R/gaussian.glmMCMC.R

In CARBayes: Spatial Generalised Linear Mixed Models for Areal Unit Data

gaussian.glmMCMC <- function(Y, offset, X.standardised, K, p, which.miss, n.miss, burnin, n.sample, thin, prior.mean.beta, prior.var.beta, prior.nu2, verbose, chain)
{
# Rcpp::sourceCpp("src/CARBayes.cpp")   
# source("R/common.functions.R")
##########################################
#### Generate the initial parameter values
##########################################
#### Generate initial values for each chain
mod.glm <- glm(Y~X.standardised-1, offset=offset, family="quasipoisson")
beta.mean <- mod.glm$coefficients
beta.sd <- 10 * sqrt(diag(summary(mod.glm)$cov.scaled))
beta <- rnorm(n=length(beta.mean), mean=beta.mean, sd=beta.sd)

mod.glm <- lm(Y~X.standardised-1, offset=offset)
beta.mean <- mod.glm$coefficients
beta.sd <- sqrt(diag(summary(mod.glm)$cov.unscaled)) * summary(mod.glm)$sigma
beta <- rnorm(n=length(beta.mean), mean=beta.mean, sd=beta.sd)
res.temp <- Y - X.standardised %*% beta.mean - offset
nu2 <- var(as.numeric(res.temp), na.rm=TRUE)


   
###################################################################
#### Compute the fitted values based on the current parameter values
####################################################################   
fitted <- as.numeric(X.standardised %*% beta) + offset
Y.DA <- Y

    
   
########################################    
#### Set up the MCMC model run quantities    
#########################################
#### Metropolis quantities
nu2.posterior.shape <- prior.nu2[1] + 0.5*K

    
#### Beta update quantities
data.precision.beta <- t(X.standardised) %*% X.standardised
    if(length(prior.var.beta)==1)
    {
    prior.precision.beta <- 1 / prior.var.beta
    }else
    {
    prior.precision.beta <- solve(diag(prior.var.beta))
    }



#### Matrices to store samples   
n.keep <- floor((n.sample - burnin)/thin)
samples.beta <- array(NA, c(n.keep, p))
samples.nu2 <- array(NA, c(n.keep, 1))
samples.loglike <- array(NA, c(n.keep, K))
samples.fitted <- array(NA, c(n.keep, K))
    if(n.miss>0) samples.Y <- array(NA, c(n.keep, n.miss))


#### Start timer
    if(verbose)
    {
    cat("\nMarkov chain", chain,  "- generating", n.keep, "post burnin and thinned samples.\n", sep = " ")
    progressBar <- txtProgressBar(style = 3)
    percentage.points<-round((1:100/100)*n.sample)
    }else
    {
    percentage.points<-round((1:100/100)*n.sample)     
    }
   


######################
#### Run an MCMC chain
######################
    for(j in 1:n.sample)
    {
    ####################################
    ## Sample from Y - data augmentation
    ####################################
        if(n.miss>0)
        {
        Y.DA[which.miss==0] <- rnorm(n=n.miss, mean=fitted[which.miss==0], sd=sqrt(nu2))    
        }else
        {}
        
        
        
    ####################
    ## Sample from beta
    ####################
    fc.precision <- prior.precision.beta + data.precision.beta / nu2
    fc.var <- solve(fc.precision)
    beta.offset <- as.numeric(Y.DA - offset)
    beta.offset2 <- t(X.standardised) %*% beta.offset / nu2 + prior.precision.beta %*% prior.mean.beta
    fc.mean <- fc.var %*% beta.offset2
    chol.var <- t(chol(fc.var))
    beta <- fc.mean + chol.var %*% rnorm(p)        
        
        
        
    ##################
    ## Sample from nu2
    ##################
    fitted.current <-  as.numeric(X.standardised %*% beta) + offset
    nu2.posterior.scale <- prior.nu2[2] + 0.5 * sum((Y.DA - fitted.current)^2)
    nu2 <- 1 / rgamma(1, nu2.posterior.shape, scale=(1/nu2.posterior.scale))    

    
        
    #########################
    ## Calculate the deviance
    #########################
    fitted <- as.numeric(X.standardised %*% beta) + offset
    loglike <- dnorm(Y, mean = fitted, sd = rep(sqrt(nu2),K), log=TRUE)
        
        
        
    ###################
    ## Save the results
    ###################
        if(j > burnin & (j-burnin)%%thin==0)
        {
        ele <- (j - burnin) / thin
        samples.beta[ele, ] <- beta
        samples.nu2[ele, ] <- nu2
        samples.loglike[ele, ] <- loglike
        samples.fitted[ele, ] <- fitted
            if(n.miss>0) samples.Y[ele, ] <- Y.DA[which.miss==0]
        }else
        {}

        
        
    ################################       
    ## print progress to the console
    ################################
        if(j %in% percentage.points & verbose)
        {
        setTxtProgressBar(progressBar, j/n.sample)
        }
    }
    
    
##### end timer
    if(verbose)
    {
    close(progressBar)
    }else
    {}



############################################
#### Return the results to the main function
############################################
#### Compile the results
    if(n.miss==0) samples.Y = NA
chain.results <- list(samples.beta=samples.beta, samples.nu2=samples.nu2, samples.loglike=samples.loglike, samples.fitted=samples.fitted,
                    samples.Y=samples.Y)

#### Return the results
return(chain.results)
}