[R-sig-Geo] spatially correlated heterosckedasticity and spatial econometric models (cont.)

[Sam Field]

Sorry about that - I hit "send" to soon! As I was saying...

List,

It seems like a sensible model for ecological level influences would be 
a multi-level model in which the level two equation incorporates some 
kind of spatial influence.  For example, if Y[i,j] is an outcome for the 
ith individual nested within  jth second level observation (e.g. census 
tract), then (sorry for the awkward notation).
Y[i,j] = b[0,j] + b1*X1[i,j] + b2*X2[i,j] + ...+ bp*Xp[i,j] + e[i,j]

where

b[0,j] = (I- rho*W)-1(g00 + g1*Z[j] + g2*Z2[j] + ...+ gq*Zq[i,j] + u[j])

The second equation is basically the spatial lag model in the reduced form.

I have seen examples where the parameters of this model are estimated in 
two stages.   In the first stage, a multi-level model is estimated and 
estimates of b[0,j] are obtained.  These estimates of ecological level 
influences can then be modeled using the spatial models in the spdep 
package. In simulations, I have seen that this two-step procedure sort 
of works- EXCEPT that in the real world, the reliability of the b[0,j] 
are not only variable (they depend on the within cluster sample size - 
n[j]), but spatially correlated (since the size of the level two units 
are unlikely to satisfy CSR).  In simulations, I have seen that the 
spatial parameters are inconsistent in the limited case of the example 
that on which I am currently working.  (I have not looked at the case in 
which the n[j] are CSR)

My question:  Is there a way of correcting the estimates of a spatial 
lag model (for example) when the source of the spatially correlated 
heterosckedaticity is known?   Maybe through a transformation of W? 


Any thoughts references would be greatly appreciated?  Sorry of the 
multiple postings!

Sam




-- 
Samuel H. Field
Division of Internal Medicine - University of Pennsylvania
CHERP - Philadelphia VA Medical Center
3900 Woodland Ave (9 East)
Philadelphia, PA 19104
(215) 823-5800 EXT. 6155 (Office)
(215) 823-6330 (Fax)