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I made a semivariogram in R using package gstat, variogram() function. I want to see if there is spatial autocorrelation in the residuals of my model (species abundance as a function of habitat, across sites spaced a few km to 900 km apart, using a glmm).

My units are in km, and so my interpretation is that the range is just over 100 km until spatial autocorrelation is no longer an "issue". I am wondering if someone can explain why the nugget seems so high? Does this mean that even at similar locations, there is still a relatively high degree of difference? Or, does this wavy variogram mean I should adjust my number of lags and lag distance until I get a more typical shape?

Using gstat, default breaks and max distance

In order to investigate a bit further, I also used the function variog() in package geoR, and used breaks=seq(0,100,10), to try and look just at the closer distances (using same points and same model residuals). This one indicates that the closest points are more different, which also doesn't make sense. Maybe this indicates there is no spatial autocorrelation, and that my model accounts for this already.

Using geoR, up to 100km

I found this excellent source, "Geostats without tears", and on page 51 has some good advice on fitting variograms. By this advice, my first one seems to have the correct range. So this goes back to the first question - how do I interpret this?

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    There seems to be no spatial autocorrelation in your residuals, so this is rather good news in your case, isn't it ? – radouxju Oct 2 '15 at 5:25
  • I was not sure that I was interpreting it correctly, but if having such a high nugget and a wavy plot indicates almost no autocorrelation (as opposed to a misfitting of a variogram), then yes - that's great news! Thanks for your opinion on interpretation, good to know I am not way off. – snowtosurf Oct 2 '15 at 17:01
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I am wondering if someone can explain why the nugget seems so high? Does this mean that even at similar locations, there is still a relatively high degree of difference?

Yes, a high nugget effect (high semivariance at origin) tells there is a weak (or none) spatial dependence (autocorrelation) among sample data at small distances. It could be the case the structure of data having a shorter range than the sampling interval, but the second picture seems to indicate it is not the case either.

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