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.
Spatial microsimulation models are increasingly being used to create realistic microdata for geographical areas, to enable statistical modelling of health, social and economic variables in a wide variety of application areas. The models combine sample records with benchmark data for pre-defined geographic areas, typically by sampling, or re-weighting sample records to fit a set of constraints for each area. The choice of constraints is a key factor in producing microdata that reflect the population structure.This paper introduces the use of within-area homogeneity for selecting categorical constraint variables for spatial microsimulation. The d-statistic is a measure of within-area homogeneity, that is equivalent to intra-area correlation for areas with equal population. It can be used to identify the spatial autocorrelation exhibited by the categories of constraint variables, or combinations of categories, an important feature to reproduce when modelling local variation in a variable. It may be used to assess the statistical significance of the within-area homogeneity for a given set of categories and can assist in validating spatial microsimulation models.
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