Generalized randomized block design

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):

lme(diversity~Treatment*Plot,random=~1|Plot/Subplot)

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,

alex





El 2013-01-28 15:56, Robert Kushler escribi?:

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

_______________________________________________
R-sig-mixed-models at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models