The SAR model for very large datasets: a reduced rank approach

Authors

Sandy Burden, University of WollongongFollow
Noel Cressie, University of WollongongFollow
David G. Steel, University of WollongongFollow

RIS ID

107338

Publication Details

Burden, S., Cressie, N. & Steel, D. G. (2015). The SAR model for very large datasets: a reduced rank approach. Econometrics, 3 (2), 317-338.

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.