[Openspace] The econometric problem with islands

[Julia Koschinsky]

Dear Mark,

As you note in points (1) and (3), island observations are 
zeroed out in the estimation (or testing) of spatial 
autocorrelation, so they don't count. However, island 
observations *are* included in the likelihood for the other 
parameters of the model. Island observations don't affect 
the row-standardization -- however, the standardization 
factors need to be adjusted for the fact that the total sum 
of weights is no longer N, but N minus the number of islands.

So your interpretation in (1) and (3) is correct but (2) is 
not necessarily a problem, as long as the S0 term and the 
other traces used in the tests, etc. are computed correctly 
and not set to N without computing. Note that in GeoDa, so 
far, *all* weights are always row-standardized.

The response above is based on Luc Anselin's teaching 
materials; a chapter you might be interested in for details 
discusses some technical aspects of incorporating islands in 
the context of the opensource language R:

Roger S. Bivand, Boris A. Portnov. (2004). "Exploring 
Spatial Data Analysis Techniques Using R: The Case of 
Observations with No Neighbors," in Luc Anselin, Raymond 
J.G.M. Florax, and Sergio J. Rey (Eds.). Advances in Spatial 
Econometrics: Methodology, Tools and Applications, pp. 121-
142.

Let me know if you have trouble accessing the article.
Julia

---- Original message ----
>Date: Wed, 21 Jun 2006 17:03:27 -0400
>From: "MONTGOMERY, MARK" <MMONTGOMERY at popcouncil.org>  
>Subject: [Openspace] The econometric problem with islands  
>To: <openspace at sal.uiuc.edu>
>
>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)
>
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