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:




#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)



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.


A Likelihood ratio test on an lme object is probably fine to test a certain hypothesis; but that is not an appropriate way to build or choose a model. You would do that with REMLoff and:

anova(fit1, fit2) 

AICc is a well developed criterion for model selection that directly implies and estimates from the data the model weight given the ensemble of models you suggest. For more information, see Burnham and Anderson (2002) or this link: http://web.ipac.caltech.edu/staff/fmasci/home/statistics_refs/AIC_in_modelselection.pdf


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