[R-sig-ME] Generalized randomized block design

leverkus leverkus at ugr.es
Mon Jan 28 21:08:32 CET 2013

Thanks for your reply, Rob,

I guess you are right about not modeling plot as a random effect. In 
any case, if I formulate it this way (as I understand you suggest):


I don´t have enough df to calculate a Plot (altitude) main effect but 
only treatment and the treatment*Plot interaction. The summary of the 
fixed effects looks like this:

Fixed effects: diversity ~ Treatment * Plot
                     Value  Std.Error  DF   t-value p-value
(Intercept)     0.8332827 0.03153322 186 26.425551  0.0000
TreatPCL        0.0250449 0.04557570  18  0.549524  0.5894
TreatSL        -0.1618297 0.04459471  18 -3.628898  0.0019
Plot2           0.1346471 0.04459471   0  3.019351     NaN # where 
these results with 0 df look like they shouldn´t be in the model.
Plot3           0.0561054 0.04459471   0  1.258118     NaN
TreatPCL:Plot2 -0.0617449 0.06376388  18 -0.968337  0.3457
TreatSL:Plot2  -0.0339678 0.06306644  18 -0.538603  0.5968
TreatPCL:Plot3  0.0217470 0.06376388  18  0.341054  0.7370
TreatSL:Plot3   0.1790523 0.06306644  18  2.839106  0.0109

My questions here are: 1) is it ok to include a Plot main effect in the 
model (as above) even though I don´t have df for it? 2) Would it be 
"allowed" instead to use diversity~Treatment+Treatment:Plot as fixed 
effects, without a Plot main effect? Or otherwise, 3) How wrong would it 
be in the random term to place plot at the level of subplots, so that 
random=~1|Plot:Subplot? I understand in this latter way I would be 
pseudoreplicating plot.

I guess the main issue is that it annoys me to have a term in the model 
which tells me nothing, and not knowing which values to report for 
altitude (the fixed effects with 0 df or the random term resulting from 
the specification of the experimental structure).

Thanks again,


El 2013-01-28 15:56, Robert Kushler escribió:
> Since Plot is confounded with "Altitude" I suggest you treat Altitude
> as a fixed effect
> and give up on trying to estimate a Plot variance component (2 df is
> not enough info
> for that).
> Regards,   Rob Kushler
> On 1/28/2013 8:57 AM, leverkus wrote:
>> Dear R users,
>> I am struggling with the formulation in lme of a generalized 
>> randomized block design with subsampling, and I would very
>> much appreciate some help. The experiment consists of 3 plots (of 
>> ca. 20 ha each) located at different altitudes on a
>> mountain slope. In each plot there are 9 subplots, which are 3 
>> replicates of 3 post-fire wood management treatments. In
>> each subplot we sampled 8 transects for plants (except in one 
>> subplot, where only 5 transects were sampled), and my
>> response variable is species diversity. In order to take account for 
>> the experimental design and get the correct number
>> of denominator degrees of freedom, I am using (1|Plot/Subplot) in 
>> the random effects. Subplot is a categorical variable
>> which joins treatment names (treatments are "SL", "NI", "PCL") and 
>> replicates (1,2,3): SL1, SL2, SL3, NI1... This gives
>> me the correct replication: 3 plots and 27 subplots. As for now, my 
>> model looks like this:
>> lme(diversity~Treatment,random=~1|Plot/Subplot)
>> However, treatment effects are likely to vary with altitude, so I 
>> wish to test for the treatment x plot interaction.
>> This is where I am stuck. By including plot as a fixed effect 
>> (diversity~Treatment*Plot) I have no df to calculate the
>> plot effect and this looks weird to me. Besides, I want to have plot 
>> as a random effect. Could anyone give me some
>> suggestions? (I don´t mind using lmer instead.)
>> Thanks in advance,
>> alex
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