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

[Dixon, Philip M [STAT]]

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