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GEOSTATS: Contiguity matrix standarization in autocorrelation analysis

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  • ELSA NICKL
    Hello , I am doing a research about the application of spatial analysis techniques oriented to relate educational and geographical variables. I started
    Message 1 of 2 , Aug 14, 2000
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      Hello ,

      I am doing a research about the application of spatial analysis techniques
      oriented to relate educational and geographical variables. I started with the
      analysis of autocorrelation for some variables using lattice data.
      I would like to know in which case it is neccesary to standarize the
      contiguity matrix by rows. I obtained Moran Indexes for both cases (with and
      without standarization) and in both the results were very different.

      Thanks


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    • Roger Bivand
      ... In general, standardisation gives more influence to the neighbours of polygons with few neighbours, and less to the neighbours of polygons with many
      Message 2 of 2 , Aug 14, 2000
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        On Mon, 14 Aug 2000, ELSA NICKL wrote:

        >
        > Hello ,
        >
        > I am doing a research about the application of spatial analysis
        > techniques
        > oriented to relate educational and geographical variables. I started
        > with the
        > analysis of autocorrelation for some variables using lattice data.
        > I would like to know in which case it is neccesary to standarize the
        > contiguity matrix by rows. I obtained Moran Indexes for both cases
        > (with and
        > without standarization) and in both the results were very different.
        >
        In general, standardisation gives more influence to the neighbours of
        polygons with few neighbours, and less to the neighbours of polygons with
        many neighbours. If all your polygons have the same number of neighbours,
        the coefficients will be similar, while if some have very few neighbours
        and others have very many, the results may differ - as in your case, I
        guess. A reference to the key article: Tiefelsdorf M, Griffith D, Boots B
        1998 A variance stabilizing coding scheme for spatial link matrices,
        Environment and Planning A, 31, pp. 165-180.

        Have a look at the distribution of numbers of neighbours of your polygons,
        and see if there are some with many, and some with very few neighbours.

        Good luck!


        Roger Bivand
        Economic Geography Section, Department of Economics, Norwegian School of
        Economics and Business Administration, Breiviksveien 40, N-5045 Bergen,
        Norway. voice: +47 55 95 93 55; fax +47 55 95 93 93
        e-mail: Roger.Bivand@...
        and: Department of Geography and Regional Development, University of
        Gdansk, al. Mar. J. Pilsudskiego 46, PL-81 378 Gdynia, Poland.

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