[R-sig-ME] Empirical Bayes and mixed effects modeling - are these the same thing?

Joshua Rosenberg jrosen at msu.edu
Fri Feb 2 21:56:53 CET 2018

Hi all, I have been curious about the similarities and differences between
Empirical Bayes and mixed effects modeling approaches. The Wikipedia page
<https://en.wikipedia.org/wiki/Empirical_Bayes_method> for Empirical Bayes,
for instance, says

"Empirical Bayes methods are procedures for statistical inference in which
the prior distribution is estimated from the data. This approach stands in
contrast to standard Bayesian methods, for which the prior distribution is
fixed before any data are observed. Despite this difference in perspective,
empirical Bayes may be viewed as an approximation to a fully Bayesian
treatment of a hierarchical model wherein the parameters at the highest
level of the hierarchy are set to their most likely values, instead of
being integrated out."

This sounds a lot like a mixed effects model, wherein the grand mean /
variance for the outcome represents the prior for the random effects
predictions. Are these the same thing? Just a curiosity and I had trouble
finding helpful answers after look elsewhere.

Joshua Rosenberg, Ph.D. Candidate
Educational Psychology ​&​ Educational Technology
Michigan State University

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