https://github.com/cran/CARBayes
Tip revision: 8d264fafc8006241da2236cc69cc2fbb6e425838 authored by Duncan Lee on 05 November 2013, 09:43:46 UTC
version 1.6
version 1.6
Tip revision: 8d264fa
binomial.iarCAR.R
binomial.iarCAR <-
function(formula, data=NULL, beta=NULL, phi=NULL, tau2=NULL, trials, W, burnin=0, n.sample=1000, thin=1, blocksize.beta=5, blocksize.phi=10, prior.mean.beta=NULL, prior.var.beta=NULL, prior.max.tau2=NULL)
{
##############################################
#### Format the arguments and check for errors
##############################################
#### Overall formula object
frame <- try(suppressWarnings(model.frame(formula, data=data, 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 and trials
## Create the response
Y <- model.response(frame)
## Check for errors
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-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(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)
if(sum(Y>trials)>0) stop("the response variable has larger values that the numbers of trials.", 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
dat <- cbind(Y, trials-Y)
if(is.null(beta)) beta <- glm(dat~X.standardised-1, offset=offset, family=binomial)$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 phi
if(is.null(phi)) phi <- rnorm(n=n, mean=rep(0,n), sd=rep(0.1, n))
if(length(phi)!= n) stop("phi is the wrong length.", call.=FALSE)
if(sum(is.na(phi))>0) stop("phi has missing 'NA' values.", call.=FALSE)
if(!is.numeric(phi)) stop("phi has non-numeric values.", call.=FALSE)
## Random effects variance tau2
if(is.null(tau2)) tau2 <- runif(1)
if(length(tau2)!= 1) stop("tau2 is the wrong length.", call.=FALSE)
if(sum(is.na(tau2))>0) stop("tau2 has missing 'NA' values.", call.=FALSE)
if(!is.numeric(tau2)) stop("tau2 has non-numeric values.", call.=FALSE)
if(tau2 <= 0) stop("tau2 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(thin)) stop("thin is not a number", call.=FALSE)
if(thin <= 0) stop("thin is less than or equal to zero.", 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.phi)) stop("blocksize.phi is not a number", call.=FALSE)
if(blocksize.phi <= 0) stop("blocksize.phi is less than or equal to zero", call.=FALSE)
if(!(floor(blocksize.phi)==ceiling(blocksize.phi))) stop("blocksize.phi has non-integer values.", call.=FALSE)
## Compute the blocking structure for beta
if(blocksize.beta >= p)
{
n.beta.block <- 1
beta.beg <- 1
beta.fin <- p
}else
{
n.standard <- 1 + floor((p-blocksize.beta) / blocksize.beta)
remainder <- p - n.standard * blocksize.beta
if(remainder==0)
{
beta.beg <- c(1,seq((blocksize.beta+1), p, blocksize.beta))
beta.fin <- c(blocksize.beta, seq((blocksize.beta+blocksize.beta), p, blocksize.beta))
n.beta.block <- length(beta.beg)
}else
{
beta.beg <- c(1, seq((blocksize.beta+1), p, blocksize.beta))
beta.fin <- c(blocksize.beta, seq((blocksize.beta+blocksize.beta), p, blocksize.beta), p)
n.beta.block <- length(beta.beg)
}
}
## Compute the blocking structure for phi
if(blocksize.phi >= n)
{
n.phi.block <- 1
phi.beg <- 1
phi.fin <- n
}else
{
n.standard <- 1 + floor((n-blocksize.phi) / blocksize.phi)
remainder <- n - (n.standard * blocksize.phi)
if(remainder==0)
{
phi.beg <- c(1,seq((blocksize.phi+1), n, blocksize.phi))
phi.fin <- c(blocksize.phi, seq((blocksize.phi+blocksize.phi), n, blocksize.phi))
n.phi.block <- length(phi.beg)
}else if(remainder==1)
{
phi.beg <- c(1, seq((blocksize.phi), n, blocksize.phi))
phi.fin <- c(blocksize.phi-1, seq((blocksize.phi+blocksize.phi-1), n, blocksize.phi), n)
n.phi.block <- length(phi.beg)
}else
{
phi.beg <- c(1, seq((blocksize.phi+1), n, blocksize.phi))
phi.fin <- c(blocksize.phi, seq((blocksize.phi+blocksize.phi), n, blocksize.phi), n)
n.phi.block <- length(phi.beg)
}
}
## Matrices to store samples
n.keep <- floor((n.sample - burnin)/thin)
samples.beta <- array(NA, c(n.keep, p))
samples.phi <- array(NA, c(n.keep, n))
samples.tau2 <- array(NA, c(n.keep, 1))
samples.deviance <- array(NA, c(n.keep, 1))
## Metropolis quantities
accept.all <- rep(0,4)
accept <- accept.all
proposal.sd.beta <- 0.01
proposal.sd.phi <- 0.1
proposal.corr.beta <- solve(t(X.standardised) %*% X.standardised)
chol.proposal.corr.beta <- chol(proposal.corr.beta)
tau2.posterior.shape <- 0.5 * n - 1
#### Priors
## Put in default priors
## N(0, 100) for beta
## U(0, 10) for tau2
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.tau2)) prior.max.tau2 <- 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.tau2)!=1) stop("the maximum prior value for tau2 is the wrong length.", call.=FALSE)
if(!is.numeric(prior.max.tau2)) stop("the maximum prior value for tau2 is not numeric.", call.=FALSE)
if(sum(is.na(prior.max.tau2))!=0) stop("the maximum prior value for tau2 has missing values.", call.=FALSE)
if(min(prior.max.tau2) <=0) stop("the maximum prior value for tau2 is less than zero", call.=FALSE)
#### CAR quantities
if(!is.matrix(W)) stop("W is not a matrix.", call.=FALSE)
if(nrow(W)!= n) stop("W has the wrong number of rows.", call.=FALSE)
if(ncol(W)!= n) stop("W has the wrong number of columns.", call.=FALSE)
if(sum(is.na(W))>0) stop("W has missing 'NA' values.", call.=FALSE)
if(!is.numeric(W)) stop("W has non-numeric values.", call.=FALSE)
if(min(W)<0) stop("W has negative elements.", call.=FALSE)
if(sum(W!=t(W))>0) stop("W is not symmetric.", call.=FALSE)
n.neighbours <- as.numeric(apply(W, 1, sum))
Q <- diag(n.neighbours) - W
## quantities required in updating phi
block.mean.part <- as.list(rep(0,n.phi.block))
block.var.chol <- as.list(rep(0,n.phi.block))
for(r in 1:n.phi.block)
{
Q.current <- Q[phi.beg[r]:phi.fin[r], phi.beg[r]:phi.fin[r]]
block.var <- chol2inv(chol(Q.current))
block.mean.part[[r]] <- - block.var %*% Q[phi.beg[r]:phi.fin[r], -(phi.beg[r]:phi.fin[r])]
block.var.chol[[r]] <- chol(block.var)
}
#### Other quantities needed for the MCMC algorithm
failures <- trials - Y
###########################
#### Run the Bayesian model
###########################
for(j in 1:n.sample)
{
####################
## Sample from beta
####################
proposal <- beta + (sqrt(proposal.sd.beta)* t(chol.proposal.corr.beta)) %*% rnorm(p)
proposal.beta <- beta
phi.offset <- phi + offset
for(r in 1:n.beta.block)
{
## Propose a value
proposal.beta[beta.beg[r]:beta.fin[r]] <- proposal[beta.beg[r]:beta.fin[r]]
logit.proposal <- as.numeric(X.standardised %*% proposal.beta) + phi.offset
logit.current <- as.numeric(X.standardised %*% beta) + phi.offset
prob.proposal <- exp(logit.proposal) / (1 + exp(logit.proposal))
prob.current <- exp(logit.current) / (1 + exp(logit.current))
## Calculate the acceptance probability
prob1 <- sum(Y * (log(prob.proposal) - log(prob.current)) + failures * (log(1-prob.proposal) - log(1-prob.current)))
prob2 <- sum(((beta[beta.beg[r]:beta.fin[r]] - prior.mean.beta[beta.beg[r]:beta.fin[r]])^2 - (proposal.beta[beta.beg[r]:beta.fin[r]] - prior.mean.beta[beta.beg[r]:beta.fin[r]])^2) / prior.var.beta[beta.beg[r]:beta.fin[r]])
prob <- exp(prob1 + prob2)
## Accept or reject the value
if(prob > runif(1))
{
beta[beta.beg[r]:beta.fin[r]] <- proposal.beta[beta.beg[r]:beta.fin[r]]
accept[1] <- accept[1] + 1
}else
{
proposal.beta[beta.beg[r]:beta.fin[r]] <- beta[beta.beg[r]:beta.fin[r]]
}
}
accept[2] <- accept[2] + n.beta.block
####################
## Sample from phi
####################
Q.temp <- Q / tau2
beta.offset <- as.numeric(X.standardised %*% beta) + offset
b <- rnorm(n)
for(r in 1:n.phi.block)
{
## Propose a value
Q.current <- Q.temp[phi.beg[r]:phi.fin[r], phi.beg[r]:phi.fin[r]]
block.mean <- block.mean.part[[r]] %*% phi[-(phi.beg[r]:phi.fin[r])]
proposal.phi <- phi[phi.beg[r]:phi.fin[r]] + (sqrt(proposal.sd.phi) * sqrt(tau2) * t(block.var.chol[[r]])) %*% b[phi.beg[r]:phi.fin[r]]
logit.proposal <- beta.offset[phi.beg[r]:phi.fin[r]] + proposal.phi
logit.current <- beta.offset[phi.beg[r]:phi.fin[r]] + phi[phi.beg[r]:phi.fin[r]]
prob.proposal <- exp(logit.proposal) / (1 + exp(logit.proposal))
prob.current <- exp(logit.current) / (1 + exp(logit.current))
## Calculate the acceptance probability
prob1 <- sum(Y[phi.beg[r]:phi.fin[r]] * (log(prob.proposal) - log(prob.current)) + failures[phi.beg[r]:phi.fin[r]] * (log(1-prob.proposal) - log(1-prob.current)))
prob2 <- t(phi[phi.beg[r]:phi.fin[r]] - block.mean) %*% Q.current %*% (phi[phi.beg[r]:phi.fin[r]] - block.mean) - t(proposal.phi - block.mean) %*% Q.current %*% (proposal.phi - block.mean)
prob <- exp(prob1 + 0.5 * prob2)
## Accept or reject the value
if(prob > runif(1))
{
phi[phi.beg[r]:phi.fin[r]] <- proposal.phi
accept[3] <- accept[3] + 1
}else
{
}
}
accept[4] <- accept[4] + n.phi.block
phi <- phi - mean(phi)
##################
## Sample from tau2
##################
tau2.posterior.scale <- 0.5 * sum(phi * (Q %*% phi))
tau2 <- 1/rtrunc(n=1, spec="gamma", a=(1/prior.max.tau2), b=Inf, shape=tau2.posterior.shape, scale=(1/tau2.posterior.scale))
#########################
## Calculate the deviance
#########################
logit <- as.numeric(X.standardised %*% beta) + phi + offset
prob <- exp(logit) / (1 + exp(logit))
deviance <- -2 * sum(dbinom(x=Y, size=trials, prob=prob, log=TRUE))
###################
## Save the results
###################
if(j > burnin & (j-burnin)%%thin==0)
{
ele <- (j - burnin) / thin
samples.beta[ele, ] <- beta
samples.phi[ele, ] <- phi
samples.tau2[ele, ] <- tau2
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.phi <- 100 * accept[3] / accept[4]
accept.all <- accept.all + accept
accept <- c(0,0,0,0)
#### beta tuning parameter
if(accept.beta > 70)
{
proposal.sd.beta <- 2 * proposal.sd.beta
}else if(accept.beta < 50)
{
proposal.sd.beta <- 0.5 * proposal.sd.beta
}else
{
}
#### phi tuning parameter
if(accept.phi > 40)
{
proposal.sd.phi <- 2 * proposal.sd.phi
}else if(accept.phi < 30)
{
proposal.sd.phi <- 0.5 * proposal.sd.phi
}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
###################################
## Acceptance rates
accept.beta <- 100 * accept.all[1] / accept.all[2]
accept.phi <- 100 * accept.all[3] / accept.all[4]
accept.tau2 <- 100
accept.final <- c(accept.beta, accept.phi, accept.tau2)
names(accept.final) <- c("beta", "phi", "tau2")
## Deviance information criterion (DIC)
median.beta <- apply(samples.beta, 2, median)
median.phi <- apply(samples.phi, 2, median)
median.logit <- as.numeric(X.standardised %*% median.beta) + median.phi + offset
median.prob <- exp(median.logit) / (1 + exp(median.logit))
fitted.median <- trials * median.prob
deviance.fitted <- -2 * sum(dbinom(x=Y, size=trials, prob=median.prob, log=TRUE))
p.d <- mean(samples.deviance) - deviance.fitted
DIC <- 2 * mean(samples.deviance) - deviance.fitted
#### transform the parameters back to the origianl covariate scale.
samples.beta.orig <- samples.beta
number.cts <- sum(X.indicator==1)
if(number.cts>0)
{
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
{
}
}
}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.keep, p),rep(accept.beta, p))
rownames(summary.beta) <- colnames(X)
colnames(summary.beta) <- c("Median", "2.5%", "97.5%", "n.sample", "% accept")
summary.hyper <- quantile(samples.tau2, c(0.5, 0.025, 0.975))
summary.hyper <- c(summary.hyper, n.keep, accept.tau2)
summary.results <- rbind(summary.beta, summary.hyper)
rownames(summary.results)[nrow(summary.results)] <- "tau2"
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.phi, 2, mean)
random.effects[ ,2] <- apply(samples.phi, 2, sd)
random.effects[ ,3:5] <- t(apply(samples.phi, 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))
residuals <- array(NA, c(n, 5))
colnames(fitted.values) <- c("Mean", "Sd", "Median", "2.5%", "97.5%")
colnames(residuals) <- c("Mean", "Sd", "Median", "2.5%", "97.5%")
fitted.temp <- array(NA, c(nrow(samples.beta), n))
residuals.temp <- array(NA, c(nrow(samples.beta), n))
for(i in 1:nrow(samples.beta))
{
temp.logit <- X.standardised %*% samples.beta[i, ] + samples.phi[i, ] + offset
temp <- trials * exp(temp.logit) / (1 + exp(temp.logit))
fitted.temp[i, ] <- temp
residuals.temp[i, ] <- Y - temp
}
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)
residuals[ ,1] <- apply(residuals.temp, 2, mean)
residuals[ ,2] <- apply(residuals.temp, 2, sd)
residuals[ ,3:5] <- t(apply(residuals.temp, 2, quantile, c(0.5, 0.025, 0.975)))
residuals <- round(residuals, 4)
## Compile and return the results
model.string <- c("Likelihood model - Binomial (logit link function)", "\nRandom effects model - Intrinsic CAR\n")
samples <- list(beta=samples.beta.orig, phi=mcmc(samples.phi), tau2=mcmc(samples.tau2))
results <- list(formula=formula, samples=samples, fitted.values=fitted.values, random.effects=random.effects, residuals=residuals, W.summary=W, DIC=DIC, p.d=p.d, summary.results=summary.results, model=model.string, accept=accept.final)
class(results) <- "carbayes"
return(results)
}