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) _______________________________________________ R-sig-Geo mailing list R-sig-Geo@stat.math.ethz.ch https://stat.ethz.ch/mailman/listinfo/r-sig-geo
