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Alleviating spatial confounding for areal data problems by displacing the geographical centroids. (English) Zbl 1421.62064
Summary: 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.
62H11 Directional data; spatial statistics
62F15 Bayesian inference
62J12 Generalized linear models (logistic models)
62P35 Applications of statistics to physics
86A32 Geostatistics
85A04 General questions in astronomy and astrophysics
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[1] Besag, J. (1974). Spatial interaction and the statistical analysis of lattice data systems (with discussion). Journal of the Royal Statistical Society, Series B36, 192-225. · Zbl 0327.60067
[2] Besag, J., J. York, and A. Mollie (1991). Bayesian image restoration with two application in spatial statistics (with discussion). Annals of the Institute Statistical Mathematics43, 1-59. · Zbl 0760.62029
[3] Breslow, N. E. and D. G. Clayton (1993). Approximate inference in generalized linear mixed models. Journal of the American statistical Association88(421), 9-25. · Zbl 0775.62195
[4] Clayton, D., L. Bernardinelli, and C. Montomoli (1993). Spatial correlation in ecological analysis. International Journal of Epidemiology6, 1193-1202.
[5] Cressie, N. (1991). Statistics for spatial data. John Wiley & Sons. · Zbl 0799.62002
[6] Gelman, A. and F. Tuerlinckx (2000). Type s error rates for classical and bayesian single and multiple comparison procedures. Computational Statistics15(3), 373-390. · Zbl 1037.62015
[7] Hanks, E. M., E. M. Schliep, M. B. Hooten, and J. A. Hoeting (2015). Restricted spatial regression in practice: geostatistical models, confounding, and robustness under model misspecification. Environmetrics26(4), 243-254.
[8] Hefley, T. J., M. B. Hooten, E. M. Hanks, R. E. Russell, and D. P. Walsh (2017). The bayesian group lasso for confounded spatial data. Journal of Agricultural, Biological and Environmental Statistics22(1), 42-59. · Zbl 1373.62561
[9] Hodges, J. S. and B. J. Reich (2011, January). Adding Spatially-Correlated Errors Can Mess Up the Fixed Effect You Love. The American Statistician64(4), 325-334. · Zbl 1217.62095
[10] Hughes, J. and X. Cui (2017). ngspatial: Fitting the Centered Autologistic and Sparse Spatial Generalized Linear Mixed Models for Areal Data. Denver, CO. R package version 1.2.
[11] Hughes, J. and M. Haran (2013). Dimension reduction and alleviation of confounding for spatial generalized linear mixed models. Journal of the Royal Statistical Society, Series B75, 139-159.
[12] Lee, D. (2013). CARBayes: An R package for Bayesian spatial modeling with conditional autoregressive priors. Journal of Statistical Software55(13), 1-24.
[13] Leroux, B. G., X. Lei, and N. Breslow (1999). Estimation of disease rates in small areas: A new mixed model for spatial dependence. In M. E. Halloran and D. Berry (Eds.), In Statistical Models in Epidemiology; the Environment and Clinical Trials, pp. 179-192. New York: Springer-Verlag. · Zbl 0957.62095
[14] Lunn, D. J., A. Thomas, N. Best, and D. Spiegelhalter (2000). WinBUGS - a Bayesian modelling framework: Concepts, structure, and extensibility. Statistics and Computing10, 325-337.
[15] Menzel, U. (2012). CCP: Significance Tests for Canonical Correlation Analysis (CCA). R package version 1.1.
[16] Murakami, D. and D. A. Griffith (2015). Random effects specifications in eigenvector spatial filtering: a simulation study. Journal of Geographical Systems17(4), 311-331.
[17] Paciorek, C. J. (2010). The importance of scale for spatial-confounding bias and precision of spatial regression estimators. Statistical Science25, 107-125. · Zbl 1328.62596
[18] Prates, M. O., Assunção, R. M., and Rodrigues, E. C. (2018). Alleviating spatial confounding for areal data problems by displacing the geographical centroids: Supplementary Material. Bayesian Analysis.
[19] R Development Core Team (2011). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0.
[20] Reich, B. J., J. S. Hodges, and V. Zadnik (2006). Effects of residual smoothing on the posterior of the fixed effects in disease-mapping models. Biometrics62, 1197-1206. · Zbl 1114.62124
[21] Rodrigues, E. C. and R. Assunção (2012). Bayesian spatial models with a mixture neighborhood structure. Journal of Multivariate Analysis109(0), 88-102. · Zbl 1241.62024
[22] Rue, H. and L. Held (2005). Gaussian Markov random fields: Theory and applications. Chapman & Hall. · Zbl 1093.60003
[23] Rue, H., S. Martino, and N. Chopin (2009). Approximate bayesian inference for latent gaussian models using integrated nested laplace approximations (with discussion). Journal of the Royal Statistical Society, Series B71, 319-392. · Zbl 1248.62156
[24] Sampson, P. D. and P. Guttorp (1992). Nonparametric estimation of nonstationary spatial covariance structure. Journal of the American Statistical Association87(417), 108-119.
[25] Wilks, S. (1935). On the independence of k sets of normally distributed statistical variables. Econometrica, Journal of the Econometric Society, 309-326. · Zbl 0012.02903
[26] Zadnik, V. and B. J. Reich (2006). Analysis of the relationship between socioeconomic factors and stomach cancer incidence in Slovenia. Neoplasma53, 103-110.
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