[R-sig-Geo] LM tests

[Munroe, Darla K]

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
> 
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-- 
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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