[R-sig-ME] A question on using LME model in species nested within a random block design

[Seth Bigelow]

Dear Faming Wang:

I took a look at your model and data. I believe that you have done the
analysis correctly. First you specified a model that had the three way
interaction Nadd*Padd*Spname, using Block as a random effect. Then you
tested to see whether there was a random plot effect
(random~1|Block/plots), since each fertilized plot should be a somewhat
uniform area containing individuals of several or all five species. But the
random effect of 'plot' was tiny and negligible, and the likelihood ratio
test did not indicate that the model with the 'plot' random effect was any
better than the model that only had 'block' as a random effect. So, to
paraphrase Pinheiro & Bates (2000), you have used multiple nested levels of
random effects to analyze a split plot experiment. I think the challenge
lies in explaining to the reviewer that you *have* done a split plot
experiment, rather than taking some different approach.

On Tue, May 9, 2017 at 2:11 PM, Faming Wang <famingw at gmail.com> wrote:

> Dear all,
>
>
>  I have conducted an N and P field addition experiment in a tropical
> forest, and we used a random block design in this experiment, briefly, we
> had four randomly distributed plots in each block (Control, +N， +P,
> and +NP), and five blocks located in the forest. Totally we have 20 plots,
> with two N treatments and two P treatment and five replicated blocks. In
> each plot, we selected five  species  plants (some plots only contains 3 or
> 4 species) to measure their leave variables, like N concentration, P
> concentration, and photosynthesis rate et al.  We want to know the effect
> of N and P addition as well as the species level changes (inter-species )
>  on leaf variables. Since some plots some specific species are missing in
> some plots some specific species, it was unbalanced at the species level.
> We used linear mixed effect models to conduct our statistical analysis:
>
>   We firstly tested the random effect with blocks, and species within plots
> within blocks, and found that nesting plots and species within block did
> not improve the model fitness, so we choose only block as random effect.
> For fixed effects, N-addition, P-addition, species and their interaction
> were considered fixed effects in models. The significance of each term was
> determined by comparing nested models using likelihood ratio tests and AICs
> to check for model improvement. Since there was better model fit (lower AIC
> values) with interaction terms, we selected the full factor model. However,
> as there was a highly significant effect of tree species identity and
> species related interactions, species-specific responses to N- and
> P-addition were also investigated with separate models with N, P and their
> interaction as fixed effects and block as a random effect.
>  however, our reviewers were not happy with this statistical methods and
> pointed out that "Species is treated as a fixed factor, generating a
> three-way factorial ANOVA. Species cannot be treated in this way because
> all five species were present in each 10-by-10-m plot. To implement a
> three-way ANOVA design, the entire experiment (five blocks of the four
> factorial N and P treatments) would have to be repeated once for each
> species. Species cannot be treated as a fixed factor because all five
> species were measured in the same experimental plots. This is a split-plot
> design. Alternatively, MANOVA might be performed treating the five species
> as five response variables. A split-plot design or a MANOVA approach would
> allow the authors to investigate interspecific variation in responses."
>
>   I am very confused on the reviewer's comments,  it seems to me that the
> reviewer compared our LME model with 3-way ANOVA. If we used 3-way ANOVA, I
> know that my experiment is species nested in a random block design, and we
> could not directly use 3-Way ANOVA, which the error df would be
> overestimated.
>
>    Below I attached my sample data and my current R script for LME model in
> dropbox. See below links:
> https://www.dropbox.com/s/6kd3kq5mlyuyqz6/NPrawdata.csv?dl=0
>
> https://www.dropbox.com/s/fpqdbm6go0g8ak0/Faming%20NP%20model.R?dl=0
>
>
> --
>
> Sincerely
>
> Faming Wang
>
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>
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>



-- 
Seth W. Bigelow, Ph.D.
Assistant Scientist of Forest Ecology
Joseph W. Jones Ecological Research Center
Newton, GA

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