Likelihood Ratio tests and fixed effects with LMER

Hello,

I am quite new to all this approach, but since it's somewhat different  
from what I've seen in classes and I have to rely on what I have been  
learning by myself and on lists such as this one, it's easy to get  
confused. Anyway, I have seen in several textbooks which take this  
anova table / LRT approach the opposite "direction" of effect testing:  
starting with the full model, removing terms (interactions first, then  
according to effect size, for example) and comparing to the previous  
one.

So, the example would go something like this:

Fprob.lmer.full x Fprob.lmer.add to test the interaction term
Fprob.lmer.add x Fprob.lmer.parr (just a guess, judging for the AIC  
value) to test for the habitat effect
Fprob.lmer.parr x Fprob.lmer.null to test for the parr effect

Only proceeding to the next step if the LRT is nonsignificant. If  
changes to the model are significant, individual terms which haven't  
been tested yet would be tested by removing them and comparing to that  
model.

In this case, only the habitat effect could have a different p value,  
but I can imagine when you are comparing models with more terms that  
results could differ. I've even seen cases in which terms are  
sequentially removed as long as they are nonsignificant, point in  
which single terms previously removed are "re-added" individually to  
see if there is improvement to the model.

This may even be kind of "off topic" for this list, but since  
considerable discussion has been going on here about hypothesis  
testing and LRT previously, and the question was originally asked  
here, I thought it wouldn't hurt to continue the discussion...

You should also compare the results to those from simple models  
ignoring
the fact that females may appear more than once.  They should be  
broadly
similar.  How large is the variance due to the random effects anyway?

There was some discussion here previously about how it wouldn't be  
good to compare likelihoods of GLMM and GLM, because they are  
generated differently or something like that... Could this be done by  
generating a dummy identity variable with no repetitions (simulating  
non-repeating individual identities), using it as a random variable,  
and comparing the models? I don't know what this could do to the  
estimation of parameters and so on...

Many thanks in advance, and sorry for anything!

Abra?os,
Rafael Maia
---
"A little learning is a dangerous thing; drink deep, or taste not the  
Pierian spring." (A. Pope)
Animal Behavior Lab
Dept. of Zoology, Universidade de Brasilia
http://www.unb.br/ib/zoo/rhmacedo/

On Tue, 16 Dec 2008, David Grimardias wrote:

So for each type of behaviour, I want to know if fixed effects  
(habitat, parr and interaction) are significant or not. As  
previously requested, and answered by Mister Bates (https://stat.ethz.ch/pipermail/r-sig-mixed-models/2008q4/001458.html 
), I tried to use Likelihood ratio tests to determine if these two  
factors are significant or not. Here are an example about one type  
of behaviour (Fprob = number of probings by female) :

Fprob.lmer.full<-lmer(Fprob ~habitat+parr+habitat:parr +(1| 
female),family=poisson)
Fprob.lmer.add<-lmer(Fprob ~habitat+ parr +(1| 
female),family=poisson)
Fprob.lmer.hab<-lmer(Fprob ~habitat+(1|female),family=poisson)
Fprob.lmer.parr<-lmer(Fprob ~ parr +(1|female),family=poisson)
Fprob.lmer.null<-lmer(Fprob ~1+(1|female),family=poisson)

So, I considered as LR test for each effect :

Habitat : Chi2 = 0.9866; df = 1; p = 0.3206
Parr : Chi2 = 2.0372; df = 1; p = 0.1535
Interaction Habitat :parr : Chi2 = 0.545; df = 1; p = 0.4604

I first would like to know if I am wrong, or if I correctly  
analysed my data?

Yes, though there has been some discussion on this list about the  
adequacy of
the chi-square approximation for the LRTS in these models.

You should also compare the results to those from simple models  
ignoring
the fact that females may appear more than once.  They should be  
broadly
similar.  How large is the variance due to the random effects anyway?

Second, I guess that LMER function is optimizing REML by default  
(if I correctly read the help file), but I had understood that we  
need to optimize ML to compare fixed effects (from  Pinheiro J C &  
Bates D M, "Mixed-effects models in S and S-PLUS"). If right, what  
do I need to change to correctly analyzed my data with Likelihood  
ratio tests ?

REML is not done for GLMMs IIRC.

David Duffy.

-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax:  
-0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research    
\_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v

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