# How can I conduct Geographically Weighted Analysis using an exponential decay function?

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
• 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
• 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
• 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