# [R-sig-Geo] LM tests

Luc Anselin anselin at uiuc.edu
Fri Feb 27 21:46:42 CET 2004

```On Feb 27, 2004, at 2:28 PM, Jill Caviglia-Harris wrote:

> Roger:
>
>> Have you tried (probably yes) and does it make a difference? Are the
>> results from a binary IDW and a row standardized IDW very different?
> Is
>> your IDW matrix full or sparse? Can Moran's I be applied instead
> (despite
>> its covering lots of misspecification problems)? Are the IDW weights
>
>> symmetric (probably, but not always)?
>
> Yes, the IDW weights are symmetric - each observation in the sample is
> considered a neighbor - therefore the inverse distance between the
> neighbors indicates the "degree of neighborliness"  I will row
> standardize these numbers and look into a rule for determining a
> neighbor form a non-neighbor in my sample (for the binary weight
> matrix)
> and get back to you about the differences.
>
>> I'm not sure why distances should be helpful if the data are observed
> on
>> areal units, so that measuring distances is between arbitrarily
> chosen
>> points in those units, a change of support problem. That may be why
> there
>> aren't methods too, though there's no reason not to try to develop
> things.
>> But error correlation specified by distance does movbe rather close
> to
>> geostatistics, doesn't it?
>
> I haven't tried these other ways of defining the weights matrix (as of
> yet) because of Anselin (1988) "...distance decay has a meaningful
> economic interpretation, scaling the rows so that the weights sum to
> one
> may result in a loss of that interpretation"

If I can pitch in, this is what this means. If you want to relate
something
to a measure of "potential" in the old Isard sense, then the potential
variable sum over j of y_j / d_ij is the same as a spatial lag with
1/d_ij as the weights. Row-standardization would be that each of
these 1/d_ij would be rescaled by the sum over j of 1 / d_ij, which
is not quite the same as what Darla suggested.
I think in a (much) earlier post Roger made the point that inverse
distance may not be that different from contiguity or distance band,
especially when d_ij is "large" (there is an obvious scale dependence
here). For example, if two units are 200 miles apart (e.g., the
centroids
of some counties in Western US), 1/d_ij is 0.005 and 1/ d_ij2 is
0.000025,
so much for "weights". Rescaling these would make them all relative
to the sum of the 1/d_ij
L.

>
> -Jill
>
>
>
>>>> Roger Bivand <Roger.Bivand at nhh.no> 02/27/04 02:40PM >>>
> On Fri, 27 Feb 2004, Jill Caviglia-Harris wrote:
>
>> List members:
>>
>> I have been using the function lm.LMtests developed using the spdep
>> package to test for spatial lag and error.  My problem is that these
>> tests assume that the weights matrix is row standardized, while I
> have a
>> weights matrix that is set up as the inverse distance between
> neighbors.
>
> Certainly lm.LMtests() prints a warning, and the tradition it comes
> from
> usually presupposes row standardisation. Curiously, quite a lot of the
>
> distribution results in Cliff and Ord actually assume symmetry, which
> can
> lead to fun with negative variance in Geary's C and join count
> statistics
> even with row standardised weights.
>
>>   Converting it into a row standardized matrix would result in the
> loss
>> of important information.  Have there been any functions developed
> that
>> any of you know about that are not dependent upon this assumption?
>
> Have you tried (probably yes) and does it make a difference? Are the
> results from a binary IDW and a row standardised IDW very different? Is
>
> your IDW matrix full or sparse? Can Moran's I be applied instead
> (despite
> its covering lots of misspecification problems)? Are the IDW weights
> symmetric (probably, but not always)?
>
> I'm not sure why distances should be helpful if the data are observed
> on
> areal units, so that measuring distances is between arbitrarily chosen
>
> points in those units, a change of support problem. That may be why
> there
> aren't methods too, though there's no reason not to try to develop
> things.
> But error correlation specified by distance does movbe rather close to
>
> geostatistics, doesn't it?
>
> Any other views, anyone?
>
> Roger
>
>> Thanks.  -Jill
>>
>>
>> ***************************************************
>> Jill L. Caviglia-Harris, Ph.D.
>> Assistant Professor
>> Economics and Finance Department
>> Salisbury University
>> Salisbury, MD 21801-6860
>>    phone: (410) 548-5591
>>    fax: (410) 546-6208
>>
>> _______________________________________________
>> R-sig-Geo mailing list
>> R-sig-Geo at stat.math.ethz.ch
>> https://www.stat.math.ethz.ch/mailman/listinfo/r-sig-geo
>>
>
> --
> Roger Bivand
> Economic Geography Section, Department of Economics, Norwegian School
> of
> Bergen,
> Norway. voice: +47 55 95 93 55; fax +47 55 95 93 93
> e-mail: Roger.Bivand at nhh.no
>
> _______________________________________________
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> R-sig-Geo at stat.math.ethz.ch
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>

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