[Openspace] The econometric problem with islands

[Rudy Banerjee]

Dear Mark,

Working with manifolds may provide the answer. A manifold, which is a
topological space that is locally Euclidean, provides the basis for
pairwise neighbors in spatial statistics and make spatially adjusted
regression possible. Here Markov Random Fields define the vector space.
So any conditional autoregressive model is based on a markov random
field assumption. However, how to exactly specify the manifold and its
subsequent algebra is beyond me. Any help to expand this discussion will
be helpful. Regards,

Rudy Banerjee,
Scientist
Berkeley, California.

>>> "MONTGOMERY, MARK" <MMONTGOMERY at popcouncil.org> 6/21/2006 2:03 PM
>>>
Dear Julia:

I'm searching for a good discussion of what goes wrong, in strictly
econometric terms, when "islands" are included in a spatial error
regression model.  If there is one island, for instance, then our weight
matrix has a row with only zero entries. What happens to the spatial
error model likelihood function in this case?

I can think of three implications. (1) An island data point doesn't
help us to identify the value of the spatial autocorrelation parameter.
However, the other data points will be informative about this parameter,
so we should be fine so long as we have enough connected observations.
(2) We can't row-standardize the weight matrix. But row-standardization
isn't necessary in specifying a weight matrix, it is just a nice option
to have. (3) Islands provide useful information on the beta parameters
of the regression model, and dropping them from the dataset means losing
information on this part of the model. 

So, what exactly happens to the likelihood function that causes things
to break down?  

Any advice would be much appreciated.  I'm a newcomer to this listserve
but am finding it really useful.

Mark R. Montgomery
Professor of Economics
State University of New York, Stony Brook
and
Senior Associate, Policy Research Division
Population Council
1 Dag Hammarskjold Plaza
New York, NY 10017

mmontgomery at popcouncil.org 
(212) 339-0673 (phone)
(212) 755-6052 (fax)

_______________________________________________
Openspace mailing list
Openspace at sal.uiuc.edu 
http://sal.uiuc.edu/mailman/listinfo/openspace