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Simplifying The Normalizing Factor In Spatial Autoregressions For Irregular Lattices

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  • Daniel A. Griffith

Abstract

ABSTRACT The Jacobian term appears in certain likelihood functions as a normalizing factor; it ensures that the use of variable transformations still leads to probability density functions whose complete integration yields unity. This term is particularly troublesome when dealing with spatial autoregressive models in that it requires numerically intensive solutions to accompanying parameter estimation problems. For these types of autoregressive models, the Jacobian term is a function of the eigenvalues of the n‐by n connectivity matrix that depicts the geographic configuration of the areal units under study. This paper reports on Jacobian approximation results, based upon supercomputer and other experiments, for irregular lattices.

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  • Daniel A. Griffith, 1992. "Simplifying The Normalizing Factor In Spatial Autoregressions For Irregular Lattices," Papers in Regional Science, Wiley Blackwell, vol. 71(1), pages 71-86, January.
    • Handle: RePEc:bla:presci:v:71:y:1992:i:1:p:71-86
    DOI: 10.1111/j.1435-5597.1992.tb01749.x
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    Cited by:

    1. Lauridsen, J. & Kosfeld, R., 2004. "A wald Test for Spatial Nonstationarity," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 22, pages 1-12, Diciembre.
    2. JesúS Mur & F. Javier Trívez, 2003. "Unit Roots and Deterministic Trends in Spatial Econometric Models," International Regional Science Review, , vol. 26(3), pages 289-312, July.
    3. Jørgen Lauridsen & Reinhold Kosfeld, 2006. "A test strategy for spurious spatial regression, spatial nonstationarity, and spatial cointegration," Papers in Regional Science, Wiley Blackwell, vol. 85(3), pages 363-377, August.
    4. James P. LeSage & R. Kelley Pace, 2008. "Spatial Econometric Modeling Of Origin‐Destination Flows," Journal of Regional Science, Wiley Blackwell, vol. 48(5), pages 941-967, December.
    5. Smirnov, Oleg & Anselin, Luc, 2001. "Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach," Computational Statistics & Data Analysis, Elsevier, vol. 35(3), pages 301-319, January.

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