Generalized randomized block design

model<-lme(asin(sqrt(annualcov))~Treat*altitude,random=~1|Subplot,method="ML",data=na.omit(divers))
model1<-update(model,~.-Treat:altitude)
anova(model,model1)

modela<-lme(asin(sqrt(annualcov))~Treat*Plot,random=~1|Subplot,method="ML",data=na.omit(divers))
model1a<-update(model,~.-Treat:Plot)
anova(modela,model1a)

Have you tried?specifying altitude (ie., as numeric), rather than?a
plot identifier, as a main effect? This may be what Rob was
suggesting.?Since altitute is a numeric gradient, and you seem to be
suspecting that something is going on that is related to that
gradient, this would seem worth a try -- implemented as an 
interaction
model, and as a non-interaction model, and then comparing with
likelihood ratio test. I would try just specifying 'subplot' as a
random effect, then examining the residuals as in the 'rails'l 
example
in Pinheiro & Bates

-Seth

?

----- Original Message -----

From: leverkus <leverkus at ugr.es>

To:"Robert Kushler" <kushler at oakland.edu>,
<r-sig-mixed-models at r-project.org>

Cc:

Sent:Mon, 28 Jan 2013 21:08:32 +0100

Subject:Re: [R-sig-ME] 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 [1] 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 -0968337 0.3457
TreatSL:Plot2 -0.0339678 0.06306644 18 -0.538603 0.5968
TreatPCL:Plot3 0.0217470 0.06376388 18 0.341054 07370
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

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