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The SAR Model for Very Large Datasets: A Reduced Rank Approach

Author

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  • Sandy Burden

    (National Institute for Applied Statistics Research Australia, University of Wollongong, Wollongong, NSW 2522, Australia)

  • Noel Cressie

    (National Institute for Applied Statistics Research Australia, University of Wollongong, Wollongong, NSW 2522, Australia)

  • David G. Steel

    (National Institute for Applied Statistics Research Australia, University of Wollongong, Wollongong, NSW 2522, Australia)

Abstract

The SAR model is widely used in spatial econometrics to model Gaussian processes on a discrete spatial lattice, but for large datasets, fitting it becomes computationally prohibitive, and hence, its usefulness can be limited. A computationally-efficient spatial model is the spatial random effects (SRE) model, and in this article, we calibrate it to the SAR model of interest using a generalisation of the Moran operator that allows for heteroskedasticity and an asymmetric SAR spatial dependence matrix. In general, spatial data have a measurement-error component, which we model, and we use restricted maximum likelihood to estimate the SRE model covariance parameters; its required computational time is only the order of the size of the dataset. Our implementation is demonstrated using mean usual weekly income data from the 2011 Australian Census.

Suggested Citation

  • Sandy Burden & Noel Cressie & David G. Steel, 2015. "The SAR Model for Very Large Datasets: A Reduced Rank Approach," Econometrics, MDPI, vol. 3(2), pages 1-22, May.
    • Handle: RePEc:gam:jecnmx:v:3:y:2015:i:2:p:317-338:d:49389
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    References listed on IDEAS

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    1. Anjana Wijayawardhana & David Gunawan & Thomas Suesse, 2024. "A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data," Mathematics, MDPI, vol. 12(23), pages 1-16, December.
    2. 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.
    3. Ul-Durar, Shajara & De Sisto, Marco & Arshed, Noman & Naveed, Shabana & Farooqi, Madiha Rehman, 2024. "FinTech adoption in achieving ecologically sustainable mineral management in Asian OBOR countries – A cross-section and time autoregressive robust analysis," Resources Policy, Elsevier, vol. 91(C).
    4. Zammit-Mangion, Andrew & Rougier, Jonathan, 2018. "A sparse linear algebra algorithm for fast computation of prediction variances with Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 116-130.

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