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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