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Structural Equation Models for Dealing With Spatial Confounding

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  • Hauke Thaden
  • Thomas Kneib

Abstract

In regression analyses of spatially structured data, it is common practice to introduce spatially correlated random effects into the regression model to reduce or even avoid unobserved variable bias in the estimation of other covariate effects. If besides the response the covariates are also spatially correlated, the spatial effects may confound the effect of the covariates or vice versa. In this case, the model fails to identify the true covariate effect due to multicollinearity. For highly collinear continuous covariates, path analysis and structural equation modeling techniques prove to be helpful to disentangle direct covariate effects from indirect covariate effects arising from correlation with other variables. This work discusses the applicability of these techniques in regression setups, where spatial and covariate effects coincide at least partly and classical geoadditive models fail to separate these effects. Supplementary materials for this article are available online.

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  • Hauke Thaden & Thomas Kneib, 2018. "Structural Equation Models for Dealing With Spatial Confounding," The American Statistician, Taylor & Francis Journals, vol. 72(3), pages 239-252, July.
    • Handle: RePEc:taf:amstat:v:72:y:2018:i:3:p:239-252
    DOI: 10.1080/00031305.2017.1305290
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    Citations

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    Cited by:

    1. Georgia Papadogeorgou, 2022. "Discussion on “Spatial+: a novel approach to spatial confounding” by Emiko Dupont, Simon N. Wood, and Nicole H. Augustin," Biometrics, The International Biometric Society, vol. 78(4), pages 1305-1308, December.
    2. Brian J. Reich & Shu Yang & Yawen Guan, 2022. "Discussion on “Spatial+: A novel approach to spatial confounding” by Dupont, Wood, and Augustin," Biometrics, The International Biometric Society, vol. 78(4), pages 1291-1294, December.
    3. Jennifer F. Bobb & Maricela F. Cruz & Stephen J. Mooney & Adam Drewnowski & David Arterburn & Andrea J. Cook, 2022. "Accounting for spatial confounding in epidemiological studies with individual‐level exposures: An exposure‐penalized spline approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1271-1293, July.
    4. Isa Marques & Thomas Kneib, 2022. "Discussion on “Spatial+: A novel approach to spatial confounding” by Emiko Dupont, Simon N. Wood, and Nicole H. Augustin," Biometrics, The International Biometric Society, vol. 78(4), pages 1295-1299, December.
    5. Emiko Dupont & Simon N. Wood & Nicole H. Augustin, 2022. "Spatial+: A novel approach to spatial confounding," Biometrics, The International Biometric Society, vol. 78(4), pages 1279-1290, December.
    6. Brian J. Reich & Shu Yang & Yawen Guan & Andrew B. Giffin & Matthew J. Miller & Ana Rappold, 2021. "A Review of Spatial Causal Inference Methods for Environmental and Epidemiological Applications," International Statistical Review, International Statistical Institute, vol. 89(3), pages 605-634, December.
    7. Carlos García & Zaida Quiroz & Marcos Prates, 2023. "Bayesian spatial quantile modeling applied to the incidence of extreme poverty in Lima–Peru," Computational Statistics, Springer, vol. 38(2), pages 603-621, June.
    8. Douglas R. M. Azevedo & Marcos O. Prates & Dipankar Bandyopadhyay, 2021. "MSPOCK: Alleviating Spatial Confounding in Multivariate Disease Mapping Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 464-491, September.
    9. Isa Marques & Thomas Kneib & Nadja Klein, 2022. "Mitigating spatial confounding by explicitly correlating Gaussian random fields," Environmetrics, John Wiley & Sons, Ltd., vol. 33(5), August.
    10. João B. M. Pereira & Widemberg S. Nobre & Igor F. L. Silva & Alexandra M. Schmidt, 2020. "Spatial confounding in hurdle multilevel beta models: the case of the Brazilian Mathematical Olympics for Public Schools," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1051-1073, June.
    11. Marcos O. Prates & Douglas R. M. Azevedo & Ying C. MacNab & Michael R. Willig, 2022. "Non‐separable spatio‐temporal models via transformed multivariate Gaussian Markov random fields," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1116-1136, November.
    12. Widemberg S. Nobre & Alexandra M. Schmidt & João B. M. Pereira, 2021. "On the Effects of Spatial Confounding in Hierarchical Models," International Statistical Review, International Statistical Institute, vol. 89(2), pages 302-322, August.
    13. Thaden, Hauke & Klein, Nadja & Kneib, Thomas, 2019. "Multivariate effect priors in bivariate semiparametric recursive Gaussian models," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 51-66.
    14. Emiko Dupont & Nicole H. Augustin, 2024. "Spatial Confounding and Spatial+ for Nonlinear Covariate Effects," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(3), pages 455-470, September.

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