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
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be


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Op vr 14 feb. 2020 om 09:31 schreef Ades, James <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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