\name{CARBayes-package}
\alias{CARBayes-package}
\alias{CARBayes}
\docType{package}

\title{
Spatial Generalised Linear Mixed Models for Areal Unit Data
}


\description{
Implements a class of univariate and multivariate spatial generalised linear mixed 
models for areal unit data, with inference in a Bayesian setting using Markov chain 
Monte Carlo (MCMC) simulation using a single or multiple Markov chains. The response 
variable can be binomial, Gaussian, multinomial, Poisson or zero-inflated Poisson 
(ZIP), and spatial autocorrelation is modelled by  a set of random effects that 
are assigned a conditional autoregressive (CAR) prior distribution. A number of 
different models are available for univariate spatial data, including models with 
no random effects as well as random effects modelled by different types of CAR 
prior, including the BYM model (Besag et al., 1991, <doi:10.1007/BF00116466>) 
and the Leroux model (Leroux et al., 2000, <doi:10.1007/978-1-4612-1284-3_4>). 
Additionally,  a multivariate CAR (MCAR) model for multivariate spatial data is 
available, as is a two-level hierarchical  model for modelling data relating to 
individuals within areas. Full details are given in the vignette accompanying this 
package. The initial creation of this package was supported by the Economic and 
Social Research Council (ESRC) grant RES-000-22-4256, and on-going development 
has been supported by the Engineering and Physical Science Research Council (EPSRC) 
grant EP/J017442/1, ESRC grant ES/K006460/1, Innovate UK / Natural Environment 
Research Council (NERC) grant NE/N007352/1 and the TB Alliance.
}

\details{
\tabular{ll}{
Package: \tab CARBayes\cr
Type: \tab Package\cr
Version: \tab 6.1.1\cr
Date: \tab 2024-03-08\cr
License: \tab GPL (>= 2)\cr
}
}




\author{
Maintainer: Duncan Lee <Duncan.Lee@glasgow.ac.uk>
}


\references{
Besag, J. and  York, J and Mollie, A (1991). Bayesian image restoration with two 
applications in spatial statistics. Annals of the Institute of Statistics and 
Mathematics 43, 1-59.

Gelfand, A and Vounatsou, P (2003). Proper multivariate conditional autoregressive
models for spatial data analysis, Biostatistics, 4, 11-25.

Kavanagh, L., D. Lee, and G. Pryce (2016). Is Poverty Decentralising? Quantifying 
Uncertainty in the Decentralisation of Urban Poverty, Annals of the American 
Association of Geographers, 106, 1286-1298.

Lee, D. and Mitchell, R (2012). Boundary detection in disease mapping studies. 
Biostatistics, 13, 415-426.

Lee, D and Sarran, C  (2015). Controlling for unmeasured confounding and spatial 
misalignment in long-term air pollution and health studies, Environmetrics, 26, 
477-487.

Lee, D (2024). Computationally efficient localised spatial smoothing of disease 
rates using anisotropic basis functions and penalised regression fitting, 
Spatial Statistics, 59, 100796.

Leroux B, Lei X, Breslow N (2000). "Estimation of Disease Rates in SmallAreas: A 
New Mixed Model for Spatial Dependence." In M Halloran, D Berry (eds.), 
\emph{Statistical Models in Epidemiology, the Environment and Clinical Trials},
pp. 179-191. Springer-Verlag, New York.

Roberts, G and Rosenthal, J (1998). Optimal scaling of discrete approximations to
the Langevin diffusions, Journal of the Royal Statistical Society Series B 60, 
255-268.
}



\examples{
## See the examples in the function specific help files and in the vignette
## accompanying this package.
}