Hi.
A month or so ago I posed a question to the list regarding spatial
autocorrelation with GAMs and GLMs (attached directly below). I received
some very helpful answers and a lot of requests for them. I have
summarized them below. I thank everyone for their useful and insightful responses.
Sincerely,
Allison DeLong
This is the original question:
>Hi
>I have a question and am hoping that someone out there can help me resolve
>it. I am planning to start building Generalized Linear and/or General
>Additive Models that predict fish relative abundance by region from
>habitat variables (such as temperature and depth). I know that this has
>been done in the past and have a number of references for these studies.
>However, I've gotten all hung up with the idea of spatial-autocorrelation
>in both the response (relative abundance) and predictor (temperature and
>depth) variables. Spatial autocorrelation like this increases the type 1
>error rate when assessing the significance of such models.
>
>Does anyone out there know any modifications to these methods that can
>take this spatial autocorrelation into account?
>
>Thank you very much.
>
>Sincerely,
>Allison DeLong
Hi Allison - I do know that many physical variables are correlated
spatially. I don't know exactly how this is handled.
There's a product within the US GLOBEC Georges Bank community called OAX
that specifically deals with the kinds of autocorrelations you find in
physical oceanographic data. My understanding is that it goes through
the data and looks for correlation length scales in x,y,z directions and
then uses that information in interpolating between observational data.
I think that Charles Hanna had a hand in building it - he does great
stuff.
Good luck
_______________________________________
John A Quinlan - [log in to unmask]
Ocean Processes Numerical Modeling Laboratory
Department of Marine Science (CB#3300)
University of North Carolina at Chapel Hill
Chapel Hill, NC 27599-3300
TEL (919)962-4466 FAX (919)962-1254
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See the following references, for examples:
Breslow, N.E., and D.G. Clayton. 1993. Approximate inference in
generalized linear mixed models. Journal of the American Statistical
Association 88:9-25.
Tsutakawa, R. 1988. Mixed model for analyzing geographic variability
in mortality rates. Journal of the American Statistical Association
83:37-42.
Wolfinger, R. and M. O'Connell. 1993. Generalized linear mixed models:
a pseudolikelihood approach. Journal of Statistical Computation
and Simulation 48:233-243.
Also, Wolfinger has produced a pretty good SAS macro based on the
last paper (http://www.sas.com/techsup/download/stat/glimmix612.sas).
I'm currently using pseudolikelihood estimation in Poisson and binomial
models for habitat effects on abundance and mortality of birds and
fishes.
The newest glimmix macro is in
http://www.sas.com/techsup/download/stat/glimm701.sas
and requires release 7.0 of SAS. I use glimm612.sas.
/s/ Steve Gutreuter U.S. Geological Survey
Upper Midwest Environmental Sciences Center
PH: (608) 783-6451 X 222 2630 Fanta Reed Road
FX: (608) 783-6066 La Crosse, WI 54603-1223 USA
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Allison,
It is possible to estimate a covariance function (i.e. semivariogram) of
distance to use in constructing a GLM model with a non-diagonal variance-covariance
matrix. It is best to use separate subsets of data to estimate the covariance
parameters and the GLM (drift model) parameters. I worked on extending these
ideas from geostatistics to more typical situation in ecology, where the most
informative predictor variables for drift are environmental gradients rather
than spatial location, per se. The idea was to use spatial autocorrelation in
the residuals as an additional source of predictive power in interpolating to
unknown locations to obtain regional estimates. We developed fortran and SAS/IML
programs to accomplish this, but they are research-grade rather than user-friendly,
supported codes. This being said, you're probably right in seeing it as a "hang-up" or
something that may be worth taking as far as looking at a simple experimental
variogram to see how strong autocorrelation is, with the hope of being able to
avoid it. In theory, a strong predictive drift model in the habitat variables will
"whiten" the residuals, precisely because the spatial autocorrelation will be
accounted for.
See:
S.P. Neuman and E.A. Jacobson. 1984. Analysis of nonintrinsic spatial variability
by residual kriging with application to regional groundwater levels. Math Geology
16(5): 499-521.
H.I. Jager and W.S. Overton. 1993. Explanatory models for ecological response surfaces.
IN Environmental Modeling with GIS. Goodchild, Parks, and Steyaert (eds.), Oxford U. Press,
New York.
I hope this helps.
Yetta
------------------------------------------------------
Yetta Jager
Environmental Sciences Division
Oak Ridge National Laboratory
P.O. Box 2008, MS 6036
Oak Ridge, TN 37831-6036
OFFICE: 423/574-8143
FAX: 423/576-8543
Work email: [log in to unmask]
Home email: [log in to unmask]
WEBpage: http://www.esd.ornl.gov/~zij/
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Perhaps I can help you at least with one little hint, if you
don't know it yet:
It's an online article about using GAM's with acoustic data written by
Gordie Swartzman and you'll find it at:
http://www.cqs.washington.edu/~gordie/about.gam.html
Hope this helps.
Best regards,
Patrick
_____________________________________________________________________
Patrick Schneider Tel. +34-93-221 64 16
Dep. de Recursos Marinos Renovables Fax +34-93-221 73 40
Desp. 137
Instituto de Ciencias del Mar E-Mail:
C.S.I.C. [log in to unmask]
Paseo Juan de Borbon, s/n [log in to unmask]
E-08039 Barcelona
ESPANA - SPAIN
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Allison DeLong [log in to unmask]
University of Rhode Island Tel: (401)874-6663
Graduate School of Oceanography Fax: (401)874-6240
"If anyone knows anything about anything, Rabbit knows something about
something."
-Winnie the Pooh
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