[R-sig-Geo] spatial autocorrelation, grids, and the ks-test
Roger.Bivand at nhh.no
Mon Feb 8 10:38:32 CET 2010
On Fri, 5 Feb 2010, ingalapuma wrote:
> I would like to run the Moran's I on a .img file of forest composition
> change categories.
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There are many questions here. Firstly, Moran's I is for continuous
variables, not categories. For categories, use join count statistics.
Secondly, the possible dependency in your data will be being driven both
by any inherent (subatantive) dependency, and by the match (or mismatch)
between the scale(s) of the phenomena and the resolution of your grid. In
addition, there may be background variables that drive the dependency,
like slope or elevation, so observed dependency even for correct scaling
may not say anything about the effect of contiguity.
You can of course compute spatial autocorrelation of your data (treat them
as having point support and use a distance criterion like the raster step
for rook neighbours or the diagonal step for queen neighbours. It's just
that the test will only reflect your resolution and possibly omitted
variables. With raster data, especially with fine resolution, one
typically has many "observations" of the same "natural" entity or object,
leading to apparent spatial autocorrelation.
> I need to know if I can treat the categories as
> independent for performing the two sample Kolmogorov-Smirnov on relative
> fire frequency distributions of these forest composition change categories.
> Without considering spatial autocorrelation, the fire frequency
> distributions of the categories are significantly different according to the
> ks-test (which I was advised to use). It is obvious that these categories
> are spatially clustered as are the areas of similar fire frequency, so my
> questions/statements are:
I think that you could consider checking your KS results against a better
null, that is generating from distributions with the same level of spatial
dependence (or rather not use KS, but fit a model and evaluate it in the
context of dependence).
> 1. Does it make sense to run the Moran's I on the thematic grid data with
> R? (Have tried to convert it to vector in both ArcGIS and Imagine and have
> run into errors...presumably because of size and complexity?)
In spdep use dnearneigh() to make a list of neighbours. If there is a lot
of data in the raster, you will not gain any insight anyway - consider
vigorous subsetting. Contrast the subsets.
> 2. I have no idea how to do anything in R (besides the ks-test) and am
> completely new to it's spatial tools (although I am keen to learn and have
> loaded several of the packages/libraries).
Since the KS test maybe isn't a good idea anyway, perhaps starting afresh?
You'd need to vary your raster resolution anyway to get any idea on how
scaling works. This is going to take substantial time to do right. In your
best case, join count tests are insignificant, and you can risk KS, but if
you can see spatial patterning and have put the question on the table, you
need an alternative approach.
> 3. How would I incorporate the p-value results of the Moran's I (if I can
> get it to work) into the ks-test of my relative frequencies?
> I have ordered the spatial data with R book but I figured I'd cut to the
> chase and see if you all could help me get a jumpstart on this.
> Thanks ahead of time.
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no
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