I was thinking about this issue, and correct me if I'm wrong -

If you row-standardize the distance weights, you will in effect rescale

them, but you will not change the scale of the weights themselves, correct?

I.e., row standardization means dividing the weight for each observation by

the total # of non-zero elements for that row, correct? Well, each

observation by definition in a distance matrix has the same number of

"neighbors" (i.e., all n-1), correct? So 1/dij (or whatever your distance

matrix is) becomes 1/dij/n.

Is that going to affect your fundamental interpretation of the structure of

spatial dependence? Probably not - unless you're trying to interpret rho or

lambda in terms of the distance units (which I wouldn't presume to do,

anyway...).

Or am I off base?

-----Original Message-----

From: Roger Bivand

To: Jill Caviglia-Harris

Cc: r-sig-geo at stat.math.ethz.ch

Sent: 2/27/04 2:40 PM

Subject: Re: [R-sig-Geo] LM tests

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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