Split-split-plot design and lme

Question

I’m working on a data set in order to evaluate the impact of drying on sediment microbial activities. The objective is to determine if the impact of drying varies among sediment types and/or depth within the sediment.

The experimental design is as follows:
The first factor Sediment corresponds to three types of sediment (coded Sed1, Sed2, Sed3).
For each type of Sediment, sampling was carried out on three sites (3 sites for Sed1, 3 sites for Sed2, 3 sites for Sed3). Site is coded : Site1, Site2, ..., Site9.
The next factor is Hydrology: within each site, sampling is carried out in a dry plot and in a wet plot (coded Dry /Wet).
Within each of the previous plot, sampling is carried out at two Depths (D1, D2) in triplicate.

There are a total of n = 108 samples = 3 Sediment * 3 Sites * 2 Hydrology * 2 Depths * 3 Replicates.

I use the lme function in R (lnme package) as follows :

Sediment<-as.factor(rep(c("Sed1","Sed2","Sed3"),each=36))
Site<-as.factor(rep(c("Site1","Site2","Site3","Site4","Site5","Site6","Site7","Site8","Site9"),each=12))
Hydrology<-as.factor(rep(rep(c("Dry","Wet"),each=6),9))
Depth<-as.factor(rep(rep(c("D1","D2"),each=3),18))
Variable<-rnorm(108)

mydata<-data.frame(Sediment,Site,Hydrology,Depth,Variable)

mod1<-lme(Variable~Sediment*Hydrology*Depth, data=mydata, random=~1|Site/Hydrology/Depth)

I found an example of a comparable split-split-plot design and its analysis in : http://www3.imperial.ac.uk/portal/pls/portallive/docs/1/1171923.PDF

Could someone confirm that this is the right way to analyze these data?
Do you think that the random structure is correctly specified according to my experimental design?

Answer 1

This comes rather late, but I think your analysis is generally correct, with 3 comments:

1. Make sure it is ok to treat depth as random rather than fixed. I guess this depends on your definition of depth. Is it just 'topsoil' and 'subsoil' or some control levels like A1, B2, C2, etc....
2. A colleague of mine always recommend people creating another variable so it doesn't confuse people when the fixed and random effects have the same name. Something like lme(Variable~Sediment_ef*Hydrology_ef*Depth_ef, data=mydata, random=~1|Site/Hydrology/Depth), even if X_ef and X are identical columns.
3. This is obviously the full model, where you might (or might not) want to reduce it to achieve parsimony.