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correlation betwee two grids acounting for univariate spatial autocorrelation, how to do it?

1 message · Jo Frabetti

#
Hi,

Sorry to revive an old topic but I have the exact same problem and was
wondering whether you found a solution. I've been looking into Lee's L
but have the same concerns. I had implemented Syrjala's test (before
the ecespa package even existed!) but it is not appropriate for the
type of data I am dealing with now (not abundances).

I would be very interested in any pointer.

The current state of my thinking about this issue is this:
- let A and B be two variables sampled at the same locations
- let r be a measure of correlation between A and B at all sites (a
simple one would be Pearson's correlation coefficient)
- let I be a measure of the global spatial autocorrelation of one
variable (for, example Moran's I)
- then, we can simulate a spatial pattern with the same spatial
autocorrelation characteristic as A (same I) and the same range of
values (by sampling them in observed values of A for example), do the
same for B, compute r for these two simulated distributions.
Repeat this 1000 times and compare r_observed to the 1000 simulated r;
that would give me a measure of the probability of getting my observed
correlation at random, taking into account the autocorrelation of each
variable.

Does this thinking make sense?

If it does, so far I am stuck trying to simulate distributions with
the same Moran's I as my observed distribution. I've seen:
https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012679.html
but I am not sure how to get from rho to I or how to estimate rho on
my observed data.

I have also found:
Simulating two?dimensional autocorrelated surfaces
R Haining, DA Griffith, R Bennett - Geographical Analysis, 1983
http://onlinelibrary.wiley.com/store/10.1111/j.1538-4632.1983.tb00785.x/asset/j.1538-4632.1983.tb00785.x.pdf?v=1&t=iaqvy4zx&s=64a6bf69d77c2588c66c332006f380f78cc8b80f
which points to
Algorithm 9: Simulation of autocorrelation for aggregate data
MF Goodchild - Environment and Planning A, 1980
http://envplan.com/fulltext_temp/0/a121073.pdf
but it is a rather brute force approach to getting close to I and it
does not seem feasible with a large number of sites.

Thanks in advance for your help! Sincerely,


On Thu, Feb 20, 2014 at 8:40 PM, Marcelino de la Cruz
<marcelino.delacruz at upm.es> wrote: