Most principled reporting of mixed-effect model regression coefficients

The "parameters" package (https://easystats.github.io/parameters/) offers some convenient functions to extract standard errors, p-values or confidence intervals for a vast range of models. Just use "model_parameters()" or "ci()" if you are only interested in CIs. Note that there is a small issue with p-values/CIs based on Kenward-Roger or Satterthwaite approximated degrees of freedom with the current CRAN version, however, these issues are fixed in the latest GitHub version.

According to your original question: it really depends on the field, or even on the journal what information is required. I would say estimate, CI and p-value are often the "standard", and some information on the random effect variances (which you can also get with the parameters-package, using "random_parameters()") and/or R2/ICC are also useful measures to have information about the proportion of explained variance that can be accounted to the random effect parameters (R2 and ICC, in turn, are available in the "performance" package - https://easystats.github.io/performance/).

I personally usually report estimates, CIs, p-values, within- and between-group-variances and ICC (and here again: "group" is sometimes called "subjects", sometimes "clusters", depending on the discipline).

Best
Daniel


-----Urspr?ngliche Nachricht-----
Von: R-sig-mixed-models <r-sig-mixed-models-bounces at r-project.org> Im Auftrag von Ades, James
Gesendet: Samstag, 15. Februar 2020 01:29
An: Thierry Onkelinx <thierry.onkelinx at inbo.be>
Cc: r-sig-mixed-models at r-project.org
Betreff: Re: [R-sig-ME] Most principled reporting of mixed-effect model regression coefficients

Thanks, Thierry. This is what I was looking for!

When I try confint(lme4_model) I get the following warning:

```{r}

Computing profile confidence intervals ...
Error in zeta(shiftpar, start = opt[seqpar1][-w]) :
  profiling detected new, lower deviance

```
Is there an easier way of extracting confidence intervals for fixed effects in lme4 than calculating them using the point estimate +/- Z * SE ?

Best,
James
________________________________
From: Thierry Onkelinx <thierry.onkelinx at inbo.be>
Sent: Friday, February 14, 2020 1:47 AM
To: Ades, James <jades at health.ucsd.edu>
Cc: r-sig-mixed-models at r-project.org <r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] Most principled reporting of mixed-effect model regression coefficients

Dear James,

IMHO the estimate and its CI works best. They instantly provide the range of uncertainty around the estimate without the reader having to do the math. CI also work with skewed distributions. p-values don't offer much added value over a CI.
Below are a few examples of four estimates and their uncertainties. The first line displays the estimate and its SE. The second line displays the estimate, SE and p-values. The third displays the estimate and a relative error. While the last one displays the estimate and 95% CI.

Keep in mind that readers are more likely to understand CI rather than SE.

"1.2 ? 0.3"  "10.5 ? 4.5" "0.0 ? 0.3"  "0.0 ? 5.0"
"1.2 ? 0.3 (p = 0.0001)"  "10.5 ? 4.5 (p = 0.0196)" "0.0 ? 0.3 (p = 1.0000)"  "0.0 ? 5.0 (p = 1.0000)"
 "1.2 ? 25.0%"  "10.5 ? 42.9%" "0.0 ? Inf%"   "0.0 ? Inf%"
"1.2 (0.6; 1.8)"   "10.5 (1.7; 19.3)" "0.0 (-0.6; 0.6)"  "0.0 (-9.8; 9.8)"

Best regards,

Thierry

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be<mailto:thierry.onkelinx at inbo.be>
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www.inbo.be<http://www.inbo.be>

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Op vr 14 feb. 2020 om 09:31 schreef Ades, James <jades at health.ucsd.edu<mailto:jades at health.ucsd.edu>>:
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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