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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