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

[Faming Wang]

Dear Seth,

  Thanks for your help. I was perplexed by this problem for several weeks.

-- 

Sincerely

Faming Wang
MBL, Woods Hole, MA




On Thu, May 11, 2017 at 9:54 PM Seth Bigelow <sbigelow at jonesctr.org> wrote:

> 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
>>
>>         [[alternative HTML version deleted]]
>>
>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>
>
>
> --
> Seth W. Bigelow, Ph.D.
> Assistant Scientist of Forest Ecology
> Joseph W. Jones Ecological Research Center
> Newton, GA
>

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