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Abstract
Spatial confounding between the spatial random effects and fixed effects covariates has been recently discovered and showed that it may bring misleading interpretation to the model results. Techniques to alleviate this problem are based on decomposing the spatial random effect and fitting a restricted spatial regression. In this paper, we propose a different approach: a transformation of the geographic space to ensure that the unobserved spatial random effect added to the regression is orthogonal to the fixed effects covariates. Our approach, named SPOCK, has the additional benefit of providing a fast and simple computational method to estimate the parameters. Also, it does not constrain the distribution class assumed for the spatial error term. A simulation study and real data analyses are presented to better understand the advantages of the new method in comparison with the existing ones.
Highlights
Spatial generalized linear mixed models (SGLMM) for areal data analysis have become a common tool for data analysis in recent years with the availability of spatially referenced data sets
We introduced an alternative way to alleviate spatial confounding
The introduced method maintains the original sparsity of the precision matrix Q and introduces no restriction in the spatial modeling setup
Summary
Spatial generalized linear mixed models (SGLMM) for areal data analysis have become a common tool for data analysis in recent years with the availability of spatially referenced data sets. Besag et al (1991) introduced a hierarchical modeling adding random spatial effects to a generalized linear regression model. The main idea behind the Reich et al (2006) and Hughes and Haran (2013) methods is to project the unobserved spatial effects vector in the linear space orthogonal to the explanatory variables As a consequence, they end up with a precision matrix that is far from sparse losing one of the main advantages of the Markov random fields. These examples illustrate that all three models lead to very similar estimates but SPOCK is one or two orders of magnitude faster than the other methods.
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