[R-sig-ME] randomized block design glmer question

[chico3 at sapo.pt]

Dear experts,



My background with mixed models is very pour. However,With the  
precious help of this forum I have implement a glmer function to test  
the experiment described below (randomized block design)

I have four luminaires randomly distributed. Two luminaires have light  
on and two luminaires have no light. Below the luminaires I have two  
treatments. Each treatment as four replicates that were randomly  
distributed below the luminaires. Moreover, I have made all the  
possible combinations of presence absence of light and treatments.

I want to check if there is a effect of each treatment and the  
interactions between all the combinations.The response variable is a  
proportion (number of specific specie/total number of species)
#define factors

Treatment1<-as.factor("Yes","No")
Treatment2<-as.factor("Yes","No")
Light<-as.factor("Yes","No")
Luminaire<-as.factor("LightYes1","LightYes2","NoLight1", "NoLight2")
Response<-cbind(number_of_specific_species, total_species)

#including individual level variability to account for overdispersion

obs <- 1:nrow(Response)

#model
library(lme4)
model<-glmer(Response ~ Treatment1*Treatment2*Light + (1|Luminaire) +  
(1|obs), family=binomial)
summary(model)
Generalized linear mixed model fit by the Laplace approximation
Formula: Response ~ Treatment1 * Treatment2 * Light + (1 | Luminaire)  
+ (1 | obs)
    AIC   BIC logLik deviance
  180.2 194.9  -80.1    160.2
Random effects:
  Groups    Name        Variance Std.Dev.
  obs       (Intercept) 0.059638 0.24421
  Luminaire (Intercept) 0.000000 0.00000
Number of obs: 32, groups: obs, 32; Luminaire, 4

Fixed effects:
                                         Estimate Std. Error z value Pr(>|z|)
(Intercept)                             -0.9283     0.1236  -7.511  
5.88e-14 ***
Treatment1Yes                            0.2416     0.1743   1.386  0.16582
Treatment2Yes                           -0.2459     0.1747  -1.408  0.15921
LightYes                                -0.2069     0.1745  -1.186  0.23562
Treatment1Yes:Treatment2Yes             -0.7517     0.2468  -3.046  0.00232 **
Treatment1Yes:LightYes                  -0.3018     0.2464  -1.225  0.22071
Treatment2Yes:LightYes                   0.2126     0.2466   0.862  0.38866
Treatment1Yes:Treatment2Yes:LightYes     0.7520     0.3488   2.156  0.03110 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
                               (Intr) Treatment1Yes Treatment2Yes   
LightYes  Treatment1Ys:Treatment2Y Treatment1Y:U Treatment2Y:Light
Treatment1Yes                 -0.709
Treatment2Yes                 -0.708    0.502
LightYes                      -0.708    0.502         0.501
Treatment1Yes:Treatment2Ys     0.501    -0.706       -0.708        -0.355
Treatment1Yes:LightYs          0.502    -0.707       -0.355         
-0.708               0.500
Treatment2Yes:LightYes         0.501    -0.355       -0.708         
-0.707               0.501               0.501
Treatment1Y:Treatment2Y:Light -0.354     0.500        0.501          
0.500               -0.707             -0.706         -0.707


-------------

The results are coherent with barplot and PCO analysis that I did  
previously, were combination of treatment1 and treatment2  have a  
greater effect than other combinations.


My question are

Is the model corrected?

How can I interpret the results, since I cannot do a Anova for example?


Cheers,

FranciscoR