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AI-GEOSTATS: SUMMARY: semivariogram for binary data

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  • Malin Fahller
    Hi again and thanks for your answers, you have really helped me out. Here are the answers I have received so far: ______________________ Pierre Goovaerts
    Message 1 of 1 , Jan 16, 2001
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      Hi again and thanks for your answers,
      you have really helped me out.

      Here are the answers I have received so far:

      ______________________
      Pierre Goovaerts answered:

      Hi Malin,

      In theory and under stationary of order 2,
      indicator semivariogram values should not exceed
      0.25 which is the maximum variance that you could obtain
      for indicator variables, for a proportion of 50%.
      I am wondering whether you have used the option
      "standardize sill" in gamv, which could explain
      these values larger than 1.

      Pierre

      __________________________

      YES I used that option and that seems to explain the situation!

      ___________________________

      Marco Alfaro answered:

      Dear Malin:
      The semivariogram of an indicator variable is always less than 1.

      Proof:
      The experimental semivariogram is (1/2) of the mean of the squared differences Z(xi+h)-Z(xi) but the values of Z are 0 or 1, then the semivariogram is (1/2) of the mean of the absolutes values of Z(xi+h)-Z(xi). Now you use the triangular inequality and you get that the semivariogram is less than 1.

      Regards
      Marco Alfaro

      _________________________


      Brian Gray wrote:

      believe that geostatisticians resolve this by setting "out of bounds" values to the extremes (eg 0 or 1). However, statisticians resolve this issue for nonspatial data by using an inverse link to a cdf--which, of course, is on [0,1]. Examples include logistic and probit regression. See Gotway, CA and WW Stroup. 1997. A generalized linear model approach to spatial data analysis and prediction. JABES 2: 157-178. Gumpertz, ML, C Wu and JM Pye. 2000. Logistic regression for Southern Pine Beetle outbreaks with spatial and temporal correlation. Forest Science 46: 95-107. Brian

      ___________________________________



      Malin Fahller
      Geographical Information Technology
      Luleå University of Technology
      SE- 971 87 LULEÅ
      SWEDEN

      phone: (+46) (0)920 914 66
      fax: (+46) (0)920 728 30





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