[R-sig-ME] repeated measures on split plot design

[Magdalena Wiedermann]

Dear Thierry

Thank you so very much for taking this on and helping out. I was 
particularly happy about the glmm wiki link you sent. It contained a lot 
of relevant information in an organized way. THANK YOU! Now I also 
understand what you are getting at with your question about the 
correlation structure of the random factors. My Crawley based 
understanding  (Crawley 2007 "The R Book" page 472-473) comes closest to 
"2. Effects are fixed if they are interesting in themselves or random if 
there is interest in the underlying population."

I am likely dealing with crossed random effects:
"Relatively few mixed effect modelling packages can handle crossed 
random effects, i.e. those where one level of a random effect can appear 
in conjunction with more than one level of another effect. (This 
definition is confusing, and I would happily accept a better one.) A 
classic example is crossed temporal and spatial effects. If there is 
random variation among temporal blocks (e.g. years) ''and'' random 
variation among spatial blocks (e.g. sites), ''and'' if there is a 
consistent year effect across sites and ''vice versa'', then the random 
effects should be treated as crossed."

However I consider some of my spacial autocorrelation weak. The main 
factor that causes variation (in just about everything) in that system 
is water table. My within block variation is greater than my between 
block variation. Where we do have a high degree of spacial 
autocorrelation is by sampling 2 depth within each plot that are more or 
less on top of each other.

When it comes to time on the other hand May 2012 is more closely related 
to June 2012 than it is to October 2012 or September 2014.

For the random part I am primarily interested in formulating the model 
as to avoid pseudoreplication. My n=316 (I have a few missing values and 
dates) but really I only have 12 plots (4 blocks if used in a split plot 
analysis). I am aware that the 4 levels of block is not a good 
representation of the population of levels which is a requirement for it 
to be a random factor. But how do I formulate the model without running 
into pseudoreplication?

For pretty much all the analysis I have ever done nlme and lme4 resulted 
in the same F-values (with marginal differences). nlme and glmmPQL (the 
SAS person had suggested a Gamma distribution, which I am not entirely 
convinced of) yield exactly the same Dd.f.

Do you have any examples of code for crossed random effects?
I ran it like this but can not tell whether or not it makes sense.

|nlme & car:
m1<-lme(||log(||responses||)||~veg*depth*year*Month, random=~1|block/veg/year/Month, data=T)||
anova(m1)|

I am actually planing to include water table too
|m2<-lme(||log(||responses||)||~veg*depth*WT*year*Month, random=~1|block/veg/year/Month, data=T)||
anova(m2)|

Thank you so much!!
Lea