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AI-GEOSTATS: Pattern-plus

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  • Yetta Jager
    Hi Lorenz, I m glad you are finding the Pattern-plus approach useful. I was unable to send this response to you directly--it looks like your server rejects
    Message 1 of 1 , May 31, 2001
      Hi Lorenz,

      I'm glad you are finding the Pattern-plus approach useful. I was unable to
      send this response to you directly--it looks like your server rejects mail
      from the .gov domain, which may be why it won't send mail here
      either? Some responses to your questions below.

      1. When calculating multiple linear regression (pattern-)model i did
      not include xy-coordinates of the sample sites as aditional predictor
      variables allthough there is considerable correlation between coordinates
      and heavy metal contents (but there is no trend in variograms!). is that ok?

      Sure, the covariates that you included in your model probably explain
      geographic drift in a more mechanistic and meaningful way.

      2. (backtransformed) semivariograms of the pattern-models still have a
      "good shape" suggesting a spatial/random variability. shouldn't they behave
      like "white noise"?

      I'm assuming you mean residual semivariograms still show autocorrelation
      structure (i.e., nugget << sill)? I would interpret this to mean that the
      deterministic model did not explain all spatial variation or remove all
      autocorrelation. That's ok -- I think its reasonable to expect small
      scale autocorrelation that is not due to in situ conditions because of
      local transport processes and other variables that were not included.
      The good news is that kriging can help add predictive power (pattern+).
      Remember to use a different subset of data to estimate the semivariogram

      3. how do i get backtransformed residuals from ln-transfortmed data ?
      when i backtransform ln-residuals of the regression/pattern-models negative
      ln-values are just interpreted as positive values below 1,0. is it possible
      to get residuals by substracting (backtransformed) predicted values
      (=exp(regression model)) from the original (= untransformed) values?

      Yes, I think the latter idea is a good one. In general I'd stay out of
      log-world when possible. Especially if the variances are going to be needed.

      4. simultanous estimation of drift and semivariogram with a single
      realization is rigorously not possible. Are there some (simple)
      aproximations for the semivariogram? What about the iterative solution for
      the simultaneaous inference of drift and semivariogram, how does it work in

      I wrote a FORTRAN program to do the iterative estimation, but that was
      quite a while ago and I think it needs some work (maybe only to find the
      right machine constants). I was last adding the capability to vary the sill
      by stratum, and still hope to get back to it someday. If you are facile
      with statistical coding and want to try it, you are welcome but I wouldn't
      be able to offer support. It uses Linpack routines for the generalized
      least squares regression and Minpack routines to estimate parameters of the
      semivariogram using iteratively reweighted non-linear least squares. I
      think Gstat could probably be used to implement it now, although it
      wouldn't be an automated stepwise procedure with visual feedback on
      anisotropy etc.. The idea of the iterative analysis derives from:

      S.P. Neuman and E.A. Jacobsen. 1984. Analysis of nonintrinsic spatial
      variability by residual kriging with application to regional groundwater
      levels, Math Geology 16(5): 499-519.

      If anyone else interested in this, there is a pdf file on my website,
      which is listed below, entitled "Spatial Modeling of Landscape Pattern".

      Good luck,


      Yetta Jager
      Environmental Sciences Division
      Oak Ridge National Laboratory
      P.O. Box 2008, MS 6036
      Oak Ridge, TN 37831-6036

      For packages, please replace "P.O. Box 2008" with
      "Bethel Valley Road" in the address above.

      OFFICE: 865/574-8143
      FAX: 865/576-8543
      Work email: jagerhi@...
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      WEBpage: http://www.esd.ornl.gov/~zij/

      "How like fish we are: ready, nay eager, to seize upon whatever new thing
      some wind of circumstance shakes down upon the river of time! And how we
      rue our haste, finding the gilded morsel to contain a hook."
      Aldo Leopold, 1949

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