[R-sig-ME] Binomial GLMM vs GLM question

Justin Touchon jtouchon at bu.edu
Thu May 15 23:40:08 CEST 2008

Dear Dr. Bates and other LMER experts,
    I am admittedly entry level in my R and mixed-model knowledge, but 
I'm hoping that someone can help me and also forgive my lack of 
insight.  Over 3 years, I monitored survival of 350 egg masses at two 
ponds.  I thus have one continuous variable (rainfall) and two discrete 
variables (year and pond).  My response variable, mortality, is coded as 
a two column matrix featuring eggs survived and eggs dead. I'm primarily 
interested in the effect of rain on survival, but also if rain has 
different impacts at the different ponds and how much survival varied 
over the three years.  Originally, I though I could tackle this with a 
binomial GLM, but do I need a binomial GLMM instead, as rainfall and 
year would be random and pond fixed?  The problem with this is trying to 
make biological sense out of the results.  I've spent the last week 
reading all the past posts about why p-values can't be calculated and 
all that, which I'm fine with.  But what can I say about the effects of 
rainfall or year on egg survival from the variance estimates?  Also, 
doesn't LMER require that random factors be normally distributed, 
because my rainfall measurements are far from it.  Is that a problem?  
Thank you in advance for any advice you can give. 
-Justin Touchon

My model and output are as follows:

 > LMER.1<-lmer(mort~Pond + (Pond|total_rainfall) + (1|Year), 
family=binomial, data= FieldData0305)

 > summary(LMER.1)
Generalized linear mixed model fit using Laplace
Formula: mort ~ Pond + (Pond | total_rainfall) + (1 | Year)
   Data: FieldData0305
 Family: binomial(logit link)
  AIC  BIC logLik deviance
 7657 7680  -3822     7645
Random effects:
 Groups         Name           Variance Std.Dev. Corr  
 total_rainfall (Intercept)    21.66535 4.65461        
                Pond[T.Ocelot]  6.44297 2.53830  -0.627
 Year           (Intercept)     0.74082 0.86071        
number of obs: 350, groups: total_rainfall, 48; Year, 3

Estimated scale (compare to  1 )  4.603433

Fixed effects:
               Estimate Std. Error z value Pr(>|z|)
(Intercept)     -0.4678     1.0173 -0.4598    0.646
Pond[T.Ocelot]  -0.9831     0.9330 -1.0538    0.292

Correlation of Fixed Effects:
Pnd[T.Oclt] -0.648

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