Christoph and others:
I did succeed, but it was not straightforward. I ended up using the
formula:
mod<-aov(Lag~Ov*Pr*He*Sp + Error(Bl/Ov/Pr:He),data=dat,na.action=na.omit)
and repartioning the sums of squares into the proper factors. I am still
not entirely sure I did it correctly or why R split the sums of squares up the
way it did, but I know I am very close. I suspect that the contrasts need to
be set differently.
I should also note that the R output is rather strange in that I had to
do a lot of searching to find which terms were actually error terms and which
ones were model terms. An example of the output from R shows this:
summary(mod)
Error: Bl
Df Sum Sq Mean Sq
Ov 1 8.466 8.466
Pr 1 10.845 10.845
He 1 72.015 72.015
Sp 2 310.009 155.005
Error: Bl:Ov
Df Sum Sq Mean Sq
Ov 1 1783.17 1783.17
Pr 1 9.70 9.70
He 1 194.48 194.48
Sp 3 66.80 22.27
Error: Bl:Ov:Pr:He
Df Sum Sq Mean Sq F value Pr(>F)
Pr 1 303.01 303.01 2.8526 0.1119
He 1 253.35 253.35 2.3851 0.1433
Sp 6 1119.67 186.61 1.7568 0.1759
Ov:Pr 1 307.52 307.52 2.8952 0.1095
Ov:He 1 88.39 88.39 0.8321 0.3761
Pr:He 1 7.64 7.64 0.0719 0.7922
Ov:Sp 6 285.01 47.50 0.4472 0.8359
Pr:Sp 2 102.27 51.14 0.4814 0.6271
He:Sp 1 43.78 43.78 0.4121 0.5306
Ov:Pr:He 1 60.07 60.07 0.5656 0.4637
Residuals 15 1593.30 106.22
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
Sp 6 23448.5 3908.1 54.1807 <2e-16 ***
Ov:Sp 6 466.6 77.8 1.0781 0.3766
Pr:Sp 6 183.3 30.6 0.4236 0.8628
He:Sp 6 571.2 95.2 1.3199 0.2494
Ov:Pr:Sp 6 360.4 60.1 0.8328 0.5457
Ov:He:Sp 6 47.6 7.9 0.1100 0.9952
Pr:He:Sp 6 384.4 64.1 0.8881 0.5044
Ov:Pr:He:Sp 6 291.2 48.5 0.6727 0.6718
Residuals 215 15508.1 72.1
---
Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
It was relatively straightforward to do the repartioning most of the
time; occasionally I couldn't figure it out, however. Those crossed factors at
the split-plot level really give me fits sometimes.
Anyway, thanks everyone for the help.
Mike
-----------------------
Dear Mike,
Have you succeeded with your split-plot ANOVA?
Best wishes,
Christoph
Mike Saunders wrote:
Christoph,
Thanks for the help. I think the place where I am having the most
problems is the crossed factors at the split-plot level. A synopsis of the
design follows:
Blocks: There are 6 blocks of treatments spread across a site.
Each block is complete in design (Block = 1-6).
Whole plot: Each block has two plots, one of which has the
residual tree overstory removed and the other intact (Overstory = yes or no).
Split plot: In each whole plot, there are 4 planting grids for the
seeds. A 2 x 2 factorial, at this level, of seed predator control (Caging = yes
or no) and herbaceous competition, i.e., grass seed (Herb = yes or no). Spatial
placement of grids in the whole plot was random and assignment of caging and
herbaceous competition treatments to each grid were random, with the
restriction that each of the four treatment combinations appeared only once.
[Note the two factors are crossed at this level and this has been giving me the
most problems when setting up the model statement].
Split-split plot: Each planting grid is a 3 x 3 array of planting
areas (individual planting areas are about 15 cm x 15 cm). Nine different tree
species (Species = 1 - 9) were randomly assigned to each planting area and 25
seeds planted in each area.
Time to germination, total germination (proportion of the 25) and
rate of germination are response variables of interest.
I am interested in the main effects Overstory, Caging, Herb, and
Species as well as all interactions (although I might throw out 3- and 4-way
interactions later).
A drawing is attached as a pdf.
Thanks in advance for any help you can provide.
Mike
Mike Saunders
Research Assistant
Forest Ecosystem Research Program
Department of Forest Ecosystem Sciences
University of Maine
Orono, ME 04469
207-581-2763 (O)
207-581-4257 (F)
----- Original Message ----- From: "Christoph Scherber" <[EMAIL
PROTECTED]>
To: <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>
Sent: Thursday, February 03, 2005 5:40 AM
Subject: Re: [R] Split-split plot ANOVA
Hi Mike,
Do you have a schematic drawing of how exactly your treatments were
applied? In split-plot experiments, it is generally very important
to
clearly define the sequence of plot sizes, because if you don�t do
this
properly, then the output will be confusing. Checking if your
degrees of
freedom at each level are correct should give you a good idea about
whether you�ve specified the model in the right way.
Generally, I see some problem with your model specification as you
seem
to have two (not one) treatments in some of your subplots.
If I got it right, the sequence of terms should be something like
Block/Whole.plot/Caging/Competition/Species
at least if it�s a full split-plot.
Can you send me some more details on the design?
Regards,
Christoph
[EMAIL PROTECTED] wrote:
I have been going over and over the examples in MASS
and the Pinheiro and Bates example, but cannot get my model to run correctly
with either aov or lme.
Could someone give me a hand with the correct model
statement?
It would help to see some of the things you have tried
already ...
First a description of the design. We are studying
germination rates for various species under a variety of treaments. This is a
blocked split-split plot design. The levels and treatments are:
Blocks: 1-6
Whole plot treatment:
Overstory: Yes or No
Split plot treatments:
Caging (to protect against seed predators): Yes or
No
Herbaceous competition (i.e., grass): Yes or No
Split-split plot treatment:
Tree species: 7 kinds
The response variable is Lag, which is a indication of
when the seeds first germinated.
I would try somthing like
lme (fixed= Lag ~ Caging + herbaceous + tree,
data= your.data,
random= ~ 1 | Overstory/split/splitsplit)
Perhaps you want/need to add some interactions as well.
Overstory, split and
splitsplit would be factors with specific levels for each of
the plots,
split plots and split-split plots, respectively.
Thus what I attempted here is to separate the variables of
the hierarchical
design of data gathering (which go into the random effects)
and the
treatments (which go into the fixed effects).
The degrees of freedom for the fixed effects are
automatically adjusted to
the correct level in the hierarchy.
Did you try that? What did not work out with it?
Lastly, I have unbalanced data since some treatment
combinations never had any germination.
In principle, the REML estimates in lme are not effected by
unbalanced data.
BUT I do not think that the missing germinations by
themselves lead to an
unbalanced data set: I assume it is informative that in some
treatment
combinations there was no germination. Thus, your lag there
is something
close to infinity (or at least longer than you cared to wait
;-). Thus, I
would argue you have to somehow include these data points as
well, otherwise
you can only make a very restricted statement of the kind: if
there was
germination, this depended on such and such.
Since the data are highly nonnormal, I hope to do a
permutations test on the F-values for each main effect and interaction in order
to get my p-values.
As these are durations a log transformation of your response
might be
enough.
Regards, Lorenz
- Lorenz Gygax, Dr. sc. nat.
Centre for proper housing of ruminants and pigs
Swiss Federal Veterinary Office
agroscope FAT T�nikon, CH-8356 Ettenhausen / Switzerland
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Mike Saunders
Research Assistant
Forest Ecosystem Research Program
Department of Forest Ecosystem Sciences
University of Maine
Orono, ME 04469
207-581-2763 (O)
207-581-4257 (F)
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