[R-sig-ME] R2 for Negative Binomial calculated with GLMMADMB

Douglas Bates bates at stat.wisc.edu
Wed Dec 17 17:26:09 CET 2014

I must admit to getting a little twitchy when people speak of the "R2 for
GLMMs".  R2 for a linear model is well-defined and has many desirable
properties.  For other models one can define different quantities that
reflect some but not all of these properties.  But this is not calculating
an R2 in the sense of obtaining a number having all the properties that the
R2 for linear models does.  Usually there are several different ways that
such a quantity could be defined.  Especially for GLMs and GLMMs before you
can define "proportion of response variance explained" you first need to
define what you mean by "response variance".  The whole point of GLMs and
GLMMs is that a simple sum of squares of deviations does not meaningfully
reflect the variability in the response because the variance of an
individual response depends on its mean.

Confusion about what constitutes R2 or degrees of freedom of any of the
other quantities associated with linear models as applied to other models
comes from confusing the formula with the concept.  Although formulas are
derived from models the derivation often involves quite sophisticated
mathematics.  To avoid a potentially confusing derivation and just "cut to
the chase" it is easier to present the formulas.  But the formula is not
the concept.  Generalizing a formula is not equivalent to generalizing the
concept.  And those formulas are almost never used in practice, especially
for generalized linear models, analysis of variance and random effects.  I
have a "meta-theorem" that the only quantity actually calculated according
to the formulas given in introductory texts is the sample mean.

It may seem that I am being a grumpy old man about this, and perhaps I am,
but the danger is that people expect an "R2-like" quantity to have all the
properties of an R2 for linear models.  It can't.  There is no way to
generalize all the properties to a much more complicated model like a GLMM.

I was once on the committee reviewing a thesis proposal for Ph.D.
candidacy.  The proposal was to examine I think 9 different formulas that
could be considered ways of computing an R2 for a nonlinear regression
model to decide which one was "best".  Of course, this would be done
through a simulation study with only a couple of different models and only
a few different sets of parameter values for each. My suggestion that this
was an entirely meaningless exercise was not greeted warmly.

On Wed Dec 17 2014 at 9:49:28 AM Jens Oldeland <fbda005 at uni-hamburg.de>

> Dear List-members,
> recently, the R2 calculations for GLMMs invented by Schielzieth and
> Nakagawa 2012 [1] were implemented into the MuMIn package. This is
> incredibly good news, as many colleagues still require R2 to understand
> a model output. I invested 2 weeks in lengthy calculations of about 20
> negative binomial GLMMs using the glmmADMB package. Now, my colleagues
> want the R2 (me too), however, sadly, the MuMIn functions do only work
> for binomial and poisson GLMMS. Further, it seems that the functions do
> not recognize the glmmADMB package but prefer (g)lmer output.
> Now my question: Does anybody of you know if this is "easy" to implement
> and if so "how"? I tried to redo the code provided here (actually posing
> the same question) but failed...:
> http://stats.stackexchange.com/questions/109215/r%C2%B2-
> squared-from-a-generalized-linear-mixed-effects-models-glmm-using-a-negat
> Or does anybody know if in the near future (this year?) it will be
> implemented somewhere?
> Is it possible to transform a GLMMADMB object into an lmer object?
> Any hints are most welcome,
> merry Xmas
> Jens
> [1] Nakagawa, S., & Schielzeth, H. (2013). A general and simple method
> for obtaining R2 from generalized linear mixed-effects models./Methods
> in Ecology and Evolution/,/4/(2), 133-142.
> --
> +++++++++++++++++++++++++++++++++++++++++
> Dr. Jens Oldeland
> Post-Doc Researcher & Lecturer @ BEE
> Managing Editor - Biodiversity & Ecology
> Biodiversity, Ecology and Evolution of Plants (BEE)
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> University of Hamburg
> Ohnhorststr. 18
> 22609 Hamburg,
> Germany
> Tel:    0049-(0)40-42816-407
> Fax:    0049-(0)40-42816-543
> Mail:   jens.oldeland at uni-hamburg.de
>          Oldeland at gmx.de
> Skype:  jens.oldeland
> http://www.biologie.uni-hamburg.de/bzf/fbda005/fbda005.htm
> http://www.biodiversity-plants.de/biodivers_ecol/biodivers_ecol.php
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