I was thinking about this issue, and correct me if I'm wrong 
If you rowstandardize 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 nonzero elements for that row, correct? Well, each observation by definition in a distance matrix has the same number of "neighbors" (i.e., all n1), 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 CavigliaHarris Cc: rsiggeo at stat.math.ethz.ch Sent: 2/27/04 2:40 PM Subject: Re: [RsigGeo] LM tests On Fri, 27 Feb 2004, Jill CavigliaHarris 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. CavigliaHarris, Ph.D. > Assistant Professor > Economics and Finance Department > Salisbury University > Salisbury, MD 218016860 > phone: (410) 5485591 > fax: (410) 5466208 > > _______________________________________________ > RsigGeo mailing list > RsigGeo at stat.math.ethz.ch > https://www.stat.math.ethz.ch/mailman/listinfo/rsiggeo >  Roger Bivand Economic Geography Section, Department of Economics, Norwegian School of Economics and Business Administration, Breiviksveien 40, N5045 Bergen, Norway. voice: +47 55 95 93 55; fax +47 55 95 93 93 email: Roger.Bivand at nhh.no _______________________________________________ RsigGeo mailing list RsigGeo at stat.math.ethz.ch https://www.stat.math.ethz.ch/mailman/listinfo/rsiggeo 
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On Fri, 27 Feb 2004, Munroe, Darla K wrote:
> I was thinking about this issue, and correct me if I'm wrong  > > If you rowstandardize 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 nonzero elements for that row, correct? Well, each > observation by definition in a distance matrix has the same number of > "neighbors" (i.e., all n1), correct? So 1/dij (or whatever your distance > matrix is) becomes 1/dij/n. > \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 CavigliaHarris > Cc: rsiggeo at stat.math.ethz.ch > Sent: 2/27/04 2:40 PM > Subject: Re: [RsigGeo] LM tests > > On Fri, 27 Feb 2004, Jill CavigliaHarris 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. CavigliaHarris, Ph.D. > > Assistant Professor > > Economics and Finance Department > > Salisbury University > > Salisbury, MD 218016860 > > phone: (410) 5485591 > > fax: (410) 5466208 > > > > _______________________________________________ > > RsigGeo mailing list > > RsigGeo at stat.math.ethz.ch > > https://www.stat.math.ethz.ch/mailman/listinfo/rsiggeo > > > >  Roger Bivand Economic Geography Section, Department of Economics, Norwegian School of Economics and Business Administration, Breiviksveien 40, N5045 Bergen, Norway. voice: +47 55 95 93 55; fax +47 55 95 93 93 email: Roger.Bivand at nhh.no
Roger Bivand
Department of Economics Norwegian School of Economics Helleveien 30 N5045 Bergen, Norway 
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