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I was doing some geostatistical analysis (variogram+kriging) for a "presence only" type data in a species distribution modeling context. Since, we know that when estimating the (empirical) variogram, the attribute is basically assumed to be a realization of continuous random variables (although an attribute can occur in counts too). If the attribute is just the presence, and no sub-categories then all the values at all positions will be same (say 1, if we denote a presence by 1). Hence the variogram can not be calculated, not even the indicator variogram. One of the approaches to deal with such data pseudo absences or background data were generated using some algorithm e.g. Maxent etc (see e.g. [1, 2]). The pseudo absences are generated taking many factors into account and stacked/combined with actual data. This is equivalent to merely generating random positions (x, y coordinates) and giving them an absence status (say 0s). The new data is now a binary data with two categories, presence 1 and absences 0.
How many absences (as compared to actual data) should be generated and how to decide it?

Reference

  1. Tomislav Hengl, Henk Sierdsema, Andreja Radović, Arta Dilo, Spatial prediction of species’ distributions from occurrence-only records: combining point pattern analysis, ENFA and regression-kriging, Ecological Modelling, Volume 220, Issue 24, 24 December 2009, Pages 3499-3511.

  2. https://cran.r-project.org/web/packages/dismo/vignettes/sdm.pdf

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  • @PolyGeo please edit this question too, if needed.
    – Asad Ali
    Feb 9, 2017 at 18:51

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Interesting method to use; have you considered running the model with equal numbers of pseudo absences and then increasing or decreasing the proportion of known absences to pseudo absences to see if a trend appears in how it effects the model output? This approach may also give you insight into the uncertainty of the model as well.

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  • There are no known absences. The data is always de-trended before variogram and kriging analysis. As you might be aware Maxent employs environmental predictors and bias to generate pseudo absences, using some regression model. It's like imposing an surface on pseudo absences. So the final data actually, in terms of geostatistics, suffers from external drift that needs to be removed before variogram is estimated. In my view, it's a conflict of concepts. You need trend-free data for kriging... Maxent gives you data that highly depends on external variables.
    – Asad Ali
    Feb 10, 2017 at 9:47

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