[R] Analyses of covariation with lme() or lm()

[CG Pettersson]

Hello all!

I have a problem that calls for a better understanding, than mine, of 
how lme() uses the random part of the call.

The dataset consists of eleven field trials (Trial) with three 
replicates (Block) and four fertiliser treatments (Treat). Analysing for 
  example yield with lme() is easy:

m1 <- lme(Yield ~ Treat, data=data,
           random =~1| Trial/Block)

giving estimates of Treat effects with good significances. If I compare 
m1 with the model without any random structure:

m2 <- lm(Yield ~ Treat, data=data),
m1 is, naturally, much better than m2. So far so good.

Now I have one (1) measure from each Trial, of soil factors weather and 
such, that I want to evaluate. Remember: only one value of the covariate 
for each Trial. The suggestion I have got from my local guru is to base 
this in m1 like:

m3 <- lme(Yield ~ Treat + Cov1 + Treat:Cov1, data=data,
           random =~1| Trial/Block)

thus giving a model where the major random factor (Trial) is represented 
  both as a (1) measure of Cov1 in the fixed part and by itself in the 
random part. Trying the simpler call:

m4 <- lm(Yield ~ Treat + Cov1 + Treat:Cov1, data=data)

gives back basically the same fixed effects as m3, but with better 
significances for Cov1. Tested with anova(m3,m4) naturally gives the 
answer that m3 is better than m4. Ok, what about dealing with Trial in 
the fixed call? :

m5 <- lm(Yield ~ Trial + Treat + Cov1 + Treat:Cov1, data=data)

lm() swallows this, but silently moves out Cov1 from the analysis, an 
action that feels very logical to me.

My guru says that using the random call secures you from overestimating 
the p-values of the covariate. I fear that the risk is as big that you 
underestimate them with the same action. Working on a paper, I naturally 
want to be able to do some sort of discussion on the impact of 
covariates... ;-)

What is the wise solution? Or, if this is trying to make other people do 
my homework, could anyone tell me where the homework is? (I´ve got both 
Pinhiero & Bates and MASS as well as some others in the bookshelf.)

Cheers
/CG

-- 
CG Pettersson MSci. PhD.Stud.
Swedish University of Agricultural Sciences (SLU)
Dep. of Crop Production Ecology (VPE).
http://www.slu.se/
cg.pettersson at evp.slu.se