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About predictions in spatial autoregressive models : Optimal and almost optimal strategies

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  • Thomas-Agnan, Christine
  • Laurent, Thibault
  • Goulard, Michel

Abstract

We address the problem of prediction in the spatial autoregressive SAR model for areal data which is classically used in spatial econometrics. With the Kriging theory, prediction using Best Linear Unbiased Predictors is at the heart of the geostatistical literature. From the methodological point of view, we explore the limits of the extension of BLUP formulas in the context of the spatial autoregressive SAR models for out-of-sample prediction simultaneously at several sites. We propose a more tractable \almost best" alternative and clarify the relationship between the BLUP and a proper EM-algorithm predictor. From an empirical perspective, we present data-based simulations to compare the efficiency of the classical formulas with the best and almost best predictions.

Suggested Citation

  • Thomas-Agnan, Christine & Laurent, Thibault & Goulard, Michel, 2013. "About predictions in spatial autoregressive models : Optimal and almost optimal strategies," TSE Working Papers 13-452, Toulouse School of Economics (TSE), revised Dec 2016.
    • Handle: RePEc:tse:wpaper:27788
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    References listed on IDEAS

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    1. Roger Bivand, 2002. "Spatial econometrics functions in R: Classes and methods," Journal of Geographical Systems, Springer, vol. 4(4), pages 405-421, December.
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    Citations

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    Cited by:

    1. Katarzyna Kopczewska, 2022. "Spatial machine learning: new opportunities for regional science," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 68(3), pages 713-755, June.
    2. Suesse, Thomas, 2018. "Marginal maximum likelihood estimation of SAR models with missing data," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 98-110.
    3. Paula Margaretic & Christine Thomas-Agnan & Romain Doucet, 2017. "Spatial dependence in (origin-destination) air passenger flows," Papers in Regional Science, Wiley Blackwell, vol. 96(2), pages 357-380, June.
    4. Thomas-Agnan, Christine & Margaretic, Paula & Laurent, Thibault, 2022. "Generalizing impact computations for the autoregressive spatial interaction model," TSE Working Papers 22-1357, Toulouse School of Economics (TSE), revised Feb 2023.
    5. Paul-Christian Bürkner & Jonah Gabry & Aki Vehtari, 2021. "Efficient leave-one-out cross-validation for Bayesian non-factorized normal and Student-t models," Computational Statistics, Springer, vol. 36(2), pages 1243-1261, June.
    6. Simon K. C. Cheung & Tommy K. Y. Cheung, 2022. "Mixed membership nearest neighbor model with feature difference," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(8), pages 1578-1594, December.
    7. Roger Bivand & Giovanni Millo & Gianfranco Piras, 2021. "A Review of Software for Spatial Econometrics in R," Mathematics, MDPI, vol. 9(11), pages 1-40, June.
    8. Dargel, Lukas, 2021. "Revisiting Estimation Methods for Spatial Econometric Interaction Models," TSE Working Papers 21-1192, Toulouse School of Economics (TSE).
    9. Laurent, Thibault & Margaretic, Paula & Thomas-Agnan, Christine, 2021. "Do neighboring countries matter when explaining bilateral remittances?," TSE Working Papers 21-1221, Toulouse School of Economics (TSE).
    10. Luo, Guowang & Wu, Mixia & Xu, Liwen, 2021. "IPW-based robust estimation of the SAR model with missing data," Statistics & Probability Letters, Elsevier, vol. 172(C).
    11. Lukas Dargel, 2021. "Revisiting estimation methods for spatial econometric interaction models," Journal of Spatial Econometrics, Springer, vol. 2(1), pages 1-41, December.
    12. Hunneman, Auke & Bijmolt, Tammo H.A. & Elhorst, J. Paul, 2023. "Evaluating store location and department composition based on spatial heterogeneity in sales potential," Journal of Retailing and Consumer Services, Elsevier, vol. 73(C).
    13. Müller, Jonas & Trutnevyte, Evelina, 2020. "Spatial projections of solar PV installations at subnational level: Accuracy testing of regression models," Applied Energy, Elsevier, vol. 265(C).
    14. Takafumi Kato, 2020. "Likelihood-based strategies for estimating unknown parameters and predicting missing data in the simultaneous autoregressive model," Journal of Geographical Systems, Springer, vol. 22(1), pages 143-176, January.
    15. Thomas Suesse, 2018. "Estimation of spatial autoregressive models with measurement error for large data sets," Computational Statistics, Springer, vol. 33(4), pages 1627-1648, December.
    16. Thomas-Agnan, Christine & Laurent, Thibault & Ruiz-Gazen, Anne & Nguyen, T.H.A & Chakir, Raja & Lungarska, Anna, 2020. "Spatial simultaneous autoregressive models for compositional data: Application to land use," TSE Working Papers 20-1098, Toulouse School of Economics (TSE).
    17. Tingting Huang & Gilbert Saporta & Huiwen Wang & Shanshan Wang, 2021. "A robust spatial autoregressive scalar-on-function regression with t-distribution," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(1), pages 57-81, March.
    18. Kerkman, Kasper & Martens, Karel & Meurs, Henk, 2018. "Predicting travel flows with spatially explicit aggregate models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 118(C), pages 68-88.

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    Keywords

    Spatial simultaneous autoregressive models; out of sample prediction; best linear unbiased prediction;
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