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AI-GEOSTATS: Variowin equations and cross-validation

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  • Juliann Aukema
    Hi, Variowin/equation questions: I have fitted models using variowin and am now trying to plot them in other graphics programs. Vario2D produces a file that I
    Message 1 of 4 , Apr 9, 2001
      Hi,

      Variowin/equation questions:

      I have fitted models using variowin and am now trying to plot them in
      other graphics programs. Vario2D produces a file that I can use to plot the
      experimental variograms, but in the modeling I get an equation like:
      gamma(h) = 14.2 + 6.399 Sph. 169.66(h)
      I am wondering how to turn the exponential, spherical or power into some
      sort of equation that another program can plot. Can anyone point me in the
      direction of these equations (other than the manual, which is out of
      print)?
      While I'm asking, the sill reported in variowin is always about half of
      what the sill appears to be from looking at it graphically. What is the
      reason for this difference?

      Cross-validation:

      Any hints for using cross-validation to compare models? What does it
      mean if the average error and the square root of the average squared
      normalized error are of both models are similar and close to 0 or 1
      respectively?
      Specifically, I fitted models using Variowin (the file is too large
      for Geoeas) and I found a pure nugget model in the same way. Variowin
      gives a goodness of fit measure, and the fitted model was in all cases
      "better" than the pure nugget model. When I did the cross validation in
      Geoeas, the models seemed pretty good (for example, with values raning
      from 0-54, average error = -0.093, and the standard deviation of the Zscore
      was 1.16. The estimated values were somewhat underestimated, only ranging
      from 0-17). However, the pure nugget effect seemed to be pretty good also
      and not terribly different from the model (in this example, av. error =
      1.665, which is further from 0, but sd of zscore = 1.027, which is closer
      to 1. The estimates ranged from 0-14). Several models I looked at didn't
      seem to have huge differences between the fitted model and a pure nugget
      model.
      So, does this mean that there is not a clear spatial effect here?
      That there may be a weak spatial effect? That there is definitely not a
      spatial effect? Is there some way to test for significance of difference
      between the models?. . .

      Thank you.

      Juliann Aukema
      jaukema@...



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    • Sara Kustron
      Let me take a stab at the cross-validation part first: Deutch and Journel (GSLib 1998) suggest examining cross-validated residuals keeping in mind that kriging
      Message 2 of 4 , Apr 9, 2001
        Let me take a stab at the cross-validation part first:

        Deutch and Journel (GSLib 1998) suggest examining cross-validated residuals
        keeping in mind that kriging estimates should be symmetric around zero with
        minimal spread, globally and conditionally unbiased, homoscedastic, and
        spatially-independent. I would hesitate on quantitatively evaluating a
        model strictly on one error statistic (see Isaaks and Srivastava 1989).

        As for the choice of your model, it depends on what makes sense for what you
        are studying. If you have a pure nugget effect (no detectable range) but
        you think there truly is a dependent effect then you might conclude that the
        spatial dependence is occurring at a resolution below the minimum lag
        distance. I've seen some folks recommend shortening the x-axis of the
        variogram to about 1/6 the total lag distance and concentrate on modeling
        the short lags well.

        Variowin: I've been using the numerical output file (.var) and importing it
        into excel to plot the "data" variograms. Just remember that the values
        aren't "standardized" in that file, so for example if you want to plot the
        covariance in the form of a variogram you have to subtract the covariance
        from the global sample variance, etc. As for the model parameters, the
        range, nugget, and sill are given in the Model program. You can plug those
        values directly into the equation for the spherical model for plotting in
        another program.

        Hope this helps.

        *************************************************
        Sara Kustron
        Boston University Department of Geography
        675 Commonwealth Avenue Rm 445
        Boston, MA 02215

        skustron@...
        office: (617) 353-8341
        **************************************************




        ----- Original Message -----
        From: "Juliann Aukema" <jaukema@...>
        To: <ai-geostats@...>
        Sent: Monday, April 09, 2001 5:22 PM
        Subject: AI-GEOSTATS: Variowin equations and cross-validation


        > Hi,
        >
        > Variowin/equation questions:
        >
        > I have fitted models using variowin and am now trying to plot them in
        > other graphics programs. Vario2D produces a file that I can use to plot
        the
        > experimental variograms, but in the modeling I get an equation like:
        > gamma(h) = 14.2 + 6.399 Sph. 169.66(h)
        > I am wondering how to turn the exponential, spherical or power into some
        > sort of equation that another program can plot. Can anyone point me in the
        > direction of these equations (other than the manual, which is out of
        > print)?
        > While I'm asking, the sill reported in variowin is always about half of
        > what the sill appears to be from looking at it graphically. What is the
        > reason for this difference?
        >
        > Cross-validation:
        >
        > Any hints for using cross-validation to compare models? What does
        it
        > mean if the average error and the square root of the average squared
        > normalized error are of both models are similar and close to 0 or 1
        > respectively?
        > Specifically, I fitted models using Variowin (the file is too large
        > for Geoeas) and I found a pure nugget model in the same way. Variowin
        > gives a goodness of fit measure, and the fitted model was in all cases
        > "better" than the pure nugget model. When I did the cross validation in
        > Geoeas, the models seemed pretty good (for example, with values raning
        > from 0-54, average error = -0.093, and the standard deviation of the
        Zscore
        > was 1.16. The estimated values were somewhat underestimated, only ranging
        > from 0-17). However, the pure nugget effect seemed to be pretty good also
        > and not terribly different from the model (in this example, av. error =
        > 1.665, which is further from 0, but sd of zscore = 1.027, which is closer
        > to 1. The estimates ranged from 0-14). Several models I looked at didn't
        > seem to have huge differences between the fitted model and a pure nugget
        > model.
        > So, does this mean that there is not a clear spatial effect here?
        > That there may be a weak spatial effect? That there is definitely not a
        > spatial effect? Is there some way to test for significance of difference
        > between the models?. . .
        >
        > Thank you.
        >
        > Juliann Aukema
        > jaukema@...
        >
        >
        >
        > --
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        > * As a general service to the users, please remember to post a summary of
        any useful responses to your questions.
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        "unsubscribe ai-geostats" followed by "end" on the next line in the message
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        >


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      • Isobel Clark
        Juliann Judging the fit of a model cannot be done from the summary statisics. See my 1986 paper The Art of Cross Validation (full reference at
        Message 3 of 4 , Apr 10, 2001
          Juliann

          Judging the fit of a model cannot be done from the
          summary statisics. See my 1986 paper "The Art of Cross
          Validation" (full reference at
          http://uk.geocities.com/drisobelclark/Publications.html)

          Better to use something like Noel Cressie's goodness
          of fit statistic which tests the semi-variogram fit to
          the experimental with a weighted least squares.

          Isobel Clark

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        • Isobel Clark
          AAgh, sprry people, Mark Burnett just pointed out that I missed a bit in the Web reference: http://uk.geocities.com/drisobelclark/resume/Publications.html Mea
          Message 4 of 4 , Apr 10, 2001
            AAgh, sprry people, Mark Burnett just pointed out that
            I missed a bit in the Web reference:


            http://uk.geocities.com/drisobelclark/resume/Publications.html

            Mea culpa
            Isobel Clark

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