[R-sig-eco] Time-varying spatial correlation

[Penelope_Pooler at nps.gov]

Hi Phillip,

Thank you for your thoughtful reply.  I was thinking those same lines, but
was concerned that I was trying to oversimplify the problem.  I think you
are exactly correct that we don't have the data to precisely account for
the small scale correlation.  Also, since these observations are recorded a
year apart, I think this small-scale spatial correlation is overshadowed by
the inter-annual variability.

My concern with respect to the within year large scale spatial correlation
is that, I worry that if I ignore it, I may be overestimating the "true"
sample size.  Perhaps I am being overcautious, but better now than when a
review of a submitted paper comes back.

Thank you again for your input.  If you have any insight on the "true"
sample size issue, I would appreciate it.

-Penelope

===========================================
Penelope S. Pooler, Ph.D.

Quantitative Ecologist, National Park Service I&M
Northeast Coastal and Barrier Network
NPS email: Penelope_Pooler at nps.gov

Adjunct Professor, Dept. of Natural Resources Science
URI Coastal Institute in Kingston
URI email: ppooler at mail.uri.edu

1 Greenhouse Rd., Rm 105
Kingston, RI 02881
Ph.: (401) 874-7060
Cell: (540) 250-1096
===========================================


                                                                           
             "Dixon, Philip M                                              
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                                       [R-sig-eco] Time-varying spatial    
                                       correlation                         
             01/14/2012 11:58                                              
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Penelope,

I agree completely with your wish to keep the model simple.  Spatial
correlation, as something separate from spatial trend, may be something
instrinic to the biology, but it can be a consequence of mis-specification
of the model.  Along those lines, I would use all the available information
to think about the rest of the model before considering the spatial
correlation.  In particular here, you have two levels of spatial
information: the large scale hexagon level, sampled every year, and the
small scale location within hexagon level, sampled only once per location.

You describe your model as containing fixed effects for year and
hexagon-level random coefficients for a linear regression on year.  That
means your model includes a random intercept for hexagon, so the
large-scale spatial trend is already described by your model.  Since
locations change within the hexagon each year, the small-scale spatail
variation is only known after fitting the linear regression for year.  Any
lack-of-fit there will complicate understanding the spatial correlation.

My sense is that you don't have enough of the right sort of data to account
for small-scale spatial correlation unless there is some simple model for a
spatial covariate that varies within hexagons (e.g depth).  Otherwise, I
would be strongly tempted to ignore what you're calling spatial correlation
under the principle that locations within hexagons are randomly sampled.

Philip Dixon
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