\name{S.glm}
\alias{S.glm}
%- Also NEED an '\alias' for EACH other topic documented here.


\title{
Fit a spatial generalised linear model to data.
}

\description{
Fit a spatial generalised linear model to data, where the response variable 
can be binomial, Gaussian or Poisson. Inference is conducted in a Bayesian 
setting using Markov chain Monte Carlo (McMC)  simulation. Missing (NA) values 
are allowed in the response, and posterior predictive  distributions are created 
for the missing values for predictive purposes. These are  saved in the`samples' 
argument in the output of the function and are denoted by `Y'. 
}


\usage{
S.glm(formula, family, data=NULL,  trials=NULL, burnin, n.sample, thin=1, 
prior.mean.beta=NULL, prior.var.beta=NULL, prior.nu2=NULL, verbose=TRUE)
}

%- maybe also 'usage' for other objects documented here.
\arguments{
  \item{formula}{
A formula for the covariate part of the model using the syntax of the
lm() function. Offsets can be included here using the offset() function. The 
response can contain missing (NA) values.
}
  \item{family}{
One of either `binomial', `gaussian' or `poisson', which respectively specify a 
binomial likelihood model with a logistic link function, a Gaussian likelihood 
model with an identity link function, or a Poisson likelihood model with a 
log link function. 
}
  \item{data}{
An optional data.frame containing the  variables in the formula.
}
 \item{trials}{
A vector the same length as the response containing the total number of trials 
for data point. Only used if family=`binomial'. 
}
  \item{burnin}{
The number of MCMC samples to discard as the burn-in period.
}
  \item{n.sample}{
The number of MCMC samples to generate.
}
  \item{thin}{
The level of thinning to apply to the MCMC samples to reduce their temporal 
autocorrelation. Defaults to 1 (no thinning).
}
  \item{prior.mean.beta}{
A vector of prior means for the regression parameters beta (Gaussian priors are 
assumed). Defaults to a vector of zeros.
}
  \item{prior.var.beta}{
A vector of prior variances for the regression parameters beta (Gaussian priors 
are assumed). Defaults to a vector with values 100000.
}  
  \item{prior.nu2}{
The prior shape and scale in the form of c(shape, scale) for an Inverse-Gamma(shape, scale) 
prior for nu2. Defaults to c(1, 0.01) and only used if family=`Gaussian'.   
}
  \item{verbose}{
Logical, should the function update the user on its progress.  
}
}




\value{
\item{summary.results }{A summary table of the parameters.}
\item{samples }{A list containing the McMC samples from the model.}
\item{fitted.values }{A vector of fitted values for each area.}
\item{residuals }{A vector of residuals for each area.}
\item{modelfit }{Model fit criteria including the Deviance Information Criterion 
(DIC) and its corresponding estimated effective number of parameters (p.d), the Log 
Marginal Predictive Likelihood (LMPL), and the Watanabe-Akaike Information Criterion 
(WAIC) and its corresponding estimated number of effective parameters (p.w).}
\item{accept }{The acceptance probabilities for the parameters.}
\item{localised.structure }{NULL, for compatability with the other models.}
\item{formula }{The formula for the covariate and offset part of the model.}
\item{model }{A text string describing the model fit.}
\item{X }{The design matrix of covariates.}
}



\author{
Duncan Lee
}




\examples{
##################################################
#### Run the model on simulated data on a lattice
##################################################
#### Set up a square lattice region
x.easting <- 1:10
x.northing <- 1:10
Grid <- expand.grid(x.easting, x.northing)
K <- nrow(Grid)

#### Generate the covariates and response data
x1 <- rnorm(K)
x2 <- rnorm(K)
logit <- x1 + x2
prob <- exp(logit) / (1 + exp(logit))
trials <- rep(50,K)
Y <- rbinom(n=K, size=trials, prob=prob)

#### Run the model
formula <- Y ~ x1 + x2
\dontrun{model <- S.glm(formula=formula, family="binomial", trials=trials, 
burnin=20000, n.sample=100000)}
}