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I have a large set of time series data, consisting of series from two different conditions, the averages of which are shown below.

I would like to fit a model to this data, to test that a) the peak value is greater in the 'conflict' condition, and b) the peak occurs earlier in this condition.

ggplot(data, aes(x=Time, y=Variable, colour=Condition)) 
    + stat_summary(fun.data=mean_se, geom="pointrange")

enter image description here

From my own research on this, I know that:

  • Growth curve analysis is the usual way of modelling time series data like this, but I can't figure out how I would fit a polynomial for this shape of curve.
    • I have some experience fitting GCA models using lme4 in R, mostly following Dan Mirman's tutorials, but I'm still learning.
  • Curves of this kind are referred to as Hubbert curves, and typically used to model oil production, as a symmetric logistic curve up and down.
  • R package grofit is maybe useful for analyses of this kind, although I would rather know I'm barking up the right tree before investing time in learning how to use this.

Can anyone point me in the right direction here?

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    $\begingroup$ I realize after posting that my reference to 'Hubbert Curves' in the question title may not be appropriate, as all I can say is that my plot looks like Hubbert curves. $\endgroup$ – Eoin May 19 '14 at 12:33

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