Moran's I vs. spatial rho
On Thu, 13 Apr 2006, Larry Layne wrote:
The relevant question would be why you expect them to be the same, when they are esimated using different techniques? ...
Apparently I have had a misconception rattling around in my head regarding estimates using the 2 approaches. Let's see if I have misconceived this next question also. I had assumed that if I used the row stochastic connectivity definition for polygons in an SAR model (Y = pWY + XB + e) that the rho estimates would be constrained between +1 and -1, similar to a Pearson correlation coefficient. Is this incorrect?
Sorry, not quite right. The constraints are the inverses of the minimum and maximum eigenvalues of W: library(spdep) data(columbus) 1/range(eigenw(nb2listw(col.gal.nb, style="W"))) is [1] -1.533849 1.000000 so the upper bound of unity holds for W with row sums of 1. For other styles of weights:
1/range(eigenw(nb2listw(col.gal.nb, style="B")))
[1] -0.3351569 0.1672385
1/range(eigenw(nb2listw(col.gal.nb, style="S")))
[1] -1.7865492 0.8866948 for example. In fact, singularities only happen on the boundaries, but for rho outside the bounds, the process would be wild. Roger
Larry Layne ljlayne at unm.edu
Roger Bivand Economic Geography Section, Department of Economics, Norwegian School of Economics and Business Administration, Helleveien 30, N-5045 Bergen, Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43 e-mail: Roger.Bivand at nhh.no