[R-sig-Geo] correlation betwee two grids acounting for univariate spatial autocorrelation, how to do it?

[JiHO]

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:
> Hi Jesús,
>
> If you are talking about gridded maps, you could consider Syrjala's test
> (Stephen E. Syrjala 1996. A Statistical Test for a Difference between the
> Spatial Distributions of Two Populations. Ecology 77:75–80.
> http://dx.doi.org/10.2307/2265656). It is implemented in the ecespa package.
>
>
> Cheers,
>
> Marcelino
>
>
>
>
> El 20/02/2014 19:51, Jesús Muñoz escribió:
>>
>> Dear colleagues,
>>
>> I needed to measure the association degree (and ideally its p-value)
>> between
>> two maps, one representing richness of European bryophytes and the other
>> vascular plant richeness. From the maps it is clear the two patterns are
>> reversed: bryophytes 'rule' in the north, and vascular plant richness is
>> higher in  southern Europe.
>>
>> I have used isodata algorithm followed by a Maximum-likelihood
>> classification to generate a map showing four different areas in Europe
>> (lowbryo-lowvasc, lowbryo-highvasc, highbryo-lowvasc, and
>> highbryo-highvasc). Additionally, I would like to run a correlation
>> analysis
>> but corrected for the univariate spatial correlation of each variable
>> (bryophytes and vascular plant richness); a global correlation map-to-map
>> is
>> meaningless here.
>>
>> I found a statistic that would suit my needs (Lee, S.-I. 2001. Developing
>> a
>> bivariate spatial association measure: An integration of Pearson's r and
>> Moran's I. Journal of Geographical Systems 3(4): 369-385). It is
>> implemented
>> in 'The Map Comparison Kit' (http://www.riks.nl/mck/), but it return
>> values
>> outside the -1 to 1 values, which makes me think there is something wrong
>> in
>> the code or the statistic.
>>
>> Can somebody guide me to a R package allowing me to measure the
>> association
>> between these two grids?
>>
>> thanks in advance,
>>
>> Jesús
>>
>>
>>
>>
>>
>> *************************************************************************
>>
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>>
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>>
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>>
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>>
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>>
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>>
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>>
>>
>>
>> KRAKEN research group (environmental modelling, data processing &
>> analysis):
>>
>>
>> http://www.unex.es/investigacion/grupos/kraken
>>
>>
>>
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>>
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>>
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>>
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