[R-sig-Geo] calculate r² between kernel-based spatial variables

[Quets Jan]

Hello list,


I have a rather theoretical question (with practical finality):

how to correctly calculate a coefficient of determination between two spatial variables which values (pixels in a window) are both kernel-based?

suppose a point pattern X, and a point pattern Y, in the same window

make density maps of both:


densX = density.ppp(X)         #the first spatial variable

densY = density.ppp(Y)          #the second spatial variable


suppose densX and densY have both 128x128 = 16384 values (pixels)

suppose there is some correlation between densX and densY.

The significance of this relationship however depends on which pixels to include in the formula: neighboring pixel values are in general similar and dependent.


I had an approach in mind:

1) choose an epanechnikov kernel (because it is spatially bound, with supposed total width = 2h) instead of a gaussian kernel (which in theory is not spatially bound) to construct both density maps with density.ppp() 

2) include in the formula of the coefficient of determination, only pixels which lay at least 2h (the total width of the epanechnikov kernel) from each other.


Would this be an sound and appropriate way to calculate the coefficient of determination between two kernel-based spatial variables (e.g. densX and densY)??

Thank you,
Jan