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[ai-geostats] n-dimension distance

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  • Christophe Z Guilmoto
    Hi, I have been trying to compare the autocorrelation of a dataset, using both spatial distance and other non spatial metrics. Yes, non spatial metrics (I m a
    Message 1 of 3 , Oct 12, 2004
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      Hi,
      I have been trying to compare the autocorrelation of a dataset, using both spatial distance and other non spatial metrics. Yes, non spatial metrics (I'm a demographer).

      1) I have a first problem when I want to compute the distance using more than two non spatial variables (ie, coordinates): I don't know of any software that would let me compute autocorrelation or a semivariogram over various distance ranges when the distance is to be computed from more than two coordinates. I'd rather avoid computing distances and autocorrelation with my usual statistical software.
      Any suggestion ?

      2) Once I do that, I have a further problem comparing spatial and non spatial autocorrelation: distances are follow different metrics and distributions are differently shaped. The idea is to contrast spatial proximity with "proximity" measured with other variables. To compare these distances, should I sort my pairs of observations into distance quantiles (the first 100 pairs, etc.), into standardized distance (with maximum range =100 or average distance=100)?
      Any idea on that?

      Thanks

      CZG




      Christophe Z. Guilmoto
      Demographe, IRD
      CEIAS-EHESS
      54, Boulevard Raspail
      75006 Paris  France
      Tél.: 06 67 19 87 10
    • Edzer J. Pebesma
      ... - there is software that lets you calculate variograms in three dimensions - there is open source software that you can modify for your purpose - you could
      Message 2 of 3 , Oct 12, 2004
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        Christophe Z Guilmoto wrote:
        Hi,
        I have been trying to compare the autocorrelation of a dataset, using both spatial distance and other non spatial metrics. Yes, non spatial metrics (I'm a demographer).

        1) I have a first problem when I want to compute the distance using more than two non spatial variables (ie, coordinates): I don't know of any software that would let me compute autocorrelation or a semivariogram over various distance ranges when the distance is to be computed from more than two coordinates. I'd rather avoid computing distances and autocorrelation with my usual statistical software.
        Any suggestion ?
        - there is software that lets you calculate variograms in three dimensions
        - there is open source software that you can modify for your purpose
        - you could use multidimensional scaling to approximate your higher
        dimensional space with a lower (2? 3?) dimensional one.

        2) Once I do that, I have a further problem comparing spatial and non spatial autocorrelation: distances are follow different metrics and distributions are differently shaped. The idea is to contrast spatial proximity with "proximity" measured with other variables. To compare these distances, should I sort my pairs of observations into distance quantiles (the first 100 pairs, etc.), into standardized distance (with maximum range =100 or average distance=100)?
        Any idea on that?
        calculation in feature space is always sensitive to scaling, as is calculation of
        distances in space-time. In the geostatisics realm I don't know of applications
        of the approach you suggest. In machine learning, people use covariance
        kernels in feature space, and like in geostatistics the problem is the inference
        of a suitable model: isotropy is an illusion when scales don't match naturally.

        Last idea: attend geoENV in Neuchatel, which starts tomorrow,
        and try to talk to as many people as you can.

        Best regards,
        --
        Edzer
      • Jakob Petersen
        Dear Christophe, Maybe you could use Mantel statistics. You first need a relevant multivariate distance measure (see e.g. Legendre & Legendre 198? Numerical
        Message 3 of 3 , Oct 12, 2004
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          Dear Christophe,
          Maybe you could use Mantel statistics. You first need a relevant multivariate
          distance measure (see e.g. Legendre & Legendre 198? "Numerical Ecology"), then
          you create a distance matrix with distances in simillarity (m x n). Finally the
          geographical distance matrix (m x n) is correlated with your multivariate
          distance matrix through Monte Carlo randomisations. Another reference here is
          'isolation by distance' in Sokal & Rohlf 199? "Biometry".

          Jakob

          Quoting Christophe Z Guilmoto <guilmoto@...>:

          > Hi,
          > I have been trying to compare the autocorrelation of a dataset, using both
          > spatial distance and other non spatial metrics. Yes, non spatial metrics
          > (I'm a demographer).
          >
          > 1) I have a first problem when I want to compute the distance using more
          > than two non spatial variables (ie, coordinates): I don't know of any
          > software that would let me compute autocorrelation or a semivariogram over
          > various distance ranges when the distance is to be computed from more than
          > two coordinates. I'd rather avoid computing distances and autocorrelation
          > with my usual statistical software.
          > Any suggestion ?
          >
          > 2) Once I do that, I have a further problem comparing spatial and non
          > spatial autocorrelation: distances are follow different metrics and
          > distributions are differently shaped. The idea is to contrast spatial
          > proximity with "proximity" measured with other variables. To compare these
          > distances, should I sort my pairs of observations into distance quantiles
          > (the first 100 pairs, etc.), into standardized distance (with maximum range
          > =100 or average distance=100)?
          > Any idea on that?
          >
          > Thanks
          >
          > CZG
          >
          >
          >
          >
          > Christophe Z. Guilmoto
          > Demographe, IRD
          > CEIAS-EHESS
          > 54, Boulevard Raspail
          > 75006 Paris France
          > Tél.: 06 67 19 87 10


          --
          Jakob Petersen
          Research Technician
          School of Biological Sciences
          M. Trimmer laboratory (1.05)
          Queen Mary
          University of London
          Mile End
          London
          E1 4NS
          United Kingdom

          Tel +44 (0)20 7882 3200
          Fax +44 (0)20 8983 0973

          Directions:
          http://www.qmul.ac.uk/contact/directions.shtml

          Map:
          http://www.qmul.ac.uk/contact/mileend.shtml
          We are in lab 1.05 on the 1st floor in building 24. The main entrance is to the
          East.
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