[R] Split-split plot ANOVA

[Christoph Scherber]

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



Lorenz.Gygax at fat.admin.ch 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 Tänikon, CH-8356 Ettenhausen / Switzerland
>
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