[R] Split-split plot ANOVA

[Lorenz.Gygax@fat.admin.ch]

> 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