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

[Elizabeth Graham]

Thanks for those prompt replies! 

m2<-lme(log(density)~Treatment*Shade*Leaves,
                        random=~1|Stream/Shade/Leaves)

was actually my original model structure, but has the same incongruity between model results and interaction plots - try interaction.plot(Shade, Treatment, density) for an example - the treatment and control lines do not intersect at all, and standard error bars do not overlap.  Thus I thought adding Treatment to the nesting structure might be necessary, as there seems to be a possible masking of a treatment effect with the random stream effect.

Thanks again S Ellison and Steve Denham, I will keep your advice in mind also.  Do people agree that the model structure above fits my experimental design?  And is there any way to investigate the treatment effect evident in the interaction plots?

Regards, 
Elizabeth
________________________________________
From: S Ellison [S.Ellison at LGCGroup.com]
Sent: Tuesday, October 22, 2013 5:00 AM
To: Elizabeth Graham; r-sig-mixed-models at r-project.org
Subject: RE: [R-sig-ME] Error structure for split-split plot with treatment across blocks

> -----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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