[R-sig-ME] Error structure for split-split plot with treatment across blocks

[S Ellison]

> -----Original Message-----
> From: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-
> models-bounces at r-project.org] On Behalf Of Elizabeth Graham
> Sent: 21 October 2013 12:45
> To: r-sig-mixed-models at r-project.org
> 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.
> 
> 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)
> 

Question: Do you really want Treatment in the random-effects structure? 
The main reason for asking is that in principle it is a two-level fixed effect of interest, so it's a bit surprising to see it over on the right at all. Further, from your data you have your streams nested in Treatment which makes me wonder how it can be sensible to have a random-effects spec that puts treatment nested in stream.

Given that you probably want Treatment tested against the Stream-level random effect that is essentially the replication level per treatment, I'd have expected something like 
m2<-lme(log(density)~Treatment*Shade*Leaves,
                        random=~1|Stream/Shade/Leaves) 

That structure also works in aov: 

> summary(aov(log(density)~Treatment*Shade*Leaves+Error(Stream/Shade/Leaves), data))

testing Treatment against the random Stream effect and other effects, but unsurprisingly returns a singular model (killing the Stream/Treatment level of analysis) when adding Treatment in the Error term. 

S Ellison



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