valid estimates using lme4?

When the reviewer is bemoaning the use of one
integration point they are not taking into account the fact that the
approximation is being evaluated at the conditional mode of the random
effects.

Maybe they are; that approximation can be terrible if there are many
weakly-identified or very correlated-given-data REs.
Expectation propagation and variational-Bayes are (often claimed)
substantially better in that regime; as best I know there is no R
package for those approaches.
A Gelmen's in-prep package "stan" seems like it will include something
along those lines, and there is the glm-ie package for Matlab/octave.
For the practical question,

It is impossible to determine if SAS, Stata, or SPSS are implementing the steps they claim to implement since the source code is not available. It is >one thing to be able to write out the algebraic expression for solving mixed models, whether using Henderson's mixed model equations (SAS) or any >other approach.

For Mixed at least, I have produced identical output on VC estimates,
FE estimate, RE estimates, likelihood values, and other output I felt
like checking using my own from-scratch supplementation given the same
data for a few design structures. I could probably do the same with
GLIMMIX, though as noted by D Bates GLIMMIX is very restricted in the
models it will fit.


C Ryan King