[R-sig-Geo] Dispersion term u in errorsarlm in spdep

[Thomas Vladeck]

Roger,

Thanks so much for your thoughtful reply. (And apologies for my lack of
experience in the field!)

On this:

This would be a spatially structured random effect, as distinct from an
> unstructured random effect in this context. See LeSage & Pace (2009) for
> more details.


Would the Besag-York-Mollié model be a more appropriate option? I have been
through the documentation on CARBayes [1], The LeSage & Pace book you
recommended, and as much other material as I could ingest & understand, and
this seems appropriate - but I'm not sure!

Here:

PS. Your comment about data size shows that you have not examined the
> method= argument to errorsarlm() - method="Matrix" will work for large
> sparse symmetric spatial neighbour graphs. However, your "distance.matrix"
> object may not be sparse - just full of lots of very small values which
> could without loss be set to zero.


It was the latter option that I hadn't realized was possible. Thanks so
much for the recommendation!

Tom

[1]
https://cran.r-project.org/web/packages/CARBayes/vignettes/CARBayesvignette.pdf




On Mon, Oct 19, 2015 at 5:44 AM, Roger Bivand <Roger.Bivand at nhh.no> wrote:

> On Sun, 18 Oct 2015, Thomas Vladeck wrote:
>
> Hi,
>>
>> I'm working on a marketing project, and could use a bit of technical help
>> and advice. I'm trying to model the spatial interdependence of a product's
>> usage (my dependent variable is the amount of usage in a given zip code
>> [1]) through a spatial error model, which is of the form:
>>
>> y = Xb + u // u = λWu + e // e ~ N(0, σ^2)
>>
>> In *Bayesian Statistics and Marketing* [2] the dispersion vector u is
>> interpreted as the "influence" of one unit over those it's related to via
>> the weighting matrix. Extracting this would be helpful from a marketer's
>> perspective as it would be advantageous to promote usage in an influential
>> area.
>>
>> I have two questions:
>>
>> First, is this a reasonable interpretation of the dispersion vector? It's
>> not clear to me that this is a reasonable interpretation.
>>
>
> This would be a spatially structured random effect, as distinct from an
> unstructured random effect in this context. See LeSage & Pace (2009) for
> more details.
>
>
>> Second, I'm using the errorsarlm function in spdep and I'd like to extract
>> u from the returned object. According to the documentation, it does not
>> seem that u is returned directly. Can I calculate it as follows?
>>
>> u = λWu + e
>> u = (I - λW)^(-1) * e
>>
>>
> The (legacy) predict method for sarlm objects reports a spatial signal, as
> distinct from the spatial trend (X \beta). Work is ongoing to fold recent
> work, including the GSoC 2015 project, on prediction into spdep.
>
> Roger
>
> PS. Your comment about data size shows that you have not examined the
> method= argument to errorsarlm() - method="Matrix" will work for large
> sparse symmetric spatial neighbour graphs. However, your "distance.matrix"
> object may not be sparse - just full of lots of very small values which
> could without loss be set to zero.
>
> Which would be the following in code:
>>
>> W <- mat2listw(
>>  distance.matrix,
>>  style = "W"
>> )
>>
>> error.sp.model <- errorsarlm(
>>  formula = fm,
>>  data = model.data[, -1],
>>  listw = W
>> )
>>
>> lambda    <- error.sp.model$lambda
>>
>> # (I - λW)^-1
>> inv.W      <- ginv((diag(1, nrow(distance.matrix)) - lambda *
>> distance.matrix))
>>
>> # the result i'm looking for
>> u <- inv.W %*% as.vector(error.sp.model$residuals)
>>
>>
>> Thanks so much! Really appreciate the help.
>>
>> Tom
>>
>>
>> [1] Actually, the average across all zip codes that start with the same
>> first three digits. (I needed to do this to make the problem
>> computationally tractable
>> [2] http://www.perossi.org/home/bsm-1
>>
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>>
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>>
>
> --
> Roger Bivand
> Department of Economics, Norwegian School of Economics,
> Helleveien 30, N-5045 Bergen, Norway.
> voice: +47 55 95 93 55; fax +47 55 95 91 00
> e-mail: Roger.Bivand at nhh.no
>



-- 
Thomas P. Vladeck
+1 202 390 0838
tomvladeck.com

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