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 factorSedimentcorresponds to three types of sediment (codedSed1,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).Siteis coded :Site1,Site2, …,Site9.

The next factor isHydrology: within each site, sampling is carried out in a dry plot and in a wet plot (codedDry/Wet).

Within each of the previous plot, sampling is carried out at twoDepths(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.PDFCould 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**

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

- 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….
- 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. - This is obviously the full model, where you might (or might not) want to reduce it to achieve parsimony.

**Attribution***Source : Link , Question Author : John Smith , Answer Author : qoheleth*