[R-sig-eco] Mixed effect (intercept) model with AR1 autocorrelation structure

[Henkelman, Jonathan]

Perhaps I should clarify.  There is a time-series trend -- daily temperature fluctuates randomly throughout the summer.  But there is not a clear long-term signal.  I have modelled the time-series effect using a gam to see if that can adequately compensate for the effect.  However, I believe this is a fundamentally flawed approach:

1) We are not interested in modelling the time-series; it merely is a way of estimating the temperature response in plot.  That is, I don't want to ask the question, can I predict the temperature given the treatment and the date, but rather, is there a treatment effect.  My inference ability is badly reduced if a model a gam.

2) The current analysis is for a single season.  In a few years we will be re-running this analysis of 5 years of data.  I do not expect the random fluctuation in seasonal temperature will be the same each year.  Hence, while this analysis sort of works now, it won't in the future.  However, it seems reasonable to model the autocorrelation effect within the time-series as constant through time.

3) When I look at the process of temperature I can say, yes today is more likely to be similar to yesterday than the day before.  There is autocorrelation and random fluctuation, hence it makes sense to model it this way.  For the record, as simple AR1 model better account for the seasonal fluctuation than a gam, and my ARMA(2,0) model does an even better job.

Hope this helps, J