Reporting results from a GLMER

Question

I have conducted a generalized linear mixed model (GLMM). For the output, see below. Normally (when reporting results from an ANOVA), I write something like this: $F(1, 116) = 6.09$, $p = .015$, $η2 = .04$. But which statistical parameters (e.g. $\beta$, ...) do I use when reporting the results below (according to APA)?

   747.5    788.7   -364.7    729.5      711
Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.4527 -0.4184  0.2273  0.4934  2.0564
Random effects:
 Groups Name        Variance Std.Dev.
 id     (Intercept) 3.006    1.734

Number of obs: 720, groups:  id, 120
Fixed effects:
                                  Estimate Std. Error z value Pr(>|z|)

(Intercept)                     -9.985e-01  5.763e-01  -1.733   0.0832 .

Risikodarstellung                1.351e+00  7.763e-01   1.740   0.0819 .

Icon                            -7.898e-01  7.961e-01  -0.992   0.3211

Position                        -8.368e-07  1.183e-01   0.000   1.0000

Risikodarstellung:Icon          -9.109e-02  1.141e+00  -0.080   0.9364

Risikodarstellung:Position       3.297e-01  1.659e-01   1.987   0.0469 *

Icon:Position                    7.937e-01  1.822e-01   4.357 1.32e-05 ***
Risikodarstellung:Icon:Position -4.527e-01  2.673e-01  -1.694   0.0903 .

Signif. codes:  0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
            (Intr) Rskdrs Icon   Positn Rskd:I Rskd:P Icn:Ps
Rskdrstllng -0.746

Icon        -0.712  0.529

Position    -0.718  0.533  0.520

Rskdrstll:I  0.502 -0.675 -0.698 -0.363

Rskdrstll:P  0.502 -0.700 -0.371 -0.713  0.480

Icon:Positn  0.446 -0.325 -0.719 -0.649  0.495  0.477

Rskdrst:I:P -0.312  0.435  0.490  0.443 -0.719 -0.620 -0.670 ```
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Answer 1

As Ben noted in the comments, there are no APA standards for reporting mixed models. However, there are certainly a good number of important parts about your analysis that should be included if this is for a published manuscript. A useful paper on this subject is Meteyard and Davies, 2020, which notes on Page 16 what you should include:

• Software and version used.
• What data cleaning/wrangling was involved and whether or not your data meets the assumptions of mixed models.
• Fixed and random effects are explicitly noted with important theoretical underpinnings noted for how the model was constructed.
• Sample size in terms of units of observations (50 subjects x 10 items = 500 observations for crossed effects models).
• Whatever model comparison was employed and the metrics that go with that (such as AIC/BIC).
• Convergence issues and how they were handled.
• The model equation and output (normally reported in a table), which includes pretty much everything it spits out (point estimates, standard errors, etc) as well as model fit metrics (pseudo R2 values for example).
• If possible, the data and code itself.

Here is an example from an article which includes a good number of these things but not all of them. They include the fixed effects on the top and the random effects on the bottom, along with the beta coefficients, the standard errors, and the t-values that go with them (I only include part of it here because its very long:

And another example here, where you can see they included the actual equations, R2 values, and p values:

Reporting of these models varies a lot. More is always better, so include as much as possible and try to follow the guides I have cited here.

Citations

Best Practice Guides

• Brown, V. A. (2021). An introduction to linear mixed-effects modeling in R. Advances in Methods and Practices in Psychological Science, 4(1), 1–19. https://doi.org/10.1177/2515245920960351
• Harrison, X. A., Donaldson, L., Correa-Cano, M. E., Evans, J., Fisher, D. N., Goodwin, C. E. D., Robinson, B. S., Hodgson, D. J., & Inger, R. (2018). A brief introduction to mixed effects modelling and multi-model inference in ecology. PeerJ, 6, e4794. https://doi.org/10.7717/peerj.4794
• Meteyard, L., & Davies, R. A. I. (2020). Best practice guidance for linear mixed-effects models in psychological science. Journal of Memory and Language, 112, 104092. https://doi.org/10.1016/j.jml.2020.104092

Example Studies

• Al-Dajani, N., & Czyz, E. K. (2022). Suicidal desire in adolescents: An examination of the interpersonal psychological theory using daily diaries. Journal of Clinical Child & Adolescent Psychology. https://doi.org/10.1080/15374416.2022.2051525

• Wang, L., Wang, J., Liu, D., & Lin, D. (2021). The role of metalinguistic awareness and character properties in early Chinese reading. Journal of Experimental Child Psychology, 210, 105185. https://doi.org/10.1016/j.jecp.2021.105185