R/binomial.bymCARMCMC.R

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

binomial.bymCARMCMC <- function(Y, failures, trials, offset, X.standardised, W, K, p, which.miss, n.miss, burnin, n.sample, thin, MALA, n.beta.block, list.block, prior.mean.beta, prior.var.beta, prior.tau2, prior.sigma2, verbose, chain)
{
# Rcpp::sourceCpp("src/CARBayes.cpp")   
# source("R/common.functions.R")
# library(spdep)
# library(truncnorm)    
#     
#     
##########################################
#### Generate the initial parameter values
##########################################
#### Generate initial values for each chain
dat <- cbind(Y, failures)
mod.glm <- glm(dat~X.standardised-1, offset=offset, family="quasibinomial")
beta.mean <- mod.glm$coefficients
beta.sd <- sqrt(diag(summary(mod.glm)$cov.scaled))
beta <- rnorm(n=length(beta.mean), mean=beta.mean, sd=beta.sd)
theta.hat <- Y / trials
theta.hat[theta.hat==0] <- 0.01
theta.hat[theta.hat==1] <- 0.99
res.temp <- log(theta.hat / (1 - theta.hat)) - X.standardised %*% beta.mean - offset
res.sd <- sd(res.temp, na.rm=TRUE)/5
phi <- rnorm(n=K, mean=rep(0,K), sd=res.sd)
tau2 <- var(phi) / 10
theta <- rnorm(n=K, mean=rep(0,K), sd=res.sd)
sigma2 <- var(theta) / 10


   
###################################################################
#### Compute the fitted values based on the current parameter values
####################################################################
lp <- as.numeric(X.standardised %*% beta) + phi + theta + offset
prob <- exp(lp)  / (1 + exp(lp))
fitted <- trials * prob
Y.DA <- Y
failures.DA <- trials - Y.DA
    
   
########################################    
#### Set up the MCMC model run quantities    
#########################################
#### Matrices to store samples
n.keep <- floor((n.sample - burnin)/thin)
samples.beta <- array(NA, c(n.keep, p))
samples.re <- array(NA, c(n.keep, K))
samples.tau2 <- array(NA, c(n.keep, 1))
samples.sigma2 <- 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))


## Metropolis quantities
accept <- rep(0,6)
proposal.sd.beta <- 0.01
proposal.sd.phi <- 0.1
proposal.sd.theta <- 0.1
sigma2.posterior.shape <- prior.sigma2[1] + 0.5 * K
tau2.posterior.shape <- prior.tau2[1] + 0.5 * K



##################################
#### Set up the spatial quantities
##################################
#### CAR quantities
W.quants <- common.Wcheckformat(W)
W <- W.quants$W
W.triplet <- W.quants$W.triplet
n.triplet <- W.quants$n.triplet
W.triplet.sum <- W.quants$W.triplet.sum
n.neighbours <- W.quants$n.neighbours 
W.begfin <- W.quants$W.begfin


#### Check for islands
W.list<- mat2listw(W, style = "B")
W.nb <- W.list$neighbours
W.islands <- n.comp.nb(W.nb)
islands <- W.islands$comp.id
n.islands <- max(W.islands$nc)
tau2.posterior.shape <- prior.tau2[1] + 0.5 * (K-n.islands)   


#### 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)     
    }
   


#### Create the MCMC samples      
    for(j in 1:n.sample)
    {
    ####################################
    ## Sample from Y - data augmentation
    ####################################
        if(n.miss>0)
        {
        Y.DA[which.miss==0] <- rbinom(n=n.miss, size=trials[which.miss==0], prob=prob[which.miss==0])
        failures.DA <- trials - Y.DA
        }else
        {}
        
        
        
    ####################
    ## Sample from beta
    ####################
    offset.temp <- phi + offset + theta
        if(MALA)
        {
        temp <- binomialbetaupdateMALA(X.standardised, K, p, beta, offset.temp, Y.DA, failures.DA, trials, prior.mean.beta, prior.var.beta, n.beta.block, proposal.sd.beta, list.block)
        }else
        {
        temp <- binomialbetaupdateRW(X.standardised, K, p, beta, offset.temp, Y.DA, failures.DA, prior.mean.beta, prior.var.beta, n.beta.block, proposal.sd.beta, list.block)
        }
    beta <- temp[[1]]
    accept[1] <- accept[1] + temp[[2]]
    accept[2] <- accept[2] + n.beta.block  



    ####################
    ## Sample from phi
    ####################
    beta.offset <- X.standardised %*% beta + theta + offset
    temp1 <- binomialcarupdateRW(Wtriplet=W.triplet, Wbegfin=W.begfin, Wtripletsum=W.triplet.sum, nsites=K, phi=phi, tau2=tau2, y=Y.DA, failures=failures.DA, phi_tune=proposal.sd.phi, rho=1, offset=beta.offset)
    phi <- temp1[[1]]
    phi[which(islands==1)] <- phi[which(islands==1)] - mean(phi[which(islands==1)])
    accept[3] <- accept[3] + temp1[[2]]
    accept[4] <- accept[4] + K
     
    

    ####################
    ## Sample from theta
    ####################
    beta.offset <- as.numeric(X.standardised %*% beta) + phi + offset
    temp2 <- binomialindepupdateRW(nsites=K, theta=theta, sigma2=sigma2, y=Y.DA, failures=failures.DA, theta_tune=proposal.sd.theta, offset=beta.offset) 
    theta <- temp2[[1]]
    theta <- theta - mean(theta)    
    accept[5] <- accept[5] + temp2[[2]]
    accept[6] <- accept[6] + K          
     


    ###################
    ## Sample from tau2
    ###################
    temp2 <- quadform(W.triplet, W.triplet.sum, n.triplet, K, phi, phi, 1)    
    tau2.posterior.scale <- temp2 + prior.tau2[2] 
    tau2 <- 1 / rgamma(1, tau2.posterior.shape, scale=(1/tau2.posterior.scale))
    
    
    
    #####################
    ## Sample from sigma2
    #####################
    sigma2.posterior.scale <- prior.sigma2[2] + 0.5*sum(theta^2)
    sigma2 <- 1 / rgamma(1, sigma2.posterior.shape, scale=(1/sigma2.posterior.scale))
    
    
    
    #########################
    ## Calculate the deviance
    #########################
    lp <- as.numeric(X.standardised %*% beta) + phi + theta + offset
    prob <- exp(lp)  / (1 + exp(lp))
    fitted <- trials * prob
    loglike <- 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.re[ele, ] <- phi + theta
        samples.tau2[ele, ] <- tau2
        samples.sigma2[ele, ] <- sigma2
        samples.loglike[ele, ] <- loglike
        samples.fitted[ele, ] <- fitted
            if(n.miss>0) samples.Y[ele, ] <- Y.DA[which.miss==0]
        }else
        {
        }


    
    ########################################
    ## Self tune the acceptance probabilties
    ########################################
        if(ceiling(j/100)==floor(j/100) & j < burnin)
        {
        #### Update the proposal sds
            if(p>2)
            {
            proposal.sd.beta <- common.accceptrates1(accept[1:2], proposal.sd.beta, 40, 50)
            }else
            {
            proposal.sd.beta <- common.accceptrates1(accept[1:2], proposal.sd.beta, 30, 40)    
            }
        proposal.sd.phi <- common.accceptrates1(accept[3:4], proposal.sd.phi, 40, 50)
        proposal.sd.theta <- common.accceptrates1(accept[5:6], proposal.sd.theta, 40, 50)
        accept <- c(0,0,0,0,0,0)
        }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.psi=samples.re, samples.tau2=samples.tau2, samples.sigma2=samples.sigma2, samples.loglike=samples.loglike, samples.fitted=samples.fitted,
                    samples.Y=samples.Y, accept=accept)

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