Thank you very much, Dr. Bivand!! This is VERY helpful. One last question --
When testing for spatial autocorrelation of a variable with MC randomization
procedures, testing the residuals for spatial autocorrelation with a Global
Moran's I or testing the lagrange multiplier diagnostics for spatial
dependence, ***is there a substantive reason for choosing an asymmetric vs
symmetric KNN spatial weights matrix?** My hunch is that there is not
substantive reason for choosing one vs another. I really appreciate your
feedback and guidance.

Dustin

On Fri, Dec 17, 2010 at 4:56 AM, Roger Bivand <Roger.Bivand@nhh.no> wrote:

> On Thu, 16 Dec 2010, Dustin Duncan wrote:
>
>  hi all,
>>
>> i have one question ***does it matter if the KNN spatial weights matrix is
>> asymmetric or symmetric for linear spatial autoregressive models? *** i am
>> getting slightly different findings depending on the weights matrix
>> specification for the Lagrange multiplier diagnostic for spatial
>> dependence.
>> i am using Bivand's spdep package for these analysis. i've read that GeoDA
>> can't fit KNN spatial models due to the asymmetry (for now), but that
>> using
>> KNN is legitimate for these spatial autoregresive models. however, i could
>> use the asymmetric version or the symmetric one (though making KNN
>> symmetric
>> sounds a bit strange to me). any insight is greatly appreciated!!
>>
>
> The approximation to the Jacobian used in GeoDa requires that W be
> symmetric (or similar to symmetric, Ord, 1975). The MC approximation used in
> the Matlab toolbox does not. In spdep, you can use method="eigen" for
> smaller data sets, "LU" for exact Jacobian larger data sets, or "MC", with
> intrinsically asymmetric W. However, note that the differences between a
> symmetricised KNN W and the original one may not be large, as in SAR
> (simultaneous rather than CAR conditional) SSE terms, you do get W'W
> appearing, though its influence will vary. Try checking to see whether
> results vary enough to change your inferences:
>
> library(spdep)
> example(columbus)
> knn4 <- knn2nb(knearneigh(coordinates(columbus), k=6))
> knn4
> knn4s <- make.sym.nb(knn4)
> lw <- nb2listw(knn4)
> lws <- nb2listw(knn4s)
> summary(lagsarlm(CRIME ~ HOVAL + INC, data=columbus, listw=lw))
> summary(lagsarlm(CRIME ~ HOVAL + INC, data=columbus, listw=lws))
>
> So if you have to make the KNN weights symmetric to use - say - GeoDa, it
> may not matter that much in practice.
>
> Hope this helps,
>
> Roger
>
>
>
>> thanks and happy holidays, dustin
>>
>>
>>
> --
> Roger Bivand
> 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@nhh.no
>
>


-- 
Dustin T. Duncan, ScM
Doctoral Candidate
Harvard School of Public Health
Department of Society, Human Development, and Health

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