I would strongly suggest not doing the model simplification.  This is a real case of where the design factors should all be retained in order to obtain meaningful comparisons.


Steve Denham
Associate Director, Biostatistics
MPI Research, Inc.


>________________________________
>From: Elizabeth Graham <sharon.graham@pg.canterbury.ac.nz>
>To: "r-sig-mixed-models@r-project.org" <r-sig-mixed-models@r-project.org> 
>Sent: Monday, October 21, 2013 7:45 AM
>Subject: [R-sig-ME] Error structure for split-split plot with treatment across blocks
>
>
>Hello,
>
>I am trying to create a LME model for a split-split-plot experiment.  Briefly, the design is as follows:
>
>Six streams, three of which received a treatment and three of which were kept as control.  Within each stream there was a shaded section and an unshaded section.  Within each shaded/unshaded section were six rock baskets (for invertebrate colonization), three of the baskets had leaves added and three did not.  Thus, there were three replicates of each treatment by shade by leaves combination.
>
>Example data can be accessed via
>https://docs.google.com/file/d/0B8zKenaVJP_hLXgyUUcwYmRXOEk/edit?usp=sharing
>
>My current model is as follows, based on the split-plot design outlined in Pinheiro and Bates 2000:
>
>model<-lme(log(density)~Treatment*Shade*Leaves, random=~1|Stream/Treatment/Shade/Leaves)
>
>However, based on the interaction plots there appears to be a treatment effect that does not show up in the model (I am performing model simplification based on t-statistics to discern significant fixed effects).  I suspect this has something to do with the structure of the error term, as treatment is not exactly nested in stream (described above).  However, I have not been able to find an alternative model structure which accounts for this, and nested stream within treatment returns a NaN for the treatment term p-value.
>
>Any advice would be much appreciated.
>
>Regards,
>
>Elizabeth Graham
>
>
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