", "alpha", "phi", "delta", "rho.int", "rho.slo")
accept.temp <- lapply(results, function(l) l[["accept"]])
accept.temp2 <- do.call(what=rbind, args=accept.temp)
accept.final[1] <- 100 * sum(accept.temp2[ ,1]) / sum(accept.temp2[ ,2])
accept.final[2] <- 100 * sum(accept.temp2[ ,3]) / sum(accept.temp2[ ,4])
accept.final[3] <- 100 * sum(accept.temp2[ ,5]) / sum(accept.temp2[ ,6])
accept.final[4] <- 100 * sum(accept.temp2[ ,7]) / sum(accept.temp2[ ,8])
if(!fix.rho.int) accept.final[5] <- 100 * sum(accept.temp2[ ,9]) / sum(accept.temp2[ ,10])
if(!fix.rho.slo) accept.final[6] <- 100 * sum(accept.temp2[ ,11]) / sum(accept.temp2[ ,12])
## Extract the samples into separate matrix and list objects
samples.beta.list <- lapply(results, function(l) l[["samples.beta"]])
samples.beta.matrix <- do.call(what=rbind, args=samples.beta.list)
samples.phi.list <- lapply(results, function(l) l[["samples.phi"]])
samples.phi.matrix <- do.call(what=rbind, args=samples.phi.list)
samples.delta.list <- lapply(results, function(l) l[["samples.delta"]])
samples.delta.matrix <- do.call(what=rbind, args=samples.delta.list)
samples.alpha.list <- lapply(results, function(l) l[["samples.alpha"]])
samples.alpha.matrix <- do.call(what=rbind, args=samples.alpha.list)
if(!fix.rho.int)
{
samples.rho.list <- lapply(results, function(l) l[["samples.rho"]])
samples.rho.matrix <- do.call(what=rbind, args=samples.rho.list)
}
if(!fix.rho.slo)
{
samples.lambda.list <- lapply(results, function(l) l[["samples.lambda"]])
samples.lambda.matrix <- do.call(what=rbind, args=samples.lambda.list)
}
samples.tau2.list <- lapply(results, function(l) l[["samples.tau2"]])
samples.tau2.matrix <- do.call(what=rbind, args=samples.tau2.list)
samples.loglike.list <- lapply(results, function(l) l[["samples.loglike"]])
samples.loglike.matrix <- do.call(what=rbind, args=samples.loglike.list)
samples.fitted.list <- lapply(results, function(l) l[["samples.fitted"]])
samples.fitted.matrix <- do.call(what=rbind, args=samples.fitted.list)
if(n.miss>0) samples.Y.list <- lapply(results, function(l) l[["samples.Y"]])
## Compute the fitted deviance
mean.phi <- apply(samples.phi.matrix, 2, mean)
mean.delta <- apply(samples.delta.matrix, 2, mean)
mean.phi.mat <- matrix(rep(mean.phi, N), byrow=F, nrow=K)
delta.time.mat <- apply(time.mat, 2, "*", mean.delta)
mean.alpha <- mean(samples.alpha.matrix)
mean.beta <- apply(samples.beta.matrix,2,mean)
regression.mat <- matrix(X.standardised %*% mean.beta, nrow=K, ncol=N, byrow=FALSE)
lp.mean <- as.numeric(offset.mat + regression.mat + mean.phi.mat + delta.time.mat + mean.alpha * time.mat)
mean.prob <- exp(lp.mean) / (1 + exp(lp.mean))
fitted.mean <- trials * mean.prob
deviance.fitted <- -2 * sum(dbinom(x=Y, size=trials, prob=mean.prob, log=TRUE), na.rm=TRUE)
modelfit <- common.modelfit(samples.loglike.matrix, deviance.fitted)
## Create the fitted values and residuals
fitted.values <- apply(samples.fitted.matrix, 2, mean)
response.residuals <- as.numeric(Y) - fitted.values
pearson.residuals <- response.residuals /sqrt(fitted.values * (1 - mean.prob))
residuals <- data.frame(response=response.residuals, pearson=pearson.residuals)
## Transform the parameters back to the original covariate scale.
samples.beta.list <- samples.beta.list
for(j in 1:n.chains)
{
samples.beta.list[[j]] <- common.betatransform(samples.beta.list[[j]], X.indicator, X.mean, X.sd, p, FALSE)
}
samples.beta.matrix <- do.call(what=rbind, args=samples.beta.list)
## Create MCMC objects
beta.mcmc <- mcmc.list(lapply(samples.beta.list, mcmc))
alpha.mcmc <- mcmc.list(lapply(samples.alpha.list, mcmc))
phi.mcmc <- mcmc.list(lapply(samples.phi.list, mcmc))
delta.mcmc <- mcmc.list(lapply(samples.delta.list, mcmc))
fitted.mcmc <- mcmc.list(lapply(samples.fitted.list, mcmc))
for(j in 1:n.chains)
{
colnames(samples.tau2.list[[j]]) <- c("tau2.int", "tau2.slo")
}
tau2.mcmc <- mcmc.list(lapply(samples.tau2.list, mcmc))
if(n.miss>0)
{
Y.mcmc <- mcmc.list(lapply(samples.Y.list, mcmc))
}else
{
Y.mcmc <- NA
}
if(fix.rho.int & fix.rho.slo)
{
rhoext.mcmc <- NA
}else if(fix.rho.int & !fix.rho.slo)
{
for(j in 1:n.chains)
{
colnames(samples.lambda.list[[j]]) <- c("rho.slo")
}
rhoext.mcmc <- mcmc.list(lapply(samples.lambda.list, mcmc))
}else if(!fix.rho.int & fix.rho.slo)
{
for(j in 1:n.chains)
{
colnames(samples.rho.list[[j]]) <- c("rho.int")
}
rhoext.mcmc <- mcmc.list(lapply(samples.rho.list, mcmc))
}else
{
rho.temp <- as.list(rep(NA, n.chains))
for(j in 1:n.chains)
{
rho.temp[[j]] <- cbind(samples.rho.list[[j]], samples.lambda.list[[j]])
colnames(rho.temp[[j]]) <- c("rho.int", "rho.slo")
}
rhoext.mcmc <- mcmc.list(lapply(rho.temp, mcmc))
}
samples <- list(beta=beta.mcmc, alpha=alpha.mcmc, phi=phi.mcmc, delta=delta.mcmc, rho=rhoext.mcmc, tau2=tau2.mcmc, fitted=fitted.mcmc, Y=Y.mcmc)
## create a summary object
n.keep <- floor((n.sample - burnin)/thin) * n.chains
summary.beta <- t(rbind(apply(samples.beta.matrix, 2, mean), apply(samples.beta.matrix, 2, quantile, c(0.025, 0.975))))
summary.beta <- cbind(summary.beta, rep(n.keep, p), rep(accept.final[names(accept.final)=="beta"],p), effectiveSize(beta.mcmc), gelman.diag(beta.mcmc)$psrf[ ,2])
rownames(summary.beta) <- colnames(X)
colnames(summary.beta) <- c("Mean", "2.5%", "97.5%", "n.sample", "% accept", "n.effective", "PSRF (upper 95% CI)")
summary.tau2 <- cbind(apply(samples.tau2.matrix, 2, mean), t(apply(samples.tau2.matrix, 2, quantile, c(0.025, 0.975))), rep(n.keep, 2), rep(100, 2),
effectiveSize(tau2.mcmc), gelman.diag(tau2.mcmc)$psrf[ ,2])
summary.alpha <- c(mean(samples.alpha.matrix), quantile(samples.alpha.matrix, c(0.025, 0.975)), n.keep, accept.final[names(accept.final)=="alpha"],
effectiveSize(alpha.mcmc), gelman.diag(alpha.mcmc)$psrf[ ,2])
summary.combine <- rbind(summary.alpha, summary.tau2)
rownames(summary.combine)[1] <- "alpha"
summary.rho <- array(NA, c(2,7))
row.names(summary.rho) <- c("rho.int", "rho.slo")
if(!fix.rho.int)
{
temp <- mcmc.list(lapply(samples.rho.list, mcmc))
summary.rho[1, 1:3] <- c(mean(samples.rho.matrix), quantile(samples.rho.matrix, c(0.025, 0.975)))
summary.rho[1, 4:7] <- c(n.keep, accept.final[names(accept.final)=="rho.int"], effectiveSize(temp), gelman.diag(temp)$psrf[ ,2])
}else
{
summary.rho[1, 1:3] <- c(rho, rho, rho)
summary.rho[1, 4:7] <- rep(NA, 4)
}
if(!fix.rho.slo)
{
temp <- mcmc.list(lapply(samples.lambda.list, mcmc))
summary.rho[2, 1:3] <- c(mean(samples.lambda.matrix), quantile(samples.lambda.matrix, c(0.025, 0.975)))
summary.rho[2, 4:7] <- c(n.keep, accept.final[names(accept.final)=="rho.slo"], effectiveSize(temp), gelman.diag(temp)$psrf[ ,2])
}else
{
summary.rho[2, 1:3] <- c(lambda, lambda, lambda)
summary.rho[2, 4:7] <- rep(NA, 4)
}
summary.results <- rbind(summary.beta, summary.combine, summary.rho)
summary.results[ , 1:3] <- round(summary.results[ , 1:3], 4)
summary.results[ , 4:7] <- round(summary.results[ , 4:7], 1)
}
###################################
#### Compile and return the results
###################################
model.string <- c("Likelihood model - binomial (logit link function)", "\nLatent structure model - Spatially autocorrelated linear time trends\n")
n.total <- floor((n.sample - burnin) / thin) * n.chains
mcmc.info <- c(n.total, n.sample, burnin, thin, n.chains)
names(mcmc.info) <- c("Total samples", "n.sample", "burnin", "thin", "n.chains")
results.final <- 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, mcmc.info=mcmc.info, X=X)
class(results.final) <- "CARBayesST"
if(verbose)
{
b<-proc.time()
cat("Finished in ", round(b[3]-a[3], 1), "seconds.\n")
}else
{}
return(results.final)
}
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