When trying to smooth spatial data, I found this very helpful tutorial regional smoothing.

There are two steps to estimate a "smoothed" value for a geographical point:

  • Finding K nearest neighbors
  • Calculate the local G statistics

My initial idea was only to calculate the average value with the KNN, to smooth the data across the geographical zone. But from this article, I also discovered Gettis-Ord statistic/local G statistic with the localG function. The author indicated that it can also smooth the spatial data.

But the locla G statistic is a zero centered variable, and the value can not directly represent an estimation of the initial variable.

Is it possible to use local G statistics to really "smooth" the data and,if so, then how?

In this example of local G official documentation of the spdep package, we can see that initial values (xyz$val) are between 30 and 120, and the g statistic value are between -5 and 5.

1 Answer 1


The local G* values for some quantity Q have no further use in making "smoothing" maps of Q. They show how Q_i compares to the neighbours (defined however: KNN, or adjacency, or distance) and for large neighbourhoods will naturally appear smooth (because two neighbouring points will share a large fraction of neighbours). The G* statistic is used in the maps of the linked article because they want to show smoothed maps of where Q is higher or lower than average.

If you want to show smoothed maps of Q, then compute the average Q over neighbours (+self), which I showed how to do in an answer to your previous question. There's no use for G* here.

The rationale for using G* in analyses is that there is a distributional model involved, which means you can make inferences about the values like saying "this area is statistically significantly higher than the average". If you compute means of Q then its not so straightforward to say if "27" is statistically significantly higher than "20" because there's no statistical distributional model there.

If you just want a smoothed map then averaging Q over neighbours will do that. If you want to make a smoothed map based on some underlying rationale, then you need a statistical model which you can justify - for example your data as a sample from a random field with some structure - and then your smoothing has meaning beyond "looking smooth". It all depends what your big question is...

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.