Berton Gunter wrote:
Duncan:
Bates and Pinheiro do show explicitly and in detail that the restricted log
likelihood depends on the parameterization: "An important difference between
the likelihood function and the restricted likelihood is that the former is
invariant to one-to-one reparametrizations of the fixed effects ... while
the latter is not." (p.76)
So that answers both your questions: With different fixed effect
parameterizations you get different restricted log likelihoods even for the
same random effects specifications. So you cannot compare models and you see
differences of the sort you saw. That's just the way REML works.
I believe the the basic issue can be summarized as: the restricted log
likelihood is a nonlinear function of the fixed effects specification. Hence
linear transformations (reparametrizations) of the fixed effects change the
log likelihood. But if you want more than that, get the book (or another
reference of your choice). You could also try googling "REML".
All the above is subject to correction by Doug Bates, of course.
Doug has nothing to add. Good explanation. Thanks.
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