Hello,

I previously read this : 
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2008q4/001458.html
but I still have some questions about my statistical analysis.

Here is my problem :

We study the effect of habitat structure on the spawning behaviour in 
salmon. So we experimentally observed the behaviour of fish (we 
considered 6 types of behaviours) during the spawning season.

Then I want to analyse if the number of behaviour (for each type) we 
observed 1 hour before the spawn is influenced by 2 factors : the 
structure of habitat (2 experimental levels : homogeneous and 
heterogeneous habitat) and the presence of parr (2 experimental levels: 
0 (absence) or 1 (presence)).

As we have got several spawning events by female (because we can not use 
a lot of females), I have to use mixed models, with female as random 
effect (a female is used only in one type of habitat and in presence OR 
absence of parr, ).

 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)

 > anova(Fprob.lmer.full,Fprob.lmer.add)
Data:
Models:
Fprob.lmer.add: Fprob ~ habitat + parr + (1 | female)
Fprob.lmer.full: Fprob ~ habitat + parr + habitat:parr + (1 | female)
                Df     AIC     BIC  logLik Chisq Chi Df Pr(>Chisq)
Fprob.lmer.add   4  319.71  326.57 -155.86                       
Fprob.lmer.full  5  321.17  329.74 -155.58 0.545      1     0.4604

 > anova(Fprob.lmer.hab,Fprob.lmer.null)
Data:
Models:
Fprob.lmer.null: Fprob ~ 1 + (1 | female)
Fprob.lmer.hab: Fprob ~ habitat + (1 | female)
                Df     AIC     BIC  logLik  Chisq Chi Df Pr(>Chisq)
Fprob.lmer.null  2  319.11  322.54 -157.55                        
Fprob.lmer.hab   3  320.12  325.26 -157.06 0.9866      1     0.3206

 > anova(Fprob.lmer.parr,Fprob.lmer.null)
Data:
Models:
Fprob.lmer.null: Fprob ~ 1 + (1 | female)
Fprob.lmer.parr: Fprob ~ parr + (1 | female)
                Df     AIC     BIC  logLik  Chisq Chi Df Pr(>Chisq)
Fprob.lmer.null  2  319.11  322.54 -157.55                        
Fprob.lmer.parr  3  319.07  324.21 -156.54 2.0372      1     0.1535/

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 ?

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 ?

I am finishing my PhD, and I have to finish to correctly analyze 
behavioural data (with Poisson distribution) and genetic data as well 
(binomial data) before publishing.
Thank you for all the help you can bring to me here.

Best regards,

David Grimardias

-- 
-------------------------------------
David GRIMARDIAS
Doctorant
UMR INRA-UPPA ECOBIOP
Quartier Ibarron
64310 SAINT PEe SUR NIVELLE

Tél.: 0559515979
Fax: 0559545152
mail: David.Grimardias@st-pee.inra.fr
http://www.st-pee.inra.fr
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