https://github.com/cran/CARBayes
Tip revision: d6d500cbf5e3654e95ab3ca6f54d5f298cbedc43 authored by Duncan Lee on 27 August 2012, 10:50:23 UTC
version 1.1
version 1.1
Tip revision: d6d500c
poisson.independent.R
poisson.independent <-
function(formula, beta=NULL, theta=NULL, sigma2=NULL, burnin=0, n.sample=1000, blocksize.beta=5, blocksize.theta=10, prior.mean.beta=NULL, prior.var.beta=NULL, prior.max.sigma2=NULL)
{
##############################################
#### Format the arguments and check for errors
##############################################
#### Overall formula object
frame <- try(suppressWarnings(model.frame(formula, na.action=na.pass)), silent=TRUE)
if(class(frame)=="try-error") stop("the formula inputted contains an error, e.g the variables may be different lengths.", call.=FALSE)
#### Design matrix
## Create the matrix
X <- try(suppressWarnings(model.matrix(object=attr(frame, "terms"), data=frame)), silent=TRUE)
if(class(X)=="try-error") stop("the covariate matrix contains inappropriate values.", call.=FALSE)
if(sum(is.na(X))>0) stop("the covariate matrix contains missing 'NA' values.", call.=FALSE)
n <- nrow(X)
p <- ncol(X)
## Check for linearly related columns
cor.X <- suppressWarnings(cor(X))
diag(cor.X) <- 0
if(max(cor.X, na.rm=TRUE)==1) stop("the covariate matrix has two exactly linearly related columns.", call.=FALSE)
if(min(cor.X, na.rm=TRUE)==-1) stop("the covariate matrix has two exactly linearly related columns.", call.=FALSE)
if(p>1)
{
if(sort(apply(X, 2, sd))[2]==0) stop("the covariate matrix has two intercept terms.", call.=FALSE)
}else
{
}
## Standardise the matrix
X.standardised <- X
X.sd <- apply(X, 2, sd)
X.mean <- apply(X, 2, mean)
X.indicator <- rep(NA, p) # To determine which parameter estimates to transform back
for(j in 1:p)
{
if(length(table(X[ ,j]))>2)
{
X.indicator[j] <- 1
X.standardised[ ,j] <- (X[ ,j] - mean(X[ ,j])) / sd(X[ ,j])
}else if(length(table(X[ ,j]))==1)
{
X.indicator[j] <- 2
}else
{
X.indicator[j] <- 0
}
}
#### Response variable
## Create the response
Y <- model.response(frame)
## Check for errors
if(sum(is.na(Y))>0) stop("the response has missing 'NA' values.", call.=FALSE)
if(!is.numeric(Y)) stop("the response variable has non-numeric values.", call.=FALSE)
int.check <- n-sum(ceiling(Y)==floor(Y))
if(int.check > 0) stop("the respons variable has non-integer values.", call.=FALSE)
if(min(Y)<0) stop("the response variable has negative values.", call.=FALSE)
#### Offset variable
## Create the offset
offset <- try(model.offset(frame), silent=TRUE)
## Check for errors
if(class(offset)=="try-error") stop("the offset is not numeric.", call.=FALSE)
if(is.null(offset)) offset <- rep(0,n)
if(sum(is.na(offset))>0) stop("the offset has missing 'NA' values.", call.=FALSE)
if(!is.numeric(offset)) stop("the offset variable has non-numeric values.", call.=FALSE)
#### Initial parameter values
## Regression parameters beta
if(is.null(beta)) beta <- glm(Y~X.standardised-1, offset=offset, family=poisson)$coefficients
if(length(beta)!= p) stop("beta is the wrong length.", call.=FALSE)
if(sum(is.na(beta))>0) stop("beta has missing 'NA' values.", call.=FALSE)
if(!is.numeric(beta)) stop("beta has non-numeric values.", call.=FALSE)
## Random effects theta
if(is.null(theta)) theta <- rnorm(n=n, mean=rep(0,n), sd=rep(0.1, n))
if(length(theta)!= n) stop("theta is the wrong length.", call.=FALSE)
if(sum(is.na(theta))>0) stop("theta has missing 'NA' values.", call.=FALSE)
if(!is.numeric(theta)) stop("theta has non-numeric values.", call.=FALSE)
## Random effects variance sigma2
if(is.null(sigma2)) sigma2 <- runif(1)
if(length(sigma2)!= 1) stop("sigma2 is the wrong length.", call.=FALSE)
if(sum(is.na(sigma2))>0) stop("sigma2 has missing 'NA' values.", call.=FALSE)
if(!is.numeric(sigma2)) stop("sigma2 has non-numeric values.", call.=FALSE)
if(sigma2 <= 0) stop("sigma2 is negative or zero.", call.=FALSE)
#### MCMC quantities
## Checks
if(!is.numeric(burnin)) stop("burn-in is not a number", call.=FALSE)
if(!is.numeric(n.sample)) stop("n.sample is not a number", call.=FALSE)
if(n.sample <= 0) stop("n.sample is less than or equal to zero.", call.=FALSE)
if(burnin < 0) stop("burn-in is less than zero.", call.=FALSE)
if(n.sample <= burnin) stop("Burn-in is greater than n.sample.", call.=FALSE)
if(!is.numeric(blocksize.beta)) stop("blocksize.beta is not a number", call.=FALSE)
if(blocksize.beta <= 0) stop("blocksize.beta is less than or equal to zero", call.=FALSE)
if(!(floor(blocksize.beta)==ceiling(blocksize.beta))) stop("blocksize.beta has non-integer values.", call.=FALSE)
if(!is.numeric(blocksize.theta)) stop("blocksize.theta is not a number", call.=FALSE)
if(blocksize.theta <= 0) stop("blocksize.theta is less than or equal to zero", call.=FALSE)
if(!(floor(blocksize.theta)==ceiling(blocksize.theta))) stop("blocksize.theta has non-integer values.", call.=FALSE)
## Matrices to store samples
samples.beta <- array(NA, c((n.sample-burnin), p))
samples.theta <- array(NA, c((n.sample-burnin), n))
samples.sigma2 <- array(NA, c((n.sample-burnin), 1))
samples.deviance <- array(NA, c((n.sample-burnin), 1))
## Metropolis quantities
accept.all <- rep(0,4)
accept <- accept.all
proposal.sd.beta <- 0.01
proposal.sd.theta <- 0.01
proposal.corr.beta <- solve(t(X.standardised) %*% X.standardised)
#### Priors
## Put in default priors
## N(0, 100) for beta
## U(0, 10) for sigma2
if(is.null(prior.mean.beta)) prior.mean.beta <- rep(0, p)
if(is.null(prior.var.beta)) prior.var.beta <- rep(1000, p)
if(is.null(prior.max.sigma2)) prior.max.sigma2 <- 1000
## Checks
if(length(prior.mean.beta)!=p) stop("the vector of prior means for beta is the wrong length.", call.=FALSE)
if(!is.numeric(prior.mean.beta)) stop("the vector of prior means for beta is not numeric.", call.=FALSE)
if(sum(is.na(prior.mean.beta))!=0) stop("the vector of prior means for beta has missing values.", call.=FALSE)
if(length(prior.var.beta)!=p) stop("the vector of prior variances for beta is the wrong length.", call.=FALSE)
if(!is.numeric(prior.var.beta)) stop("the vector of prior variances for beta is not numeric.", call.=FALSE)
if(sum(is.na(prior.var.beta))!=0) stop("the vector of prior variances for beta has missing values.", call.=FALSE)
if(min(prior.var.beta) <=0) stop("the vector of prior variances has elements less than zero", call.=FALSE)
if(length(prior.max.sigma2)!=1) stop("the maximum prior value for sigma2 is the wrong length.", call.=FALSE)
if(!is.numeric(prior.max.sigma2)) stop("the maximum prior value for sigma2 is not numeric.", call.=FALSE)
if(sum(is.na(prior.max.sigma2))!=0) stop("the maximum prior value for sigma2 has missing values.", call.=FALSE)
if(min(prior.max.sigma2) <=0) stop("the maximum prior value for sigma2 is less than zero", call.=FALSE)
###########################
#### Run the Bayesian model
###########################
for(j in 1:n.sample)
{
####################
## Sample from beta
####################
#### Create the blocking structure
if(blocksize.beta >= p)
{
n.block <- 1
beg <- 1
fin <- p
}else
{
init <- sample(1:blocksize.beta, 1)
n.standard <- floor((p-init) / blocksize.beta)
remainder <- p - (init + n.standard * blocksize.beta)
if(n.standard==0)
{
beg <- c(1,(init+1))
fin <- c(init,p)
}else if(remainder==0)
{
beg <- c(1,seq((init+1), p, blocksize.beta))
fin <- c(init, seq((init+blocksize.beta), p, blocksize.beta))
}else
{
beg <- c(1, seq((init+1), p, blocksize.beta))
fin <- c(init, seq((init+blocksize.beta), p, blocksize.beta), p)
}
n.block <- length(beg)
}
#### Update the parameters in blocks
proposal.beta <- beta
for(r in 1:n.block)
{
## Propose a value
n.current <- length(beg[r]:fin[r])
proposal.beta[beg[r]:fin[r]] <- mvrnorm(n=1, mu=beta[beg[r]:fin[r]], Sigma=(proposal.sd.beta * proposal.corr.beta[beg[r]:fin[r], beg[r]:fin[r]]))
fitted.proposal <- exp(as.numeric(X.standardised %*% proposal.beta) + theta + offset)
fitted.current <- exp(as.numeric(X.standardised %*% beta) + theta + offset)
## Calculate the acceptance probability
prob1 <- sum(Y * (log(fitted.proposal) - log(fitted.current)) + fitted.current - fitted.proposal)
prob2 <- sum(((beta[beg[r]:fin[r]] - prior.mean.beta[beg[r]:fin[r]])^2 - (proposal.beta[beg[r]:fin[r]] - prior.mean.beta[beg[r]:fin[r]])^2) / (2 * prior.var.beta[beg[r]:fin[r]]))
prob <- exp(prob1 + prob2)
## Accept or reject the value
if(prob > runif(1))
{
beta <- proposal.beta
accept[1] <- accept[1] + 1
accept[2] <- accept[2] + 1
}else
{
proposal.beta <- beta
accept[2] <- accept[2] + 1
}
}
####################
## Sample from theta
####################
#### Create the blocking structure
if(blocksize.theta >= n)
{
n.block <- 1
beg <- 1
fin <- n
}else
{
init <- sample(1:blocksize.theta, 1)
n.standard <- floor((n-init) / blocksize.theta)
remainder <- n - (init + n.standard * blocksize.theta)
if(n.standard==0)
{
beg <- c(1,(init+1))
fin <- c(init,n)
}else if(remainder==0)
{
beg <- c(1,seq((init+1), n, blocksize.theta))
fin <- c(init, seq((init+blocksize.theta), n, blocksize.theta))
}else
{
beg <- c(1, seq((init+1), n, blocksize.theta))
fin <- c(init, seq((init+blocksize.theta), n, blocksize.theta), n)
}
n.block <- length(beg)
}
#### Update the parameters in blocks
proposal.theta <- theta
beta.offset <- X.standardised %*% beta + offset
for(r in 1:n.block)
{
## Propose a value
n.current <- length(beg[r]:fin[r])
proposal.theta[beg[r]:fin[r]] <- rnorm(n=n.current, mean=theta[beg[r]:fin[r]], sd=rep(proposal.sd.theta, n.current))
fitted.proposal <- exp(beta.offset[beg[r]:fin[r]] + proposal.theta[beg[r]:fin[r]])
fitted.current <- exp(beta.offset[beg[r]:fin[r]] + theta[beg[r]:fin[r]])
## Calculate the acceptance probability
prob1 <- sum(Y[beg[r]:fin[r]] * (log(fitted.proposal) - log(fitted.current)) + fitted.current - fitted.proposal)
prob2 <- sum(theta[beg[r]:fin[r]]^2 - proposal.theta[beg[r]:fin[r]]^2) / (2 * sigma2)
prob <- exp(prob1 + prob2)
## Accept or reject the value
if(prob > runif(1))
{
theta[beg[r]:fin[r]] <- proposal.theta[beg[r]:fin[r]]
accept[3] <- accept[3] + 1
accept[4] <- accept[4] + 1
}else
{
proposal.theta[beg[r]:fin[r]] <- theta[beg[r]:fin[r]]
accept[4] <- accept[4] + 1
}
}
theta <- theta - mean(theta)
####################
## Sample from sigma2
####################
sigma2 <- rinvgamma(n=1, shape=(0.5*n-1), scale=(0.5*sum(theta^2)))
while(sigma2 > prior.max.sigma2)
{
sigma2 <- rinvgamma(n=1, shape=(0.5*n-1), scale=(0.5*sum(theta^2)))
}
#########################
## Calculate the deviance
#########################
fitted <- exp(as.numeric(X.standardised %*% beta) + theta + offset)
deviance <- -2 * sum(Y * log(fitted) - fitted - lfactorial(Y))
###################
## Save the results
###################
if(j > burnin)
{
ele <- j - burnin
samples.beta[ele, ] <- beta
samples.theta[ele, ] <- theta
samples.sigma2[ele, ] <- sigma2
samples.deviance[ele, ] <- deviance
}else
{
}
########################################
## Self tune the acceptance probabilties
########################################
k <- j/100
if(ceiling(k)==floor(k))
{
#### Determine the acceptance probabilities
accept.beta <- 100 * accept[1] / accept[2]
accept.theta <- 100 * accept[3] / accept[4]
accept.all <- accept.all + accept
accept <- c(0,0,0,0)
#### beta tuning parameter
if(accept.beta > 40)
{
proposal.sd.beta <- 2 * proposal.sd.beta
}else if(accept.beta < 30)
{
proposal.sd.beta <- 0.5 * proposal.sd.beta
}else
{
}
#### theta tuning parameter
if(accept.theta > 40)
{
proposal.sd.theta <- 2 * proposal.sd.theta
}else if(accept.theta < 30)
{
proposal.sd.theta <- 0.5 * proposal.sd.theta
}else
{
}
}else
{
}
#######################################
#### Print out the number of iterations
#######################################
k <- j/1000
if(ceiling(k)==floor(k))
{
cat("Completed ",j, " samples\n")
flush.console()
}else
{
}
}
###################################
#### Summarise and save the results
###################################
## Deviance information criterion (DIC)
median.beta <- apply(samples.beta, 2, median)
median.theta <- apply(samples.theta, 2, median)
fitted.median <- exp(X.standardised %*% median.beta + median.theta + offset)
deviance.fitted <- -2 * sum(Y * log(fitted.median) - fitted.median - lfactorial(Y))
p.d <- mean(samples.deviance) - deviance.fitted
DIC <- 2 * mean(samples.deviance) - deviance.fitted
residuals <- Y - fitted.median
#### transform the parameters back to the origianl covariate scale.
samples.beta.orig <- samples.beta
for(r in 1:p)
{
if(X.indicator[r]==1)
{
samples.beta.orig[ ,r] <- samples.beta[ ,r] / X.sd[r]
}else if(X.indicator[r]==2 & p>1)
{
X.transformed <- which(X.indicator==1)
samples.temp <- as.matrix(samples.beta[ ,X.transformed])
for(s in 1:length(X.transformed))
{
samples.temp[ ,s] <- samples.temp[ ,s] * X.mean[X.transformed[s]] / X.sd[X.transformed[s]]
}
intercept.adjustment <- apply(samples.temp, 1,sum)
samples.beta.orig[ ,r] <- samples.beta[ ,r] - intercept.adjustment
}else
{
}
}
#### 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.sample-burnin), p), as.numeric(100 * (1-rejectionRate(samples.beta.orig))))
rownames(summary.beta) <- colnames(X)
colnames(summary.beta) <- c("Median", "2.5%", "97.5%", "n.sample", "% accept")
summary.hyper <- quantile(samples.sigma2, c(0.5, 0.025, 0.975))
summary.hyper <- c(summary.hyper, (n.sample-burnin), as.numeric(100 * (1-rejectionRate(mcmc(samples.sigma2)))))
summary.results <- rbind(summary.beta, summary.hyper)
rownames(summary.results)[nrow(summary.results)] <- "sigma2"
summary.results[ , 1:3] <- round(summary.results[ , 1:3], 4)
summary.results[ , 4:5] <- round(summary.results[ , 4:5], 1)
#### Create the random effects summary
random.effects <- array(NA, c(n, 5))
colnames(random.effects) <- c("Mean", "Sd", "Median", "2.5%", "97.5%")
random.effects[ ,1] <- apply(samples.theta, 2, mean)
random.effects[ ,2] <- apply(samples.theta, 2, sd)
random.effects[ ,3:5] <- t(apply(samples.theta, 2, quantile, c(0.5, 0.025, 0.975)))
random.effects <- round(random.effects, 4)
#### Create the Fitted values
fitted.values <- array(NA, c(n, 5))
colnames(fitted.values) <- c("Mean", "Sd", "Median", "2.5%", "97.5%")
fitted.temp <- array(NA, c(nrow(samples.beta), n))
for(i in 1:nrow(samples.beta))
{
fitted.temp[i, ] <- exp(X.standardised %*% samples.beta[i, ] + samples.theta[i, ] + offset)
}
fitted.values[ ,1] <- apply(fitted.temp, 2, mean)
fitted.values[ ,2] <- apply(fitted.temp, 2, sd)
fitted.values[ ,3:5] <- t(apply(fitted.temp, 2, quantile, c(0.5, 0.025, 0.975)))
fitted.values <- round(fitted.values, 4)
#### Print a summary of the results to the screen
cat("\n#################\n")
cat("#### Model fitted\n")
cat("#################\n\n")
cat("Likelihood model - Poisson (log link function) \n")
cat("Random effects model - Independent\n")
cat("Regression equation - ")
print(formula)
cat("\n\n############\n")
cat("#### Results\n")
cat("############\n\n")
cat("Posterior quantiles and acceptance rates\n\n")
print(summary.results)
cat("\n\n")
cat("Acceptance rate for the random effects is ", round(100 * accept.all[3] / accept.all[4],1), "%","\n\n", sep="")
cat("DIC = ", DIC, " ", "p.d = ", p.d, "\n")
## Compile and return the results
results <- list(formula=formula, samples.beta=samples.beta.orig, samples.theta=mcmc(samples.theta), samples.sigma2=mcmc(samples.sigma2), fitted.values=fitted.values, random.effects=random.effects, residuals=residuals, DIC=DIC, p.d=p.d, summary.results=summary.results)
return(results)
}