CARBayesST (version 1.0)

CARBayesST-package: Poisson Log-linear Models with Spatio-temporal Random Effects

Description

Implements a series of Poisson log-linear models with spatio-temporal random effects. The spatial and temporal autocorrelation in the random effects are induced using the class of Conditional AutoRegressive (CAR) priors, which are a special case of Gaussian Markov Random Fields (GMRF). All models are fitted in a Bayesian context using Markov chain Monte Carlo (McMC) simulation.

Details

ll{ Package: CARBayesST Type: Package Version: 1.0 Date: 2014-08-05 License: GPL (>= 2) }

Implements Bayesian Poisson log-linear models for spatio-temporal areal unit count data. The models assume the response is Poisson, and model the mean as a multiplicative combination of an offset term E and a risk term theta. The log-risk is modelled by random effects and five different models are considered. The first two are the models proposed by Knorr-Held and Besag (1998) and Knorr-Held (2000), while the latter three are clustering models proposed in Lee (2014).

References

Knorr-Held, L. and J. Besag (1998). Modelling Risk from a Disease in Time and Space. Statistics in Medicine 17, 2045-2060.

Knorr-Held, L. (2000). Bayesian modelling of inseparable space-time variation in disease risk. Statistics in Medicine, 19, 2555-2567.

Lee, D. and A. Lawson (2014). Cluster detection and risk estimation for spatio-temporal health data. arXiv:1408.1191.

Examples

#### Artificial data generated on a square

#### Set up a square lattice region
x.easting <- 1:10
x.northing <- 1:10
Grid <- expand.grid(x.easting, x.northing)
n <- nrow(Grid)
t <- 10


#### set up distance and neighbourhood (W, based on sharing a common border) matrices
distance <-array(0, c(n,n))
W <-array(0, c(n,n))
     for(i in 1:n)
     {
		for(j in 1:n)
		{
		temp <- (Grid[i,1] - Grid[j,1])^2 + (Grid[i,2] - Grid[j,2])^2
		distance[i,j] <- sqrt(temp)
			if(temp==1)  W[i,j] <- 1 
		}	
	}
	
	
#### Generate data
n.all <- n * t
E <- rep(100, n.all)
log.risk <- log(rep(c(rep(1, 70), rep(2, 30)),t))
x <- rnorm(n.all)
risk <- exp(log.risk + 0.1 * x)
mean <- E * risk
Y <- rpois(n=n.all, lambda=mean)
formula <- Y~ offset(log(E)) + x
     

#### Run the models     
model1 <- ST.knorrheld.main(formula, data=NULL, W=W, burnin=5000, n.sample=10000)
model2 <- ST.knorrheld.int(formula, data=NULL, W=W, burnin=5000, n.sample=10000)
model3 <- ST.clustonly(formula, data=NULL, G=3, K=100, burnin=5000, n.sample=10000)
model4 <- ST.clustcar(formula, data=NULL, G=3, W=W, burnin=5000, n.sample=10000)
model5 <- ST.clustconv(formula, data=NULL, G=3, coordinates=Grid, burnin=5000, 
n.sample=10000)
print.CARBayesST(model5)