[R-sig-Geo] LM tests

[Jill Caviglia-Harris]

List members:

A few months ago I posted an email to the group concerning trouble I
was having with estimating regressions that test and correct for spatial
lag and error.  My problem was that these tests as designed for R assume
that the neighbors list is row standardized, while I have a weights
matrix that is set up as the inverse distance between neighbors.  I was
concerned with converting my weights matrix into a neighbors format
because this could result in the loss of potentially important
information.  Some what I have done is tested three ways to identify the
weights matrix: 1) inverse distance 2) row standardized and 3) binary
neighbors.  When using each of the derived neighbors lists form these
matrices in the LM test I still get the error: "Spatial weights matrix
not row standardized" except in the application using the binary
neighbors.  

Roger Bivand responded with the following questions (my answers are in
bold):

1) Are the results from a binary IDW and a row standardized IDW very
different? Response: The results for the LMerr, LMlag, RLMerr, RLMlag,
and SARMA are not identical but statistically similar between 1) and 2)
- but different between these and 3) - but perhaps this could simply be
due to the definition of a neighbor used?  I would think this might be
getting into a theoretical question rather than an empirical one, but
the posted error is what made me wonder if perhaps the results are
invalid?

2) Is your IDW matrix full or sparse?  Response: The matrix is full -
no missing observations.

3) Can Moran's I be applied instead (despite its covering lots of
misspecification problems)? Yes, and the results are somewhat consistent
in identifying spatial autocorrelation - but this does not differentiate
between spatial lag and error.

4) Are the IDW weights symmetric (probably, but not always)?  Response:
Yes, the weights are symmetric.

5) I'm not sure why distances should be helpful if the data are
observed on areal units, so that measuring distances is between
arbitrarily chosen points in those units, a change of support problem.
But error correlation specified by distance does may be rather close to
geostatistics, doesn't it?  

Response: Distances are important and useful because they imply a range
of influences.  My database includes a stratified random sample of
households in the Amazon.  Therefore, the closest "neighbors" are
those with the largest possible influence on household land use (and
other) decisions.  These same neighbors would have the largest value for
the inverse distance - the greater the number the greater the influence.
 This weighted influence (or differing degrees of influence) is lost
when using dummy variables or a binary definition of neighbors.  

I have also run the spatial error, lag and combined models to correct
for autocorrelation.  I have attached my results for anyone that's
interested.  Any insights about the questions above or the estimations
are welcome.  Thanks.  -Jill


***************************************************
Jill L. Caviglia-Harris, Ph.D.
Associate Professor
Economics and Finance Department
Salisbury University
Salisbury, MD 21801-6860
   phone: (410) 548-5591
   fax: (410) 546-6208
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