A multivariate Gaussian random field prior against spatial confounding

Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed covariates modeling the mean of the response are correlated with the spatial random effect. As a result, estimates for regression coefficients of the covariates can be severely biased and interpretation of these is no longer valid. Recent literature has shown that typical solutions for reducing spatial confounding can lead to misleading and counterintuitive results. In this paper, we develop a computationally efficient spatial model in a Bayesian framework integrating novel prior structure that reduces spatial confounding. Starting from the univariate case, we extend our prior structure to case of multiple spatially confounded covariates. In a simulation study, we show that our novel model flex-

[1]  F. Lindgren,et al.  Spatial models with explanatory variables in the dependence structure , 2014 .

[2]  Garritt L. Page,et al.  Estimation and Prediction in the Presence of Spatial Confounding for Spatial Linear Models , 2017 .

[3]  Jennifer A Hoeting,et al.  Model selection for geostatistical models. , 2006, Ecological applications : a publication of the Ecological Society of America.

[4]  H. Rue,et al.  Fitting Gaussian Markov Random Fields to Gaussian Fields , 2002 .

[5]  V. Zadnik,et al.  Effects of Residual Smoothing on the Posterior of the Fixed Effects in Disease‐Mapping Models , 2006, Biometrics.

[6]  Leonhard Held,et al.  Gaussian Markov Random Fields: Theory and Applications , 2005 .

[7]  Matti Vihola,et al.  Robust adaptive Metropolis algorithm with coerced acceptance rate , 2010, Statistics and Computing.

[8]  A. Gelman,et al.  Weak convergence and optimal scaling of random walk Metropolis algorithms , 1997 .

[9]  Thomas Kneib,et al.  Structural Equation Models for Dealing With Spatial Confounding , 2018 .

[10]  C Montomoli,et al.  Spatial correlation in ecological analysis. , 1993, International journal of epidemiology.

[11]  P. Moran.  Notes on continuous stochastic phenomena. , 1950, Biometrika.

[12]  Catherine A. Calder,et al.  Restricted Spatial Regression Methods: Implications for Inference , 2019, Journal of the American Statistical Association.

[13]  H. Rue,et al.  An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach , 2011 .

[14]  Mevin B. Hooten,et al.  Restricted spatial regression in practice: geostatistical models, confounding, and robustness under model misspecification , 2015 .

[15]  Thiago G. Martins,et al.  Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors , 2014, 1403.4630.

[16]  Murali Haran,et al.  Dimension reduction and alleviation of confounding for spatial generalized linear mixed models , 2010, 1011.6649.

[17]  Rutger van Haasteren,et al.  Gibbs Sampling , 2010, Encyclopedia of Machine Learning.

[18]  R. A. Fisher,et al.  Statistical methods for research workers. Biological monographs and manuals. No. V. , 1950 .

[19]  Chun-Shu Chen,et al.  An adjusted parameter estimation for spatial regression with spatial confounding , 2019, Stochastic Environmental Research and Risk Assessment.

[20]  Luca Vogt.  Statistics For Spatial Data , 2016 .

[21]  Christopher J Paciorek,et al.  The importance of scale for spatial-confounding bias and precision of spatial regression estimators. , 2010, Statistical science : a review journal of the Institute of Mathematical Statistics.

[22]  Widemberg S. Nobre,et al.  On the Effects of Spatial Confounding in Hierarchical Models , 2020, International Statistical Review.

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

[24]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[25]  M. Kendall.  Statistical Methods for Research Workers , 1937, Nature.