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A Variance-Stabilizing Coding Scheme for Spatial Link Matrices

Author

Listed:
  • M Tiefelsdorf

    (Department of Geography, Centre for Earth Observation Science, University of Manitoba, 211 Isbister Building, Winnipeg, Manitoba R3T 2N2, Canada)

  • D A Griffith

    (Department of Geography, Syracuse University, 144 Eggers Hall, Syracuse, NY 13244, USA)

  • B Boots

    (Department of Geography and Environmental Studies, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada)

Abstract

In spatial statistics and spatial econometrics two coding schemes are used predominately. Except for some initial work, the properties of both coding schemes have not been investigated systematically. In this paper we do so for significant spatial processes specified as either a simulta-neous autoregressive or a moving average process. Results show that the C -coding scheme emphasizes spatial objects with relatively large numbers of connections, such as those in the interior of a study region. In contrast, the W -coding scheme assigns higher leverage to spatial objects with few connections, such as those on the periphery of a study region. To address this topology-induced heterogeneity, we design a novel S -coding scheme whose properties lie in between those of the C -coding and the W -coding schemes. To compare these three coding schemes within and across the different spatial processes, we find a set of autocorrelation parameters that makes the processes stochastically homologous via a method based on the exact conditional expectation of Moran's I . In the new S -coding scheme the topology induced heterogeneity can be removed in toto for Moran's I as well as for moving average processes and it can be substantially alleviated for autoregressive processes.

Suggested Citation

  • M Tiefelsdorf & D A Griffith & B Boots, 1999. "A Variance-Stabilizing Coding Scheme for Spatial Link Matrices," Environment and Planning A, , vol. 31(1), pages 165-180, January.
    • Handle: RePEc:sae:envira:v:31:y:1999:i:1:p:165-180
    DOI: 10.1068/a310165
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    References listed on IDEAS

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    1. Luc Anselin & Daniel A. Griffith, 1988. "Do Spatial Effecfs Really Matter In Regression Analysis?," Papers in Regional Science, Wiley Blackwell, vol. 65(1), pages 11-34, January.
    2. Luc Anselin & Raymond J. G. M. Florax, 1995. "Small Sample Properties of Tests for Spatial Dependence in Regression Models: Some Further Results," Advances in Spatial Science, in: Luc Anselin & Raymond J. G. M. Florax (ed.), New Directions in Spatial Econometrics, chapter 2, pages 21-74, Springer.
    3. L W Hepple, 1995. "Bayesian Techniques in Spatial and Network Econometrics: 2. Computational Methods and Algorithms," Environment and Planning A, , vol. 27(4), pages 615-644, April.
    4. Sawa, Takamitsu, 1978. "The exact moments of the least squares estimator for the autoregressive model," Journal of Econometrics, Elsevier, vol. 8(2), pages 159-172, October.
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