Replicating type III anova tests for glmer/GLMM

? On the other hand, I don't understand how Cai et al. (2012) p.842,
? "combined analysis experiments 1 and 2", reported the main effect
? of a factor with 4 levels via a single estimate, SE, z, p coefficient.
? How did they obtain this and is this the right way?

It's just a guess, but any sum-of-square can be seen as a particular
contrast, that is a particular combination of the coefficients in the
model (or of the different means, expressed another way) that is
tested against 0. So I guess this single estimate is the value of the
contrast associated to the corresponding sum-of-squares, and SE/z/p
are derived similarly.

You can play with multcomp::glht to test this, but knowing which
contrast is tested by which sum of square in a specific desing may be
tricky: it depends on the coding, on the (un)balance...

Kowing if this is the ? right ? way is I think the same debate that
knowing which kind of sum-of-square should be used and the question is
very application dependent. Just, if you don't know what this single
estimate estimates really, interpretation is at best difficult...

Emmanuel CURIS
                                emmanuel.curis at parisdescartes.fr

Page WWW: http://emmanuel.curis.online.fr/index.html