[R-sig-ME] Time as both fixed and random term

[Lionel]

Hi Paul,

Thanks for your answer, there are (as always) some complexities:

- we usually measure and assume our units to be homogeneously affected 
by time (ie no time|plot terms), this is because our units are either on 
the same site or come from microcosm/mesocosm.

- we usually have limited time repetition (~5) so modelling it using 
complex autocorrelation structure is not possible.

Yours,
Lionel

On 25/11/2015 08:42, paul debes wrote:
> 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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>
>