LM tests

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LM tests

Jill Caviglia-Harris
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"

-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
Economics and Business Administration, Breiviksveien 40, N-5045
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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LM tests

Luc Anselin

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
> Economics and Business Administration, Breiviksveien 40, N-5045
> Bergen,
> Norway. voice: +47 55 95 93 55; fax +47 55 95 93 93
> e-mail: Roger.Bivand at nhh.no
>
> _______________________________________________
> R-sig-Geo mailing list
> R-sig-Geo at stat.math.ethz.ch
> https://www.stat.math.ethz.ch/mailman/listinfo/r-sig-geo
>