Hi:

On Thu, Oct 14, 2010 at 3:58 PM, Eugenio Larios
<elariosc@email.arizona.edu>wrote:

> Hi Everyone,
>
> I am trying to analyze a split plot experiment in the field that was
> arranged like this:
> I am trying to measure the fitness consequences of seed size.
>
> Factors (X):
> *Seed size*: a continuous variable, normally distributed.
> *Water*: Categorical Levels- wet and dry.
> *Density*: Categorical Levels- high, medium and solo
> *Plot*: Counts from 1 to 20
> The *response variable *(Y) was the number of seeds produced at the end of
> the season.
>
> The experiment started 15 days after plants germinated in the field.
> 20 plots were chosen where there was high enough density so I could
> manipulate it. In an area where artificial irrigation was possible for the
> wet treatment, dry treatment was natural precip.
> Water was blocked so 10 plots were wet and the other 10 were dry. Randomly
> assigned.
> Within those 20 plots 6 focal plants were chosen and randomly assigned the
> three densities. (split plot design)
> I did not control for seed size since it is continuous and normally
> distributed, hoping that with 120 plants total (6 in each 20 blocks) I
> could
> get all kind of sizes for every treatment. It worked ok.
>

>From the description, it appears you have the following:
    * water is a whole-plot treatment, each level assigned to 10 plots
    * seed size is a plot-level covariate
    * whole plot units are the plots

At this level, the ANOVA table is

Water                    1
Seed size              1
Water x seed size 1
Whole plot error   16   [plots]

The split plot treatment is density, and after its main effect is accounted
for, it is crossed with every term in the whole-plot ANOVA:

Density                                       2
Density * Water                          2
Density * seed size                    2
Density * Water * seed size       2
Residual                                    92           [subplots]

Total df  = 119

The ANOVA exercise is useful for understanding the structure of the
split-plot design - it is not exactly what lme() will fit (especially the
df), since lme() is fitting the model via likelihood rather than least
squares.

Your full lme model, including the test of unequal slopes in the two water
levels, should be

m <- lme(log(fitness) ~ seedsize * water * density, random = ~1|plot,
data=dataset)

Without the unequal slopes term (i.e., a parallel slopes model), it should
be

m2 <- lme(log(fitness) ~ (seedsize + water) * density, random = ~1 | plot,
data = dataset)

The specification of the first two terms on the RHS of the model formula is
associated with the whole-plot structure of your design.

I have been trying to analyze this with lme (library NLME). I am not quiet
> sure which are my random variables. models I have used are:
>
> m<-lme(log(fitness)~seedsize*density,random=~1|plot,data=dataset)
> m<-lme(log(fitness)~seedsize+density+water,random=~1|plot,data=dataset)
>
> I have also tried to include plot and water as random effects:
>
>
> m<-lme(log(fitness)~seedsize+density+water,random=~1|plot/water,data=dataset)
>
> I am actually not sure if I am using the right random variables here. Also
> for some reason, it won't let me include seedsize*density*water triple
> interaction
>

You mentioned imbalance in your mail header - how imbalanced are you talking
about? The structure of the imbalance could have some impact on which
effects are or are not estimable, depending on its severity.


HTH,
Dennis


> help!
> thanks
>
> --
> Eugenio Larios
> PhD Student
> University of Arizona.
> Ecology & Evolutionary Biology.
> (520) 481-2263
> elariosc@email.arizona.edu
>
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>
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