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 /////////////////////////////////////////////////////////////////////////////////////////// To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher The plural of anecdote is not data. ~ Roger Brinner The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data. ~ John Tukey /////////////////////////////////////////////////////////////////////////////////////////// <https://www.inbo.be> 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 [[alternative HTML version deleted]]
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