[R-sig-ME] Most principled reporting of mixed-effect model regression coefficients

[Emmanuel Curis]

Hello,

For what it's worth, here a few ides about the different reporting.
The main one being that it is, first of all, a matter of conventions
that may vary with the community and time, so you should first see
what are the usages in your field, then decide if you find them suited
or not for your own purpose and follow them or not.

For instance, physicists and some chemists do like standard errors:
quite often, it is because error come from small measurement
uncertainties and the Gaussian approximation fairly holds, so
interpreting standard errors is straightforward - confidence intervals
are roughly ±2 standard error in this case, for the usual 95 % level.

Other chemists and most population-pharmacokineticians do not use
standard errors, but instead coefficient of variation, expressed as
percent (that is, 100×standard error/coefficient estimation). Beside
usage, this is also because quite often, the underlying assumption is
that variance change with the value or even more specifically that a
log-normal distribution holds, and interpretation as relative error is
then more straightforward.

Both methods can be quite misleading if the underlying distribution
assumption is not met, and especially in case of strongly skewed
distributions. In that case, confidence intervals are not anymore
given by ±2 standard error, and can be fairly different.  In such
cases, giving confidence intervals seems better, because
interpretation is straightforward.

P-values answer a quite different question: they say, more or less, if
the coefficient is different from a reference value, typically 0, but
they do not really convey any information about the coefficient
precision.

Hope this helps a little bit to make a thinked-about selection...  Of
course, this reflects only my own perception of these notions.

Best regards,

On Fri, Feb 14, 2020 at 07:59:34AM +0000, Ades, James wrote:
« Hi all,
« 
« 
« 
« It?s been surprisingly difficult to find the most principled reporting of mixed-effect model regression coefficients (for individual fixed-effects). One stack overflow article lead me to this paper?a systematic review of the incorporating and reporting of GLMMs ( https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0112653#pone.0112653.s001)  which references a paper by Ben Bolker (https://www.sciencedirect.com/science/article/pii/S0169534709000196). Oddly, I don?t really find an answer to this in either of those. I?ve heard mixed things regarding fixed effect coefficients in LMM (that LMM/and GLMMs are more about the predictive power of an entire model than the individual predictors themselves), but overall, my understanding is that it?s kosher (and informative) to look at effect sizes of regression (fixed effect) coefficients?only that lme4 doesn?t currently provide p values (though Lmertest does).
« 
« 
« 
« It seems like reporting effect size of regression coefficients and their SEs should suffice; though sometimes people report CI with those as well (but isn?t that a little redundant). My PI is telling me to include p-values. So many different things, so little agreement.
« 
« 
« 
« I figured I?d turn here for something of a ?definitive? answer.
« 
« 
« 
« Ben, I definitely need to go back and read through your paper more thoroughly for a deeper understanding of the nuances of GLMMs. Currently watching?and reading?McElreath?s Statistical Rethinking, but I?m not quite at the level of implementing MCMCs.
« 
« 
« Much thanks,
« 
« 
« James
« 
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                                Emmanuel CURIS
                                emmanuel.curis using parisdescartes.fr

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