[R-sig-ME] Ad-hoc LRT for single term in binomial GLMM, with DF from cAIC4

[Juho Kristian Ruohonen]

Hi,

Conditional setting here, with BLUPs of inherent interest (clusters likely
to recur in future).

When analyzing the importance of fixed effects in a conditional setting, is
there something wrong with using just a basic Deviance comparison of nested
GLMMs? As I understand it, the main difficulty resides in determining the
effective degrees of freedom when the analysis is conditional on the BLUPs.
But nowadays we have the cAIC4 package, which seems to do a respectable job
at estimating those DF.

So, why not just call pchisq(deviance(SmallMod)-deviance(BigMod), df =
BigModCAIC$df-SmallModCAIC$df, lower.tail = FALSE), and be done with it?
Seems more straightforward, as well as conceptually simpler, than that
parametric bootstrap business.

One awkwardness that I do notice about this procedure is that sometimes the
smaller model is estimated to have more effective parameters (a larger df)
than the bigger model. I guess the reason is that sometimes the random
effects manage to "bail the model out and then some" when a fixed effect is
removed. But whether this invalidates the whole procedure, I don't know. My
intuition says no, it doesn't. But I'm a lowly non-statistician. Would
therefore love to hear what the gurus think.

Best,

Juho

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