# [R] The mathematics inside lme()

Date: Fri 07 Oct 2005 - 22:57:22 EST

Hello all!

Consider a dataset with a grouping structure, Group (factor) Several treatments, Treat (factor)
Some sort of yield, Yield (numeric)
Something, possibly important, measured for each group; GroupCov (numeric)

To look for fixed effects from Treat on Yield, a first attempt could be:

m1 <- lm(Yield ~ Treat)

which gives, in a symmetric situation, the same estimated fixed effects as:

m2 <- lme(Yield ~ Treat,

random =~1| Group)

but m2 is a much better model with safer significances.

Now I want to evaluate GroupCov as a covariate to Treat. I can then start with either m1 or m2 as base, but what is most correct when GroupCov has only one value for each Group?

m3 <- lm(Yield ~ Treat + GroupCov + Treat:GroupCov)

m4 <- lme(Yield ~ Treat + GroupCov + Treat:GroupCov,

random =~1| Group)

but this time the prob.values for GroupCov is much stronger in m3 than in m4. Needless to say, anova(m3,m4) tells that m4 is a better *model* than m3. But is it better for my purpose? Trying an old-fashioned style model with only fixed effects? (Don´t shout at me, it is only a dirty test of the system):

m5 <- lm(Yield ~ Group + Treat + GroupCov + Treat:GroupCov)

is accepted by lm() but here GroupCov is silently removed from the analysis by lm(). I accept this removal, but I get even more suspicious that something fishy is going on in m4. My gut-feeling is that m3 is the right starting point but I have got a general recommendation always to start with m4-type calls when evaluating numeric covariates. I need one (or two) "doctor second opinion" on this.

How is the mathematics inside lme() working? Is some part of the variation I want to catch as an effect from GroupCov already removed by the random call, or why do I get better significances in the pure fixed call? Could these sigificances be some sort of artefact?

Cheers
/CG

PS.
I sent basically this question, but in a more special case and with another header, to the list two days ago. Nobody was interested, hopefully this is more tasty ;-)
DS.

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