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Some Practical Applications Of Moran'S I'S Exact Conditional Distribution

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  • Michael Tiefelsdorf

Abstract

ABSTRACT This article uses statistical results on ratios of quadratic forms to present a closed theory of Moran's I's exact conditional distribution, its moments and feasible range subject to a significant underlying Gaussian spatial process. These results allow one (i) to give by means of the conditional expectation a direct link of an observed value of Moran's I to the autocorrelation level of an underlying spatial process, (ii) to calculate the distribution of local Moran's Ii subject to the forces of a global spatial process which permits the exploration of local heterogeneities within the global process, and (iii) to distinguish between two competing spatial processes. A preliminary regression model to describe the spatial distribution of bladder cancer incidence rates in 219 counties of the former German Democratic Republic is used to demonstrate the feasibility and flexibility of the proposed exact conditional approach. Furthermore, a theoretical basis to address the migration problem in spatial epidemiology is given and tested against simple spatial clustering.

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  • Michael Tiefelsdorf, 1998. "Some Practical Applications Of Moran'S I'S Exact Conditional Distribution," Papers in Regional Science, Wiley Blackwell, vol. 77(2), pages 101-129, April.
    • Handle: RePEc:bla:presci:v:77:y:1998:i:2:p:101-129
    DOI: 10.1111/j.1435-5597.1998.tb00710.x
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    Cited by:

    1. Michael Tiefelsdorf & Daniel A Griffith, 2007. "Semiparametric Filtering of Spatial Autocorrelation: The Eigenvector Approach," Environment and Planning A, , vol. 39(5), pages 1193-1221, May.
    2. Lawrence A. Brown & Sang-Il Lee & Linda Lobao & Su-Yeul Chung, 2005. "Continuity amidst Restructuring: The U.S. Gender Division of Labor in Geographic Perspective, 1970 and 1990," International Regional Science Review, , vol. 28(3), pages 271-301, July.
    3. Yajuan Wang & Xi Wu & Hongbo Zhu, 2022. "Spatio-Temporal Pattern and Spatial Disequilibrium of Cultivated Land Use Efficiency in China: An Empirical Study Based on 342 Prefecture-Level Cities," Land, MDPI, vol. 11(10), pages 1-15, October.
    4. Min Xu & Chang-Lin Mei & Na Yan, 2014. "A note on the null distribution of the local spatial heteroscedasticity (LOSH) statistic," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(3), pages 697-710, May.

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