CARBayes-package {CARBayes}R Documentation

Spatial Generalised Linear Mixed Models for Areal Unit Data


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. 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>), the Leroux model (Leroux et al. (2000) <doi:10.1007/978-1-4612-1284-3_4>) and the localised model (Lee et al. (2015) <doi:10.1002/env.2348>). 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.


Package: CARBayes
Type: Package
Version: 5.2.5
Date: 2021-09-30
License: GPL (>= 2)


Maintainer: Duncan Lee <>


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.

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.), 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.


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

[Package CARBayes version 5.2.5 Index]