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

Sandy Burden (), Noel Cressie () and David G. Steel ()
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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

Econometrics, 2015, vol. 3, issue 2, 1-22

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.

Keywords: asymmetric spatial dependence matrix; Australian census; heteroskedasticity; Moran operator; spatial autoregressive model; spatial basis functions; spatial random effects model (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2015
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