[R-sig-eco] Family and population level variation in mixed model

[Linda Bürgi]

Hello! I'm looking for advice on how to determine the significance/ contribution of family and population level variation using a mixed effects model with the following data structure:

- We used 100 different moth families from 10 populations in 2 regions
(5 populations per region, 2-15 families per population)

- Each family was set up in a cage with 25 individuals per family

- We wanted to test the effect of: host plant (2 levels), disease (2 levels), moth origin (2 regions)


- We exposed 1 family to only one combination of treatments (e.g.
family 1 is from region 1, has disease level 2 and was put on host plant 1; family 2 is from region 2, has disease level 2 and was put on host plant 2, ... ), resulting in 5-15 reps (families) per treatment combination


- Survival as response variable (#alive, #dead) (always adds up
to 25)

- Model: lmer((#dead,#alive) ~ host plant * region + disease +(1|family)
+(1|population), family = binomial)


Research question (apart from fixed level significance):
which level (family or population) contributes more to variation?

But: by including family as a random factor, we have “nothing
left for error”. Am I overparameterizing the model and/or does model output even make sense? Would it be better to try some
bootstrapping method? I’ve never done that, any pointers to text books or
publications? 
And: can I use AIC of model with and without random factors to determine significance of random factors? 

Model output:Generalized linear mixed model fit by maximum likelihood ['glmerMod']
 Family: binomial ( logit )
Formula: y ~ pla * lo + nos + (1 | population) + (1 | family) 

      AIC       BIC    logLik  deviance 
 526.6389  544.2915 -256.3195  512.6389 

Random effects:
 Groups Name              Variance Std.Dev.
 family        (Intercept) 3.1057   1.7623  
 population    (Intercept) 0.2328   0.4825  
Number of obs: 92, groups: lot, 92; pop, 11

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)  
(Intercept) -0.67657    0.60726  -1.114   0.2652  
plantS        -1.50391    0.83761  -1.796   0.0726 .
regionV         -0.01176    0.69456  -0.017   0.9865  
diseasey        -0.31352    0.44933  -0.698   0.4853  
plantS:regionV    -0.75070    0.96990  -0.774   0.4389  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Correlation of Fixed Effects:
         (Intr) plaS   loV    nosy  
plantS     -0.591                     
regionV      -0.796  0.502              
diseasey     -0.250  0.046 -0.093       
plantS:regionV  0.517 -0.865 -0.571 -0.065


AIC for random factor significance: 

mo<-lmer(y~plant*region + disease +(1|population)+(1|family), family=binomial)
mo1<-lmer(y~plant*region + disease +(1|family), family=binomial)   
mo2<-glm(y~plant*region + disease , family=binomial)

AIC(mo)  526.6389
AIC(mo1) 525.5622
AIC(mo2) 1001.55


Thanks already for your help! 		 	   		   		 	   		  
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