A shared neighbor conditional autoregressive model for small area spatial data

The use of conditional autoregressive (CAR) models for spatial effects is commonplace, especially when dealing with aggregated count data in health studies. CAR models are convenient and relatively easy to implement but suffer from the fact that they have limited flexibility in modeling correlation. We introduce a new CAR model that can accommodate different neighborhood features (including shared neighbors). Further, we examine via simulation how this model performs in comparison with standard CAR models. We also consider the application to a small area health data example. Copyright © 2015 John Wiley & Sons, Ltd.

[1]  M. Wall.  A close look at the spatial structure implied by the CAR and SAR models , 2004 .

[2]  Sylvia Richardson,et al.  A comparison of Bayesian spatial models for disease mapping , 2005, Statistical methods in medical research.

[3]  Duncan Lee,et al.  A Bayesian localized conditional autoregressive model for estimating the health effects of air pollution , 2013, Biometrics.

[4]  Andrew B. Lawson,et al.  Gaussian component mixtures and CAR models in Bayesian disease mapping , 2012, Comput. Stat. Data Anal..

[5]  Noel A. C. Cressie,et al.  Statistics for Spatial Data: Cressie/Statistics , 1993 .

[6]  M. Lavine,et al.  On Rigorous Specification of ICAR Models , 2012 .

[7]  N. Cressie,et al.  Some Diagnostics for Markov Random Fields , 2008 .

[8]  Renato Assunção,et al.  Bayesian spatial models with a mixture neighborhood structure , 2012, J. Multivar. Anal..

[9]  D. Higdon,et al.  Exploring Space-Time Structure in Ozone Concentration Using a Dynamic Process Convolution Model , 2002 .

[10]  D. Higdon.  Space and Space-Time Modeling using Process Convolutions , 2002 .

[11]  Fabio Divino,et al.  Disease mapping models: an empirical evaluation , 2000 .

[12]  N. Cressie,et al.  Spatial Modeling of Regional Variables , 1993 .

[13]  J. Besag,et al.  Bayesian image restoration, with two applications in spatial statistics , 1991 .

[14]  E. Krainski,et al.  Neighborhood Dependence in Bayesian Spatial Models , 2009, Biometrical journal. Biometrische Zeitschrift.

[15]  Gentry White,et al.  A stochastic neighborhood conditional autoregressive model for spatial data , 2009, Comput. Stat. Data Anal..

[16]  J. Hodges,et al.  Adding Spatially-Correlated Errors Can Mess Up the Fixed Effect You Love , 2010 .