[R-sig-Geo] LM tests

[Roger Bivand]

On Fri, 27 Feb 2004, Munroe, Darla K wrote:

> 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.
> 
I'm not sure about that. What you are dividing by is the row sum:

\sum_j w_{ij}, and w_{ij} = 1/d_{ij}, so the sum will be smaller for 
places a long way from others, and larger for places near most others, 
won't it?

In the R spirit, try it out:

> set.seed(1)
> try <- 1/as.matrix(dist(cbind(rnorm(100), rnorm(100))))
> diag(try) <- 0
> summary(rowSums(try))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  45.07   68.97   90.05   91.78  113.40  153.10 

So places with different "connectedness" will get "flattened", I think. 
But then I'm not sure that full matrices are so very informative (there is 
a literature about reconstructing maps of relative position from neighbour 
graphs, I think, so the sparse binary weights actually carry quite a lot 
of information - more parsimonious anyway).

Roger

> 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