CARBayes (version 4.4)

CARBayes-package: Spatial Generalised Linear Mixed Models for Areal Unit Data

Description

Implements a class of 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 or Poisson. The spatial autocorrelation is modelled by a set of random effects, which are assigned a conditional autoregressive (CAR) prior distribution. A number of different CAR priors are available for the random effects, and 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 was supported by the Engineering and Physical Science Research Council (EPSRC) grant EP/J017442/1.

Version 4.4 has two main changes from version 4.3. Firstly, the three functions S.CARiar(), S.independent() and S.CARleroux() have been merged into S.CARleroux(), as the latter is a generalisation of the other two. This has been achieved by adding two additional arguments to S.CARleroux, fix.rho (logical) and rho (numeric). The old model S.independent() can be obtained by setting (fix.rho=TRUE, rho=0), which corresponds to independent random effects. Similarly, the old model S.CARiar() corresponding to the intrinsic CAR model can be obtained by setting (fix.rho=TRUE, rho=1). The second change is that the modelfit component of the fitted model object now additionally returns the Watanabe-Akaike Information Criterion (WAIC) and an estimate of the effective number of effective parameters (p.w).

Details

ll{ Package: CARBayes Type: Package Version: 4.4 Date: 2016-02-03 License: GPL (>= 2) }

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.

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 and Breslow, N (1999). Estimation of disease rates in small areas: A new mixed model for spatial dependence, Chapter Statistical Models in Epidemiology, the Environment and Clinical Trials, Halloran, M and Berry, D (eds), pp. 135-178. Springer-Verlag, New York.

Examples

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