## GEOSTATS: Spatial autoregressive parameter restrictions

Expand Messages
• Kelejian and Robinson discuss this issue in: Kelejian and Robinson (1995), Spatial Correlation: A Suggested Alternative to the Autoregressive Model, in New
Message 1 of 1 , Nov 12 10:27 PM
• 0 Attachment
Kelejian and Robinson discuss this issue in:

Kelejian and Robinson (1995), "Spatial Correlation: A Suggested Alternative
to the Autoregressive Model," in New Directions in Spatial Econometrics
edited by Luc Anselin and R. Florax, Springer

Of course, as you state, the variance-covariance matrix and the inverse
variance-covariance matrix are still p.d.

I have never encountered a situation such as you mention. Of course, I
usually restrict myself to row-stochastic matrices or matrices similar to a
row-stochastic matrix. In addition, positive spatial dependence is almost
guaranteed for my data.

I do have one idea (possibly bad!). Consider the SAR variance-covariance
matrix that you mentioned with symmetric W.

SAR: Sigma=inv((I-2 rho W + rho^2 W'W))

Now W'W=WW by symmetry of W. The multiplication of an adjacency matrix by
an adjacency matrix (i.e., WW) captures the effect of neighbors of the
neighbors and by construction this has a positive weight in inv(Sigma) via
rho^2. A large value for rho may be allowing the model to differentially
weigh the nearby and far dependence. Hence, by respecifying W (picking via
max likelihood) one might be able to obtain values for rho more in the
conventional range.

Ripley (1981) points out that for small values of rho, SAR will usually
produce autoregressive estimates approximately half that of CAR. This is
easy to see with the above formula as the squared rho term virtually
vanishes for small rho. In my work, SAR has always had a lower magnitude
autoregressive parameter than CAR.

By the way, did the SAR or CAR have the highest likelihood?

Kelley Pace
2164 CEBA Building
Department of Finance
Louisiana State University
Baton Rouge, LA 70803-6308
kelley@...
www.spatial-statistics.com
www.finance.lsu.edu/re
225-388-6256
225-334-1227 (FAX)
--
*To post a message to the list, send it to ai-geostats@....
*As a general service to list users, please remember to post a summary
of any useful responses to your questions.
*To unsubscribe, send email to majordomo@... with no subject and
"unsubscribe ai-geostats" in the message body.
DO NOT SEND Subscribe/Unsubscribe requests to the list!
Your message has been successfully submitted and would be delivered to recipients shortly.