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

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.