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I would like to study the spatial dependency in my dataset of a variable (crop yield) spread across a country with 250 sites.

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A first guess was to use a variogram on the data. However, I am not sure if the distribution of the sites is appropriate to perform a variogram analysis.

What are the assumptions made on the data to perform such analysis, and how might the clustering structure be problematic?

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A variogram makes no assumptions on the data, it is a measure of the data, and if binned, it is a summary measure of the data.

Your clustered points mean you will have a lot of close pairs of points going into your variogram. This might give you a good estimate of the variogram at small distance, which is a good thing. There's often problems when samples are spaced out, then you don't have a good estimate of the variogram at any distance below the distance of the closest pair. You don't have that problem.

Your clusters aren't regularly spaced, so you'll probably get a lot of distance pairs at a wide range of distances.

Your problems might come if you then go on to try and predict from the variogram, for example using Kriging. You'll get very large error estimates on points away from your clusters, most likely, compared to a sample design with more even coverage. Your estimates might only be useful within those circular buffers, and outside it might revert to a point estimate at the mean of your data with very wide errors.

Another problem might be bias in your sampling design. Suppose these are pollution measurements and you have clusters because you have put a few instruments in each town. You'll get biased predictions in the countryside. But again, that's not related to the variogram given the clustered sampling design that you have, its inherent in any biased sampling design.

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