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2429Re: [ai-geostats] Re: Software for Automatic Semivariogram Estimation

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  • Edzer J. Pebesma
    Feb 28, 2006
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      Isobel Clark wrote:

      > Behrang
      > What weighting do you use in the weighted least squares?
      > Isobel

      I have found choosing suitable weights always a frustrating
      event. Cressie's weights, let's say N_h/[(gamma(h))^2], has
      attractive properties, both intuitively and statistically. Here,
      gamma(h) is the model value, not the sample variogram
      value (because that might be zero; think of binary data). N_h
      is the number of point pairs used to estimate semivariance
      at lag (interval) h.

      It's downside is that while fitting the variogram, gamma(h)
      changes, and so the weights change. This has consequences:
      while fitting, the criterion you try to minimize may actually
      increase while the fit gets better. This is hard to deal with.
      If you calculate e.g. a weighted R^2, and look at the trace,
      it will go up, down, and then up, down, etc. The context changes.

      If you fix gamma(h), say to it's starting values, then the final
      fit may very much depend on which starting values you used.

      Isobel, how do you deal with this?

      As an alternative, (and the default value in gstat under R or
      S-Plus), I now tend to use N_h/h^2 [*], which is equivalent to
      Cressie's weights for a linear variogram with no nugget. It
      works often, but will give rediculusly large weight to a
      semivariance value with h very close to zero (think duplicate
      measurements). Besides these two, gstat has the options
      of weights N_h, and of no (=constant) weights.

      [*] If I'm correct, this was first suggested in a paper by
      Zhang and ... in Computers & Geosciences, early nineties.
      I strongly disliked it then, but consider it acquired taste.
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