# Some doubts about using GLMM

I'm analyzing the results of a hormone manipulation experiment. I measured a number of variables at three times in three groups. The groups are different sizes and not all individuals were measured every time, so I'm using GLMM rather than a repeated-measures ANOVA. I created the model then tested the significance of the terms (time, treatment, and time x treatment) with ANOVA.

I'm quite new to GLMM, but after doing the tests, further reading suggests that my approach may be inappropriate, particularly with small data sets (I have ~seven animals per group). It seems that there is disagreement about what the degrees of freedom should be. This leads me to three questions:

1) Is this method acceptable?

2) If so, what would be an appropriate method to do post-hoc analyses to determine which groups differ?

3) Like the fake data, I have a number of negative results. Specifically, I often see significant time effects, but no effect of treatment or treatment X time. If I stick with this method, how can I calculate effects sizes and/or confidence intervals for such tests?

Here are some fake data:

library(nlme)

datums<-data.frame(id=rep(1:20,each=3),var1=runif(60,4,6),var2=runif(60,25,30),var3=runif(60,0,1),var4=runif(60,10,15),var.time=rep(1:3,times=20),var.treatment=rep(c('a','b','c'),each=20))

datums$var.time<-as.factor(datums$var.time)
datums$id<-as.factor(datums$id)

#and now the GLMMs on each variable - I'll show just two here

var1.glmm<-lme(var1~var.time + var.treatment + var.time*var.treatment, data=datums, random = ~1| id)

var2.glmm<-lme(var2~var.time + var.treatment + var.time*var.treatment, data=datums, random = ~1|id)

summary(var1.glmm)

anova(var1.glmm)


I'm aware that the place for me to go is probably the Pinheiro and Bates book, but I don't have access to it at this time. Thanks in advance for any advice.

anova(fit1, fit2)