Dimension reduction and alleviation of confounding for spatial generalized linear mixed models

By John Hughes, Murali Haran. 2010

368 citations recorded by the source corpus.

Summary. Non‐Gaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression coefficients. The spatial generalized linear mixed model offers a very popular and flexible approach to modelling such data, but this model suffers from two major shortcomings: variance inflation due to spatial confounding and high dimensional spatial random effects that make fully Bayesian inference for such models computationally challenging. We propose a new parameterization of the spatial generalized linear mixed model that alleviates spatial confounding and speeds computation by greatly reducing the dimension of the spatial random effects. We illustrate the application of our approach to simulated binary, count and Gaussian spatial data sets, and to a large infant mortality data set.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ace6a74bee9c4e4cb329e76848d34b4bd63b604a

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Citations in the corpus

Spatial Regression Modeling for Compositional Data With Many Zeros (2013, methodology): “(2006) and Hughes and Haran (2013) provide methods for alleviating this problem, though these approaches would be more challenging for multivariate spatial random effects.”
A Moran coefficient-based mixed effects approach to investigate spatially varying relationships (2016, methodology): “+ [the centered spatially dependent component, (1) ( ) ~ MC ek s ], whose contribution ratios are 1ws and ws, respectively. xk has strong spatial dependence when ws is near 1. Some studies (e.g., 28 Hughes and Haran, 2013) reveal that coefficient estimates tend to be unstable when explanatory variab”
Multi-retinal disease classification by reduced deep learning features (2017, background): “The generalized regression neural network (GRNN) [22] is capable of gathering the average behavior of the data patterns given and the first layer of HL.”
Structural Equation Models for Dealing With Spatial Confounding (2018, methodology): “Hughes and Haran (2013) provided methods to alleviate spatial confounding by reparametrization of geoadditive models and apply CONTACT Thomas Kneib tkneib@uni-goettingen.de Department of Statistics and Econometrics, Georg-August University of Göttingen, Germany.”
Basis-Function Models in Spatial Statistics (2021, methodology): “This approach has been taken up by Hodges & Reich (2010), Paciorek (2010), Hughes & Haran (2013), and Bradley et al. (2015), and the use of these basis functions in Equations 9 and 10 has become known as restricted spatial regression (RSR).”
Hierarchical statistical modeling of big spatial datasets using the exponential family of distributions (2013, methodology): “In a recent article, Hughes and Haran (2013) consider a Bayesian hierarchical model with a hidden Gaussian MRF and use a dimension-reduction approach to deal with spatial confouding and computational complexity that arise when analyzing a large spatial dataset.”