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

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  • Michel Goulard
  • Thibault Laurent
  • Christine Thomas-Agnan

Abstract

About predictions in spatial autoregressive models: optimal and almost optimal strategies. Spatial Economic Analysis. This paper addresses the problem of prediction in the spatial autoregressive (SAR) model for areal data, which is classically used in spatial econometrics. With kriging theory, prediction using the best linear unbiased predictors (BLUPs) is at the heart of the geostatistical literature. From a methodological point of view, we explore the limits of the extension of BLUP formulas in the context of 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 expectation–maximization (EM) algorithm predictor. From an empirical perspective, we present data-based simulations to compare the efficiency of classical formulas with the best and almost best predictions.

Suggested Citation

  • Michel Goulard & Thibault Laurent & Christine Thomas-Agnan, 2017. "About predictions in spatial autoregressive models: optimal and almost optimal strategies," Spatial Economic Analysis, Taylor & Francis Journals, vol. 12(2-3), pages 304-325, July.
    • Handle: RePEc:taf:specan:v:12:y:2017:i:2-3:p:304-325
    DOI: 10.1080/17421772.2017.1300679
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    Cited by:

    1. Lukas Dargel, 2021. "Revisiting estimation methods for spatial econometric interaction models," Journal of Spatial Econometrics, Springer, vol. 2(1), pages 1-41, December.
    2. Katarzyna Kopczewska, 2023. "Spatial bootstrapped microeconometrics: Forecasting for out‐of‐sample geo‐locations in big data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1391-1419, September.
    3. 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.
    4. 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).
    5. 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).
    6. Suesse, Thomas, 2018. "Marginal maximum likelihood estimation of SAR models with missing data," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 98-110.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Christine Thomas-Agnan & Thibault Laurent & Anne Ruiz-Gazen & Thi Huong An Nguyen & Raja Chakir & Anna Lungarska, 2021. "Spatial Simultaneous Autoregressive Models for Compositional Data: Application to Land Use," Springer Books, in: Peter Filzmoser & Karel Hron & Josep Antoni Martín-Fernández & Javier Palarea-Albaladejo (ed.), Advances in Compositional Data Analysis, pages 225-249, Springer.
    12. 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.
    13. 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.
    14. Dargel, Lukas, 2021. "Revisiting Estimation Methods for Spatial Econometric Interaction Models," TSE Working Papers 21-1192, Toulouse School of Economics (TSE).
    15. 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).
    16. 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.
    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. Villarraga, Daniel F. & Daziano, Ricardo A., 2025. "Hierarchical Nearest Neighbor Gaussian Process models for discrete choice: Mode choice in New York City," Transportation Research Part B: Methodological, Elsevier, vol. 191(C).
    19. 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.
    20. 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).

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