I am currently trying to fix an unbalanced split-split plot design using lmer().  The design is:

B = Block (site) in two levels
T = Trenching (whole-plot treatment) in two levels (untrenched vs trenched), replicated 4 times per site
W = Weeding (split-plot treatment) in two levels (weeded vs unweeded), applied to each whole-plot
S = Species (split-split plot treatment) in two levels (chestnut vs oak), with 1-2 trees of each in each split plot treatment (we had mortality, otherwise it would be balanced)

My response variable is Photo (photosynthesis levels).

I specified my full model as:
fullmod<-lmer(Photo ~ B + T + W + S + B:T + B:W + B:S + T:W + T:S + W:S + B:T:W + B:T:S + B:W:S + T:W:S + B:T:W:S + (1|B) + (1|B:T) + (1|B:T:W),data=light,REML=F)
QUESTION 1:  Is the code correct?

In my output, I have no variance or standard deviation associated with the B, B:T, B:T:W random effects.  I am assuming that this is because I have only two levels at each split.

QUESTION 2: Is that assumption correct?

Lastly, my plans were to drop each higher-order interaction in succession and use the anova comparison between the successively simplified models (i.e., full vs. no 4-way; no 4-way vs. no 3-way; etc.) to get p-values for the fixed effects (obviously not using REML).

QUESTION 3: Is this a proper approach?

I am self taught in mixed-models and R, so any help is appreciated.  lme4 is new to me.

Thanks in advance,
Mike

Mike Saunders
Asst. Professor of Silviculture
Purdue University

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