[R-sig-Geo] Moran's I vs. spatial rho

[Roger Bivand]

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