Wald tests for glmer

Michael Allen <michael.allen at ...> writes:

Hello,
In the Bolker et al. 2009 TREE paper, what is exactly meant by Wald t or F
tests (e.g., in the flow chart)? Is this similar to the z tests for each
parameter estimate provided in the "summary()" output? Can it be calculated
from this? Is there a function available to perform it? Thank you.

This is a bit of a hangover from when I knew and understood less than
I do now about GLMMs (although I'm still not quite sure what to do).
What I had in mind at the time was that one should take the "Z score"
reported by summary() and treat it as a t score instead, with the number
of degrees of freedom guessed from classical design principles (or from
what lme() reported about a model with similar structure).  Alternatively,
one could do the equivalent of the sort of "likelihood F test" that's done
with anova(...,test="F") for quasilikelihood models.

  I'm no longer sure this is a great idea, but it's at least a first
hack at a small-sample correction.  If you extract coefficients C and
standard errors S from summary() then

2*pt(abs(C/S),df=df,lower.tail=FALSE)

  with the "appropriate" df should give you the t-test.

  Unfortunately, this is one of those situations where as far as I can
tell all of the real statisticians are out there playing with large data
sets where the small-sample corrections are not so important and leaving the
rest of us to figure it out for ourselves ...