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Re: AI-GEOSTATS: data transformation and variograms

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  • Nicholas Lewin-Koh
    Hi, I think the problem might be even more subtle. Essentially you are looking at a marked point process, and trying to apply methods designed principally for
    Message 1 of 2 , Apr 19, 2001
      Hi,
      I think the problem might be even more subtle. Essentially you are looking
      at a marked point process, and trying to apply methods designed
      principally for data that is continuous throughout the sampling domain.

      I would suggest looking at the following paper:
      Stoyan and Waelder 2000. On variograms in point process statistics
      II. Models of markings and ecological interpretation. Biometrical journal
      42(2):171-187

      Another approach you might think about is spatial cdf estimation. take a
      look at the work of cressie and friends.

      Nicholas

      CH3
      |
      N Nicholas Lewin-Koh
      / \ Dept of Statistics
      N----C C==O Program in Ecology and Evolutionary Biology
      || || | Iowa State University
      || || | Ames, IA 50011
      CH C N--CH3 http://www.public.iastate.edu/~nlewin
      \ / \ / nlewin@...
      N C
      | || Currently
      CH3 O Graphics Lab
      School of Computing
      National University of Singapore
      The Real Part of Coffee kohnicho@...

      On Thu, 19 Apr 2001, Juliann Aukema wrote:

      > Hi. I have a question about transforming data.
      >
      > I have infection prevalence data for many points- a proportion of
      > trees infected. Numbers are between 0 and 1. Sample size varies for the
      > different points (because density of trees varies). When I plot a variogram
      > of the prevalence data, I get a nice sill for about 4000 meters and then a
      > rise in the variogram. If I take the residuals of prevalence against
      > elevation the second rise goes away. Biologically this all makes sense and
      > makes a nice story.
      > However for some other analyses that I also did with this data, I
      > was advised to logit transform the prevalence data because it is a
      > proportion and should be binomially distributed.
      > If I plot the variogram of the logit transformed prevalence, the
      > first sill is much less distinct if it is there at all - this seems to be
      > mostly due to one point, the last point before the rise, which now goes up
      > instead of being about even with the previous point. ( I guess this
      > difference is due to the stretching of zero prevalence values that occurs
      > with the logit transformation.) And if I look at smaller lags, it looks
      > like a power function with no sill. Biologically, that is harder to
      > explain. If I plot the residuals of the (logit transformed prevalence)
      > against ( elevation), the variogram has a nice sill and is similar, even
      > prettier than the analysis of the untransformed data (but based on the
      > previous variogram, I don't have a very good reason for plotting the
      > residuals).
      > My question, then is whether the logit transformation is necessary
      > and/or appropriate for the geostatistical analysis. Does it make sense to
      > use the transformed data for both variograms, for just the residuals
      > (because the residuals are based on regression for which the transformation
      > ought to be done) or for neither?
      > Thank you very much.
      >
      > Juliann
      > jaukema@...
      >
      >
      >
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