A close look at the spatial structure implied by the CAR and SAR models

By Melanie M. Wall. 2004

372 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/258945e90415ea60f607040cf41e1582973f4dcc

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In Economics and Econometrics

Citations in the corpus

Regional fertility data analysis: A small area Bayesian approach (2013, background): “Observationally, these two models are very similar (Wall, 2004), even if the interpretation of the models is somewhat different.”
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach (2011, methodology): “…j (Besag et al., 1991; Arjas and Gasbarra, 1996; Weir and Pettitt, 2000; Pettitt et al., 2002; Gschlößl and Czado, 2007), however a more detailed analysis shows that such a rationale is suboptimal (Besag and Kooperberg, 1995; Rue and Tjelmeland, 2002) and can give surprising effects (Wall, 2004).”
Small Area Estimation via Multivariate Fay–Herriot Models with Latent Spatial Dependence (2013, methodology): “We recommend Unif(0, 1) priors on the spatial parameters rather than Unif(−1, 1) priors on the basis of the work of Wall (2004), which demonstrates that CAR models possess a variety of undesirable properties for spatial datasets with negative spatial autocorrelation.”
Methods to account for spatial autocorrelation in the analysis of species distributional data : a review (2007, methodology): “A good introduction to the CAR and SAR methodology is given by Wall (2004) .”
Modelling hedonic residential rents for land use and transport simulation while considering spatial effects (2010, background): “Wall (2004) compared conditional autoregressive models (CAR) and simultaneously autoregressive models, but found possible counter-intuitive or impractical results.”
Spatial modelling: a comprehensive framework for principal coordinate analysis of neighbour matrices (PCNM) (2006, methodology): “The reader should consult Wall (2004) for a comprehensive description of SAR and CAR, 1 9 ing (including the eigenvector approach) and the consistency of their results with those obtained by a spatial autoregressive model.”
Testing environmental and genetic effects in the presence of spatial autocorrelation (2014, methodology): “But autoregressive models have notable drawbacks as models of spatial autocorrelation (Wall 2004, Martellosio 2012), and will not be discussed here, although a CAR has been implemented in the spaMM package.”
Dimension reduction and alleviation of confounding for spatial generalized linear mixed models (2010, background): “But Wall (2004) showed that this is not so, and Assunção and Krainski (2009) recently showed why it is not so: the a priori covariance structure of the proper conditional auto-regression and the a posteriori covariance structure of the intrinsic conditional auto-regression both depend, in a rather…”
On the relationship between conditional (CAR) and simultaneous (SAR) autoregressive models (2017, background): “…SAR models (e.g., Wall, 2004), and how one model might or might not be expressed in terms of the other (Haining, 1990; Cressie, 1993; Martin, 1987; Waller and Gotway, 2004), but there is little clarity in the existing literature on the relationships between these two classes of autoregressive…”