[R-sig-Geo] Geographically weighted regression on categorical variable

[Barry Rowlingson]

I don't think the point pattern analysis will help you at all - your
sampling locations aren't a point pattern (although they form a
pattern of points) - their location has been decided by whoever
decided where to take the samples. Point pattern analysis is
appropriate where you are interested in the process that produced the
pattern of points.

If you had continuous data the answer might be obvious - kriging with
distance-to-source as a regression covariate, and then your answer as
to whether your continuous variable was related to the distance would
be inferred from the regression parameter and its standard error, as
per any GLM. I think there's an example like this for gstat where the
usual meuse data set is used to model Zinc with distance-to-river as a
covariate.

Your complication is that your categorical variable makes it a
*multinomial* regression problem. If this wasn't a spatial problem,
and your data were independent samples in some sort of designed
experiment, then standard multinomial regression techniques can be
applied and out pop estimates and standard errors of the regression
coefficients of your distance-to-source covariate. You could, as an
initial experiment, treat your data like this and see what happens.

But you have spatial data, and hence spatially correlated
observations, so you can't just throw it into a standard multinomial
and believe the inference. You would seem to want some sort of
multinomial regression kriging approach, but I can't find anything
appropriate. Discussions over coffee with colleagues just now
dissolved into all sorts of stuff I don't understand, but maybe we'll
come up with something after a few more coffees.

Barry






On Mon, Jul 18, 2016 at 7:13 PM, Guy Bayegnak <Guy.Bayegnak at gov.ab.ca> wrote:
>
> Hi All,
>
> I am trying to perform geographically weighted regression on categorical variables.  The majority of answers I found on the web suggest that this is not doable or not recommended.  I found only one post from Roger Bivan (https://stat.ethz.ch/pipermail/r-help/2007-September/141586.html ) that indicated that it was possible, and that the R-sig-geo list is more focused on this kind of question. I have therefore registered, but I am not sure if the mailing list is "searchable".
>
> I have point data collected over a geographical area A.  My data are groundwater quality type. And I have 3 types. When I plot it of a map it looks like 2 of the types are clustered and occur next to each other.  My suspicion is that these two clustered type may be influenced by their proximity to the some potential sources.  I used the spatstats package to explore the data,  using L-cross function.  The result of the analysis show that the 3 types appear to be influenced by the source, although the two groundwater that are clustered appear to deviate much more from the theoretical L-cross.  Now I am trying to explore the relationship between the water types and the potential source using geographically weighted regression on categorical variables.  Most of the material a read deals with continuous variables, and tend to focus on areal (polygons) features rather than point features.
>
> Is there any way to perform geographically weighted regression on points categorical variables using R?
>
> Thanks,
> GAB
>
>
>
>
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