[Openspace] Bounds on spatial lag coefficient

[Luis Galvis]

Krista,
Your recollection was on the right track. The parameter boundaries do have
to do with the eigenvalues of the weights matrix. In page 234 of Anselin &
Bera 1998, it says that the constraints imposed in a maximum likelihood
framework require the spatial autoregressive parameter to be constrained to
lie in the interval 1/(min eigenvalue of W) and 1/(max eigenvalue of W), so
if the constraints are imposed in the maximization procedure I'll say that
you shouldn't find otherwise, unless your estimation, for whatever fluky
reasons, do not converge to to the optimal value of the likelihood function.
Regarding this point the chapter also refers to Anselin (1982), "A note on
Small Sample Properties of Estimators in a First-Order Spatial
Autoregressive Model, Environment and Planning A, 14, 1023-1030.

Luis.

On 3/19/07, William Pan <wpan at jhsph.edu> wrote:
>
> You might also want to look at:
> de Jong, P., C. Sprenger & F van Veen (1984) "On extreme values of
> Moran's I and Geary's c" /Geographical Analysis/ 16:17-24
>
> Bill
>
> **********************************
> William K.Y. Pan, DrPH MS MPH
> Department of International Health
> Johns Hopkins Bloomberg School of Public Health
> 410-502-2141 (office)
> 410-502-6733 (fax)
> **********************************
>
>
>
> Julia Koschinsky wrote:
>
> >Krista,
> >
> >The bounds are larger than -1 and smaller than 1 (note that you can
> >sometimes get values for spatial coefficients outside of this allowable
> >parameter space with GMM/IV estimators but this is a problem).
> >
> >A possible reference to use is Luc Anselin's "Under the Hood" p. 10
> >http://sal.uiuc.edu/users/anselin/papers/hood.pdf
> >
> >Julia
> >
> >-----Original Message-----
> >From: openspace-bounces at sal.uiuc.edu [mailto:
> openspace-bounces at sal.uiuc.edu]
> >On Behalf Of Krista.Collins at statcan.ca
> >Sent: Monday, March 19, 2007 4:09 PM
> >To: openspace at sal.uiuc.edu
> >Subject: [Openspace] Bounds on spatial lag coefficient
> >
> >Hello,
> >
> >What are the bounds of the possible values for the spatial lag
> >coefficient, rho, in the spatial lag model?  I have written down in my
> >own notes that it is bounded between the smallest and largest
> >eigenvalues of the weights matrix, but I cannot find any reference to
> >confirm this is true.  Does any one know the answer?
> >
> >Thanks in advance.
> >
> >Krista
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> >
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