Nothing
gaussian.MVCARar1 <- function(formula, data=NULL, W, burnin, n.sample, thin=1, n.chains=1, n.cores=1, prior.mean.beta=NULL, prior.var.beta=NULL, prior.nu2=NULL, prior.Sigma.df=NULL, prior.Sigma.scale=NULL, rho.S=NULL, rho.T=NULL, verbose=TRUE)
{
##############################################
#### Format the arguments and check for errors
##############################################
#### Verbose
a <- common.verbose(verbose)
#### Frame object
frame.results <- common.frame.MVST(formula, data, "gaussian")
NK <- 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$Y
N.all <- length(Y)
J <- ncol(Y)
which.miss <- frame.results$which.miss
n.miss <- N.all - sum(which.miss)
#### W matrix
if(!is.matrix(W)) stop("W is not a matrix.", call.=FALSE)
W.quants <- common.Wcheckformat.leroux(W)
K <- W.quants$n
N <- NK / K
if(ceiling(N)!= floor(N)) stop("The number of data points in Y divided by the number of rows in W is not a whole number.", call.=FALSE)
#### Create a missing list
if(n.miss>0)
{
miss.locator <- array(NA, c(n.miss, 2))
colnames(miss.locator) <- c("row", "column")
locations <- which(which.miss==0)
miss.locator[ ,1] <- ceiling(locations/J)
miss.locator[ ,2] <- locations - (miss.locator[ ,1]-1) * J
}else
{
miss.locator <- NA
}
#### Check on the rho arguments
if(is.null(rho.S))
{
rho <- runif(1)
fix.rho.S <- FALSE
}else
{
rho <- rho.S
fix.rho.S <- TRUE
}
if(!is.numeric(rho)) stop("rho.S is fixed but is not numeric.", call.=FALSE)
if(rho<0 ) stop("rho.S is outside the range [0, 1].", call.=FALSE)
if(rho>1 ) stop("rho.S is outside the range [0, 1].", call.=FALSE)
if(is.null(rho.T))
{
alpha <- runif(1)
fix.rho.T <- FALSE
}else
{
alpha <- rho.T
fix.rho.T <- TRUE
}
if(!is.numeric(alpha)) stop("rho.T is fixed but is not numeric.", call.=FALSE)
if(length(alpha)!=1) stop("rho.T is fixed but is not of length 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.Sigma.df)) prior.Sigma.df <- 2
if(is.null(prior.Sigma.scale)) prior.Sigma.scale <- rep(100000, J)
if(is.null(prior.nu2)) prior.nu2 <- c(1, 0.01)
prior.beta.check(prior.mean.beta, prior.var.beta, p)
prior.var.check(prior.nu2)
if(!is.numeric(prior.Sigma.scale)) stop("prior.Sigma.scale has non-numeric values.", call.=FALSE)
if(sum(is.na(prior.Sigma.scale))!=0) stop("prior.Sigma.scale has missing values.", call.=FALSE)
#### 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 <- gaussian.MVCARar1MCMC(Y=Y, offset=offset, X.standardised=X.standardised, W=W, rho=rho, alpha=alpha, fix.rho.S=fix.rho.S, fix.rho.T=fix.rho.T, K=K, N=N, NK=NK, J=J, N.all=N.all, p=p, miss.locator=miss.locator, n.miss=n.miss, burnin=burnin, n.sample=n.sample, thin=thin, prior.mean.beta=prior.mean.beta, prior.var.beta=prior.var.beta, prior.nu2=prior.nu2, prior.Sigma.df=prior.Sigma.df, prior.Sigma.scale=prior.Sigma.scale, 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]] <- gaussian.MVCARar1MCMC(Y=Y, offset=offset, X.standardised=X.standardised, W=W, rho=rho, alpha=alpha, fix.rho.S=fix.rho.S, fix.rho.T=fix.rho.T, K=K, N=N, NK=NK, J=J, N.all=N.all, p=p, miss.locator=miss.locator, n.miss=n.miss, burnin=burnin, n.sample=n.sample, thin=thin, prior.mean.beta=prior.mean.beta, prior.var.beta=prior.var.beta, prior.nu2=prior.nu2, prior.Sigma.df=prior.Sigma.df, prior.Sigma.scale=prior.Sigma.scale, 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=gaussian.MVCARar1MCMC, Y=Y, offset=offset, X.standardised=X.standardised, W=W, rho=rho, alpha=alpha, fix.rho.S=fix.rho.S, fix.rho.T=fix.rho.T, K=K, N=N, NK=NK, J=J, N.all=N.all, p=p, miss.locator=miss.locator, n.miss=n.miss, burnin=burnin, n.sample=n.sample, thin=thin, prior.mean.beta=prior.mean.beta, prior.var.beta=prior.var.beta, prior.nu2=prior.nu2, prior.Sigma.df=prior.Sigma.df, prior.Sigma.scale=prior.Sigma.scale, 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", "phi", "rho.S", "rho.T", "nu2", "Sigma")
accept.final[1] <- 100
accept.final[2] <- 100 * results$accept[1] / results$accept[2]
if(!fix.rho.S) accept.final[3] <- 100 * results$accept[3] / results$accept[4]
if(!fix.rho.T) accept.final[4] <- 100
accept.final[5] <- 100
accept.final[6] <- 100
## Compute the fitted deviance
mean.beta <- matrix(apply(results$samples.beta, 2, mean), nrow=p, ncol=J, byrow=F)
mean.phi <- matrix(apply(results$samples.phi, 2, mean), nrow=NK, ncol=J, byrow=T)
fitted.mean <- X.standardised %*% mean.beta + mean.phi + offset
nu2.mean <- apply(results$samples.nu2,2,mean)
deviance.fitted <- -2 * sum(dnorm(as.numeric(t(Y)), mean = as.numeric(t(fitted.mean)), sd=rep(sqrt(nu2.mean), K*N), log = TRUE), na.rm=TRUE)
modelfit <- common.modelfit(results$samples.loglike, deviance.fitted)
## Create the fitted values and residuals
fitted.values <- matrix(apply(results$samples.fitted, 2, mean), nrow=NK, ncol=J, byrow=T)
response.residuals <- Y - fitted.values
nu.mat <- matrix(rep(sqrt(nu2.mean), N*K), nrow=N*K, byrow=T)
pearson.residuals <- response.residuals / nu.mat
residuals <- list(response=response.residuals, pearson=pearson.residuals)
## Transform the parameters back to the original covariate scale
samples.beta.orig <- results$samples.beta
for(r in 1:J)
{
samples.beta.orig[ ,((r-1)*p+1):(r*p)] <- common.betatransform(results$samples.beta[ ,((r-1)*p+1):(r*p) ], X.indicator, X.mean, X.sd, p, FALSE)
}
## Create the samples object
if(fix.rho.S & fix.rho.T)
{
samples.rhoext <- NA
}else if(fix.rho.S & !fix.rho.T)
{
samples.rhoext <- results$samples.alpha
colnames(samples.rhoext) <- c("rho.T")
}else if(!fix.rho.S & fix.rho.T)
{
samples.rhoext <- results$samples.rho
names(samples.rhoext) <- "rho.S"
}else
{
samples.rhoext <- cbind(results$samples.rho, results$samples.alpha)
colnames(samples.rhoext) <- c("rho.S", "rho.T")
}
samples <- list(beta=mcmc(samples.beta.orig), phi=mcmc(results$samples.phi), nu2=mcmc(results$samples.nu2), Sigma=results$samples.Sigma, rho=mcmc(samples.rhoext), fitted=mcmc(results$samples.fitted), Y=mcmc(results$samples.Y))
## Create a summary object
n.keep <- floor((n.sample - burnin)/thin)
summary.beta <- t(rbind(apply(samples.beta.orig, 2, mean), apply(samples.beta.orig, 2, quantile, c(0.025, 0.975))))
summary.beta <- cbind(summary.beta, rep(n.keep, p), rep(accept.final[names(accept.final)=="beta"],p), effectiveSize(samples.beta.orig), geweke.diag(samples.beta.orig)$z)
col.name <- rep(NA, p*(J-1))
if(is.null(colnames(Y)))
{
for(r in 1:J)
{
col.name[((r-1)*p+1):(r*p)] <- paste("Variable ", r, " - ", colnames(X), sep="")
}
}else
{
for(r in 1:J)
{
col.name[((r-1)*p+1):(r*p)] <- paste(colnames(Y)[r], " - ", colnames(X), sep="")
}
}
rownames(summary.beta) <- col.name
colnames(summary.beta) <- c("Mean", "2.5%", "97.5%", "n.sample", "% accept", "n.effective", "Geweke.diag")
summary.hyper <- array(NA, c((2*J+2) ,7))
for(r in 1:J)
{
summary.hyper[r, 1] <- mean(results$samples.nu2[ ,r])
summary.hyper[r, 2:3] <- quantile(results$samples.nu2[ ,r], c(0.025, 0.975))
summary.hyper[r, 4] <- n.keep
summary.hyper[r, 5] <- 100
summary.hyper[r, 6] <- effectiveSize(results$samples.nu2[ ,r])
summary.hyper[r, 7] <- geweke.diag(results$samples.nu2[ ,r])$z
summary.hyper[r+J, 1] <- mean(results$samples.Sigma[ ,r,r])
summary.hyper[r+J, 2:3] <- quantile(results$samples.Sigma[ ,r,r], c(0.025, 0.975))
summary.hyper[r+J, 4] <- n.keep
summary.hyper[r+J, 5] <- 100
summary.hyper[r+J, 6] <- effectiveSize(results$samples.Sigma[ ,r,r])
summary.hyper[r+J, 7] <- geweke.diag(results$samples.Sigma[ ,r,r])$z
}
if(!fix.rho.S)
{
summary.hyper[(2*J+1), 1:3] <- c(mean(results$samples.rho), quantile(results$samples.rho, c(0.025, 0.975)))
summary.hyper[(2*J+1), 4:5] <- c(n.keep, accept.final[names(accept.final)=="rho.S"])
summary.hyper[(2*J+1), 6:7] <- c(effectiveSize(results$samples.rho), geweke.diag(results$samples.rho)$z)
}else
{
summary.hyper[(2*J+1), 1:3] <- c(rho, rho, rho)
summary.hyper[(2*J+1), 4:5] <- rep(NA, 2)
summary.hyper[(2*J+1), 6:7] <- rep(NA, 2)
}
if(!fix.rho.T)
{
summary.hyper[(2*J+2), 1:3] <- c(mean(results$samples.alpha), quantile(results$samples.alpha, c(0.025, 0.975)))
summary.hyper[(2*J+2), 4:5] <- c(n.keep, accept.final[names(accept.final)=="rho.T"])
summary.hyper[(2*J+2), 6:7] <- c(effectiveSize(results$samples.alpha), geweke.diag(results$samples.alpha)$z)
}else
{
summary.hyper[(2*J+2), 1:3] <- c(alpha, alpha, alpha)
summary.hyper[(2*J+2), 4:5] <- rep(NA, 2)
summary.hyper[(2*J+2), 6:7] <- rep(NA, 2)
}
summary.results <- rbind(summary.beta, summary.hyper)
rownames(summary.results)[((J*p)+1): nrow(summary.results)] <- c(paste(rep("nu2",J), 1:J, sep=""), paste(rep("Sigma",J), 1:J, 1:J, sep=""), "rho.S", "rho.T")
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", "phi", "rho.S", "rho.T", "nu2", "Sigma")
accept.final[1] <- 100
accept.final[5] <- 100
accept.final[6] <- 100
accept.temp <- lapply(results, function(l) l[["accept"]])
accept.temp2 <- do.call(what=rbind, args=accept.temp)
accept.final[2] <- 100 * sum(accept.temp2[ ,1]) / sum(accept.temp2[ ,2])
if(!fix.rho.S) accept.final[3] <- 100 * sum(accept.temp2[ ,3]) / sum(accept.temp2[ ,4])
if(!fix.rho.T) accept.final[4] <- 100
## 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.nu2.list <- lapply(results, function(l) l[["samples.nu2"]])
samples.nu2.matrix <- do.call(what=rbind, args=samples.nu2.list)
if(!fix.rho.S)
{
samples.rho.list <- lapply(results, function(l) l[["samples.rho"]])
samples.rho.matrix <- do.call(what=rbind, args=samples.rho.list)
}
if(!fix.rho.T)
{
samples.alpha.list <- lapply(results, function(l) l[["samples.alpha"]])
samples.alpha.matrix <- do.call(what=rbind, args=samples.alpha.list)
}
samples.Sigma.list <- lapply(results, function(l) l[["samples.Sigma"]])
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.beta <- matrix(apply(samples.beta.matrix, 2, mean), nrow=p, ncol=J, byrow=F)
mean.phi <- matrix(apply(samples.phi.matrix, 2, mean), nrow=NK, ncol=J, byrow=T)
fitted.mean <- X.standardised %*% mean.beta + mean.phi + offset
nu2.mean <- apply(samples.nu2.matrix,2,mean)
deviance.fitted <- -2 * sum(dnorm(as.numeric(t(Y)), mean = as.numeric(t(fitted.mean)), sd=rep(sqrt(nu2.mean), K*N), log = TRUE), na.rm=TRUE)
modelfit <- common.modelfit(samples.loglike.matrix, deviance.fitted)
## Create the fitted values and residuals
fitted.values <- matrix(apply(samples.fitted.matrix, 2, mean), nrow=NK, ncol=J, byrow=T)
response.residuals <- Y - fitted.values
nu.mat <- matrix(rep(sqrt(nu2.mean), N*K), nrow=N*K, byrow=T)
pearson.residuals <- response.residuals / nu.mat
residuals <- list(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)
{
for(r in 1:J)
{
samples.beta.list[[j]][ ,((r-1)*p+1):(r*p)] <- common.betatransform(samples.beta.list[[j]][ ,((r-1)*p+1):(r*p) ], 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))
phi.mcmc <- mcmc.list(lapply(samples.phi.list, mcmc))
nu2.mcmc <- mcmc.list(lapply(samples.nu2.list, mcmc))
fitted.mcmc <- mcmc.list(lapply(samples.fitted.list, mcmc))
if(n.miss>0)
{
Y.mcmc <- mcmc.list(lapply(samples.Y.list, mcmc))
}else
{
Y.mcmc <- NA
}
if(fix.rho.S & fix.rho.T)
{
rhoext.mcmc <- NA
}else if(fix.rho.S & !fix.rho.T)
{
for(j in 1:n.chains)
{
colnames(samples.alpha.list[[j]]) <- c("rho.T")
}
rhoext.mcmc <- mcmc.list(lapply(samples.alpha.list, mcmc))
}else if(!fix.rho.S & fix.rho.T)
{
for(j in 1:n.chains)
{
colnames(samples.rho.list[[j]]) <- c("rho.S")
}
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.alpha.list[[j]])
colnames(rho.temp[[j]]) <- c("rho.S", "rho.T")
}
rhoext.mcmc <- mcmc.list(lapply(rho.temp, mcmc))
}
samples <- list(beta=beta.mcmc, phi=phi.mcmc, nu2=nu2.mcmc, rho=rhoext.mcmc, Sigma=samples.Sigma.list, 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)$psrf[ ,2])
col.name <- rep(NA, p*(J-1))
if(is.null(colnames(Y)))
{
for(r in 1:J)
{
col.name[((r-1)*p+1):(r*p)] <- paste("Variable ", r, " - ", colnames(X), sep="")
}
}else
{
for(r in 1:J)
{
col.name[((r-1)*p+1):(r*p)] <- paste(colnames(Y)[r], " - ", colnames(X), sep="")
}
}
rownames(summary.beta) <- col.name
colnames(summary.beta) <- c("Mean", "2.5%", "97.5%", "n.sample", "% accept", "n.effective", "PSRF (upper 95% CI)")
summary.hyper <- array(NA, c((2*J+2) ,7))
for(r in 1:J)
{
temp <- NA
temp2 <- as.list(rep(NA, n.chains))
for(v in 1:n.chains)
{
temp <- c(temp, samples.Sigma.list[[v]][ ,r,r])
temp2[[v]] <- mcmc(samples.Sigma.list[[v]][ ,r,r])
}
temp <- temp[-1]
summary.hyper[r, 1] <- mean(samples.nu2.matrix[ ,r])
summary.hyper[r, 2:3] <- quantile(samples.nu2.matrix[ ,r], c(0.025, 0.975))
summary.hyper[r, 4] <- n.keep
summary.hyper[r, 5] <- 100
summary.hyper[r, 6] <- effectiveSize(nu2.mcmc)[r]
summary.hyper[r, 7] <- (gelman.diag(nu2.mcmc)$psrf[ ,2])[r]
summary.hyper[r+J, 1] <- mean(temp)
summary.hyper[r+J, 2:3] <- quantile(temp, c(0.025, 0.975))
summary.hyper[r+J, 4] <- n.keep
summary.hyper[r+J, 5] <- 100
summary.hyper[r+J, 6] <- effectiveSize(mcmc.list(temp2))
summary.hyper[r+J, 7] <- gelman.diag(mcmc.list(temp2))$psrf[ ,2]
}
if(!fix.rho.S)
{
temp <- mcmc.list(lapply(samples.rho.list, mcmc))
summary.hyper[(2*J+1), 1:3] <- c(mean(samples.rho.matrix), quantile(samples.rho.matrix, c(0.025, 0.975)))
summary.hyper[(2*J+1), 4:5] <- c(n.keep, accept.final[names(accept.final)=="rho.S"])
summary.hyper[(2*J+1), 6:7] <- c(effectiveSize(temp), gelman.diag(temp)$psrf[ ,2])
}else
{
summary.hyper[(2*J+1), 1:3] <- c(rho, rho, rho)
summary.hyper[(2*J+1), 4:5] <- rep(NA, 2)
summary.hyper[(2*J+1), 6:7] <- rep(NA, 2)
}
if(!fix.rho.T)
{
temp <- mcmc.list(lapply(samples.alpha.list, mcmc))
summary.hyper[(2*J+2), 1:3] <- c(mean(samples.alpha.matrix), quantile(samples.alpha.matrix, c(0.025, 0.975)))
summary.hyper[(2*J+2), 4:5] <- c(n.keep, accept.final[names(accept.final)=="rho.T"])
summary.hyper[(2*J+2), 6:7] <- c(effectiveSize(temp), gelman.diag(temp)$psrf[ ,2])
}else
{
summary.hyper[(2*J+2), 1:3] <- c(alpha, alpha, alpha)
summary.hyper[(2*J+2), 4:5] <- rep(NA, 2)
summary.hyper[(2*J+2), 6:7] <- rep(NA, 2)
}
summary.results <- rbind(summary.beta, summary.hyper)
rownames(summary.results)[((J*p)+1): nrow(summary.results)] <- c(paste(rep("nu2",J), 1:J, sep=""), paste(rep("Sigma",J), 1:J, 1:J, sep=""), "rho.S", "rho.T")
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 - Gaussian (identity link function)", "\nRandom effects model - Multivariate Autoregressive order 1 CAR model\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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