[R-sig-ME] Time as both fixed and random term
paul debes
paul.debes at utu.fi
Wed Nov 25 08:42:16 CET 2015
Hi Lionel & List,
An easy-to-implement approach estimating overall time trends (i.e.,
including Time as a fixed effect) while accounting for deviations from
this trend for each plot could be to include random Time-by-Plot trends.
This will result in the 'right' degrees of freedom for the overall time
trend (have you thought about possible Treatment-by-Time interactions?) so
statement ii) may be true if the Time trend varies among Plots or if you
want to account for your study design in terms of Time. Possible meanings
of including "Time" as both a fixed and a random term was just recently
discussed by the list, but I think here you actually refer to having a
random Time-by-Plot interaction term in your model.
Nevertheless, you can model this potential within-plot across-time data
correlation by many other different ways, depending on your data. The
above-mentioned random coefficient model (fitting random Time trends for
each Plot) is only one way and your data may fit other covariance models
better (e.g., when treating Time as a factor: ar1, us, ante, etc). Maybe
it is best you check a book on time series models to get a better overview
what is possible and how to decide on an adequate covariance structure for
your data.
Not all of the many possible covariance structures can be fitted in lme4,
nlme may be more flexible.
One of the most complicated covariance structures (that needs loads of
data) to start with would be:
Biomass ~ Treatment + Time + (factor(Time)|Plot)
One of the least complicated would be:
Biomass ~ Treatment + Time + (Time|Plot)
Hope this helps,
Paul
On Wed, 25 Nov 2015 00:06:51 +0200, Lionel <hughes.dupond at gmx.de> wrote:
> Dear List,
>
> In my work we usually deals with measures sampled repeatedly on
> experimental units over several time points and with specific
> treatments. For example we sampled plant biomass on 100 experimental
> plots at 5 different time point (say season or year). Some people argue
> that in this context we should model time as both a fixed effect term
> (as continuous variable) and random effect term in order to compute the
> correct numbers of degrees of freedom to test our treatment effects
> (usually considered as a continuous variables).
>
> This is how such a model would look like:
>
> Biomass ~ Treatment + Time + (1|Plot) + (1|Time)
>
> In my experience having the same term has both fixed and random results
> in very low estimated standard deviation for the random term, which
> makes me skeptical about this approach. But having very little knowledge
> about how to correctly estimate the numbers of degrees of freedom I
> would like to ask you:
>
> (i) if such a model makes sense,
> (ii) if the argument "we need to have time as both fixed and random term
> to get the correct number of degrees of freedom" is valid
> (iii) if such an alternative model: "Biomass ~ Treatment + Time +
> (1|Plot)" would be more appropriate.
>
> Thanks for your input,
> Lionel
>
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--
Paul Debes
DFG Research Fellow
University of Turku
Department of Biology
Itäinen Pitkäkatu 4
20520 Turku
Finland
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