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The spatial autocorrelation problem in spatial interaction modelling: a comparison of two common solutions

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Abstract

Spatial interaction models of the gravity type are widely used to describe origin-destination flows. They draw attention to three types of variables to explain variation in spatial interactions across geographic space: variables that characterize the origin region of interaction, variables that characterize the destination region of interaction, and variables that measure the separation between origin and destination regions. A violation of standard minimal assumptions for least squares estimation may be associated with two problems: spatial autocorrelation within the residuals, and spatial autocorrelation within explanatory variables. This paper compares a spatial econometric solution with the spatial statistical Moran eigenvector spatial filtering solution to accounting for spatial autocorrelation within model residuals. An example using patent citation data that capture knowledge flows across 257 European regions serves to illustrate the application of the two approaches.

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Notes

  1. Both estimation procedures are numerically intensive, making execution of a sufficient number of replications to take advantage of the Law of Large Numbers (e.g., 10,000) impractical.

  2. The two models we compare assume a different DGP for the underlying empirical (i.e., generation of knowledge flows) data. If, for example, we assume a DGP consistent with the eigenvector spatial filter specification, the results of a Monte Carlo study would, of course, show that model to produce superior estimates and inferences. In contrast, if we conduct a Monte Carlo experiment that assumes the Bayesian model DGP, of course, that model would produce superior estimates and inferences. We see little value in showing that each specification is superior when its DGP generates flows. Already existing Monte Carlo studies of both methods (i.e., spatial filtering and Bayesian spatially structured effects) show good performance when the true DGP is consistent with the specific model specifications. Another such study seems unneeded and unnecessary.

  3. Although the five-year horizon appears to be short, it does capture a significant amount of a typical patent’s citation life. Note that the mean citation lag of all high-technology patent citations in 1985–2002 is 4.62 years.

  4. NUTS is an acronym of the French for the “nomenclature of the territorial units for statistics,” which is a hierarchical system of regions used by the statistical office of the European Community for the production of regional statistics. At the top of the hierarchy are the NUTS-0 regions representing countries, with NUTS-1 regions below, representing regions within countries, and then NUTS-2 regions reflecting subdivisions of NUTS-1 regions.

  5. The frequentist model specification includes fixed effects, which are the origin/destination balancing factors. The Bayesian model is not an unconstrained version of the gravity model. This latter specification includes random effects, which involve four degrees of freedom. These two specifications reflect the common fixed versus random effects debate. Furthermore, if we were to make both model specifications identical, then both models would produce identical estimates. MCMC estimation (Bayesian) is merely a different way of maximizing the objective/likelihood function (à la maximum likelihood techniques; frequentist).

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Authors and Affiliations

  1. School of EPPS, University of Texas at Dallas, 800 W. Campbell Road, Richardson, TX, 75080, USA

    Daniel A. Griffith

  2. Department of SocioEconomics, Vienna University of Economics and Business, Welthandelsplatz 1, A-1020, Vienna, Austria

    Manfred M. Fischer

  3. Texas State University, San Marcos, USA

    James LeSage

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  1. Daniel A. Griffith
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  2. Manfred M. Fischer
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  3. James LeSage
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Correspondence to Daniel A. Griffith.

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Griffith, D.A., Fischer, M.M. & LeSage, J. The spatial autocorrelation problem in spatial interaction modelling: a comparison of two common solutions. Lett Spat Resour Sci 10, 75–86 (2017). https://doi.org/10.1007/s12076-016-0172-8

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  • DOI: https://doi.org/10.1007/s12076-016-0172-8

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