Time as both fixed and random term

Dear all,


Could I additonally ask a question?
     fit1 <- Biomass ~ Treatment + Time + (1|Plot), where 'Time' is a continuous covariate
     fit2 <- Biomass ~ Treatment  + (1|Time/Plot), where 'Time' is a factor variable


     fit3 <- Biomass ~ Treatment + (1|Time), where 'Time' is also a factor variable


If AIC(fit3) is smaller than AIC(fit1) and AIC(fit2), can we choose fit3 rather than fit1?


Thanks a lot!


Best regards,


Joe



--


Peijian (Joe)  Shi, Ph.D.

Research interests: forest ecology; theoretical ecology; thermal biology

Member of China Ornithological Society from 2005 up to the present

Bamboo Research Institute, Nanjing Forestry University, P.R. China

159 Longpan Road, Nanjing City, Jiangsu Province 210037

Office:  60817  Biotechnology Building

Tel:  +86 25 85427231

E-mail addresses:  peijianshi at gmail.com

                                shi_peijian at 163.com




At 2015-11-25 06:06:51, "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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