[R-sig-ME] Suggestions on how to correct a misapprehension?

[Douglas Bates]

So my family is having to live through a "Someone is wrong on the
internet", https://xkcd.com/386/, moment. In the past couple of days I have
twice encountered the same mistaken characterization of how the parameter
estimates in lmer and in the MixedModels.jl package are evaluated.

As we documented in our 2015 paper http://dx.doi.org/10.18637/jss.v067.i01
in lme4 the REML estimates or the ML estimates for the parameters of a
linear mixed-effects model are evaluated by constrained optimization of a
profiled log-likelihood or profiled log-restricted-likelihood.  The
parameters directly being optimized are the elements of relative covariance
factors.  The profiling involves solving a penalized least squares
problem.  This PLS representation, and the use of sparse matrices, is what
allows for fitting models with random effects associated with crossed or
partially crossed grouping factors, such as "subject" and "item".  To many
users this capability is one of the big selling points for lme4.

In our paper we explain in great detail why this approach is, in our
opinion, superior to earlier approaches.  And if someone doesn't believe
us, both lme4 and MixedModels.jl are Open Source projects so anyone who
wants to do so can just go read the code to find out what actually is done.

So it came as a surprise when reading the Wikipedia entry on mixed models,
https://en.wikipedia.org/wiki/Mixed_model, to learn that lme4 and
MixedModels.jl use an EM algorithm that Mary Lindstrom and I described (
https://doi.org/10.1080%2F01621459.1988.10478693) in 1988.  It is possible
that in the early days of lme4 there was such an implementation, but not in
the last 15 years, and there definitely has never been such an
implementation in MixedModels.jl.  I noticed that the Python package
statsmodels is described in the Wikipedia article and in their
documentation, https://www.statsmodels.org/stable/mixed_linear.html, as
using that EM algorithm. I didn't verify this in the code because reading
code based on numpy and scipy causes me to start ranting and raving to the
extent that family members need to take away my laptop and put me in a
quiet room with the window shades drawn until I promise to behave myself.

Anyway the Python statsmodels documentation claims that lme4 uses this
method, which it doesn't.

I have never gone through the process of proposing an edit in a Wikipedia
article.  As I understand it I would need to create a login etc.  Would
anyone who does have such a login be willing to propose an edit and save me
the steps?

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