I have some points (representing 30 study sites) and I want to calculate the weighted mean of several variables (landscape layers) using a negative exponential decay (weights function) to give more weight to the landscape features closer to the points (study sites) than the features (grid cells) further away. (The series of underlying grid layers represent landscape features such as roads; habitat etc.)

Also, how can I use spatial statistics to find the optimal distance (bandwidth) for my distance-decay function? In the literature everyone resorts to creating buffers (vector) at different distances (say 1km, 3km & 5km) to quantify the variables and then uses statistics to determine which buffer distance is significant. Other ecologists (Rhodes et al. 2006) have used the “negative exponential distance weighted density” of each variable and provided a scale parameter (L) which controls how rapidly the influence (ie weighting) of the variable declines with distance, eg L = EXP(-0.002*Distance)

I’m using ArcGIS spatial statistics; grid (raster) spatial analysis tools; and investigating GWmodel for R-stats from an earlier post.

  • This sounds like you need help with a HW problem. Check out the SPGWR package cran.r-project.org/web/packages/spgwr/vignettes/GWR.pdf – SoilSciGuy Mar 24 '14 at 2:37
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    Also, a post should only contain 1 question, not two. – SoilSciGuy Mar 24 '14 at 2:37
  • Thanks for the reference. I'm still unclear how to first calculate the weighted mean of all my variables, within a decay distance of my sites. Sorry, I'm new to this and thought the optimal distance was part of the same decay problem (or I could just use a biological meaningful distance such as the home range size). – HJPreece Mar 24 '14 at 7:34
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    I haven't time to provide a full answer, so please forgive me for pointing out a direction in this comment. Your principal question is answered by a convolution of an exponential kernel with the landscape grid. This is efficiently performed in R using fft. Cross-validation can be used to address your second question. For advice about that consider posting that question on Cross Validated. – whuber Mar 24 '14 at 14:48
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    Four people have already voted to close your Question, so I recommend following the advice of @whuber to remove the second question from your Question and post that at stats.stackexchange.com. You can revise your Question using the edit button beneath it. A protocol here is "one question per Question". Welcome to GIS SE! 6 upvotes already on your first Question is excellent! – PolyGeo Mar 25 '14 at 4:23

You should look into variograms (look in the documentation under kriging). The variogram indicates the level of cross-correlation between observed features. If you plot the variogram you see it rising rapidly, then tapering off to level (the so-called sill). That would give you a quantitative indication of your "optimal distance". Quite possibly, though, you 30 points are not enough to show a stable trend but I suggest you give it a try.

  • Thanks for the suggestion. Before I can look at the variogram I'll still need a way to calculate the weighted means of all my variables, or, perhaps resort to simply buffering my points and intersecting them with the underlying landscape layers and forget the idea of using weighted means. – HJPreece Mar 24 '14 at 7:42
  • It is unclear how a variogram could be used to address any aspect of this question. Could you be more explicit about that? – whuber Mar 24 '14 at 14:45

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