Is it possible to get effect sizes for the omnibus F-test returned by `mixed`?

[smithdanielle]

Some journals request effect sizes to be included in the analysis. I don't know if this is possible, but can a specialised effect statistic (such as eta-squared) be returned alongside the F-test? Effect sizes such as standardised beta in a LMM table are not interpretable when using sum contrast coding (especially when number of levels of a factor are >= 3).

[singmann]

Unfortunately not at the moment. The problem is not trivial and to my knowledge no general solution has as of yet been proposed. Some discussion on this issue can be found at the lme4 faq and in Westfall et al. (2014).

My recommendation is to report effects on the response scale. We have done so in e.g., Kellen et al. (2015).

References:

• Kellen, D., Singmann, H., Vogt, J., & Christoph Klauer, K. (2015). Further Evidence for Discrete-State Mediation in Recognition Memory. Experimental Psychology, 62(1), 40–53. http://doi.org/10.1027/1618-3169/a000272
• Westfall, J., Kenny, D. A., & Judd, C. M. (2014). Statistical power and optimal design in experiments in which samples of participants respond to samples of stimuli. Journal of Experimental Psychology: General, 143(5), 2020–2045. http://doi.org/10.1037/xge0000014

[singmann]

See also the response at: https://afex.singmann.science/forums/topic/compute-effect-sizes-for-mixed-objects/#post-295

[mattansb]

I've seen a simple solution for calculating partial eta square in some paper with LMM, which I have back tracked to: Friedman, H. (1982). Simplified determinations of statistical power, magnitude of effect and research sample sizes. Educational and Psychological Measurement, 42(2), 521-526. [Table 2 ]

pes = F*df1 / (F*df1 + df) (in ANOVAs this is an exact calculation, in LMM I guess this is some estimate)

These are available here: https://easystats.github.io/effectsize/articles/from_test_statistics.html