[Openspace] The use of regional dummy variables

[Luc Anselin]

This is a quiet list, but that's not necessarily bad :)
On dummy variables, the main issue is to make sure that
the asymptotics remain valid. The spatial lag model
requires a N to go to infinity. If this creates "new regions"
(i.e., new dummies) there is an incidental parameter
problem, that is, the number of parameters grows with
the sample size. If the number of regions is fixed, then
somehow there must be a mechanism for the number
of observational units within each "region" (dummy) to
grow as N increases. This type of asymptotics is called
"infill asymptotics" and it is not the same as the more
familiar "expanding domain asymptotics". Some methods
break down under infill asymptotics.
It very much depends on what it is one models. For example,
in real estate analysis, it would be legitimate to introduce
a school district dummy and have many housing units in
each district. The asymptotics are such that the number of
school districts is fixed (fixed effects) but the number of
housing units increases (infill asymptotics).
However, in other situations, this would not be appropriate.
For example, consider planning regions in a state with
counties as the observational unit. To "grow" the sample,
one can think of adding counties at the boundary
(not adding new counties in each region, since the
space is already exhausted), but then those counties
do not necessarily fall within the existing regions, requiring
a new dummy for a new region = incidental parameter
problem.
Typically, if you work with spatial units that exhaust the
space it is best to avoid dummy variables. However, in
the infill setting, it is fine.
In practice, regional dummies are often used to "remove"
spatial autocorrelation and this can work quite well,
depending on the form of the clusters in question. However,
it is important to keep in mind that such a solution is a
"fixed effects" solution, not the random effects used in
spatial process models.
L.


On Tuesday, December 2, 2003, at 02:05 PM, taehyun nam wrote:

> Just a comment for the sake of discussion (this list
> is too quiet OR Am I missing something?):
> I myself as a novice in this field have browsed
> spatial autocorrelation research and found no model
> using dummy variables.
> Have you?
>
> Taehyun Nam
>
> --- Justin Scoggins <original_jscogg at yahoo.com> wrote:
>> Hi all,
>>
>> I have a question regarding the use of regional
>> dummy variables in a spatial lag regression. We have
>> a model that attempts to predict cancer risk as a
>> function of several factors using Census tract level
>> data. Included in these factors is a set of regional
>> dummy variables, which by nature are highly
>> spatially autocorrelated within any of the given
>> regions. Does anyone have any experience with the
>> use of regional dummy variables in a spatial
>> autoregressive model, or know anything about why
>> they should or should not be included.
>>
>> Any help comments/suggestions would be much
>> appreciated.
>>
>> Thanks,
>>
>> Justin.
>>
>>
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