[R-sig-eco] Autocorrelation structures and simplicity of analysis

[Dixon, Philip M [STAT]]

Jonathan,

The AR(1) + compound symmetry model does make sense.  It is a model where the correlation over time declines with the separation between times points, but it does not decline to zero.  There is a constant non-zero (at least potentially) correlation arising from the compound symmetry (constant correlation between all pairs of observations on the same plot) part of the model.  I have found it fits many data sets better than either AR(1) only or CS only.

However, I suggest you completely rethink the analysis.  I am a great fan of the approach recommended by Paul Murtaugh a few years ago.  The paper is "Simplicity and complexity in ecological data analysis" Author(s): Murtaugh, Paul A.  Source: ECOLOGY  Volume: 88   Issue: 1   Pages: 56-62   Published: JAN 2007

Your situation is almost identical to one he considers in his paper.  His advice: remember that you have experimental units randomly assigned to warming treatments.  Your analysis currently ignores time, except for accounting for the autocorrelation.  You seem to care only about the treatment effect.  If that's the case, you don't need to worry about days.  Just focus the analysis on plots and the treatment effect.  Specifically, figure out an informative summary statistic for each plot (e.g., average over time, median over time), calculate those 12 numbers, then analyze those.  No need to worry about the autocorrelation structure then!

The beauty of this approach is that if you want to ask a different question, e.g. about day-day variability instead of the average, you just change your summary statistic to something that measures variability, e.g. log sd.

Best wishes,
Philip Dixon