[R-sig-ME] Calculating effect sizes of fixed effects in lmer

James Pustejovsky jepu@to @end|ng |rom gm@||@com
Thu Sep 24 16:57:39 CEST 2020

Hi Amie,

I agree very much with Wolfgang's perspective that one would ideally use
outcomes such that unstandardized effects can be interpreted directly. If
one does have to fall back on standardized effect sizes, there's a further
question of what metric to use. Researchers often jump immediately to
standardized mean differences, but there are certainly other possibilities,
such as log response ratios for outcomes that are measured on ratio scales.

All that said, there has been a fair amount of work on standardized mean
difference effect sizes for certain types of research designs that would
usually be analyzed with multi-level models. A sampling (including some of
my own):

   - Hedges, L. V. (2007). Effect sizes in cluster-randomized designs. *Journal
   of Educational and Behavioral Statistics*, *32*(4), 341-370.
   - Hedges, L. V. (2011). Effect sizes in three-level cluster-randomized
   experiments. *Journal of Educational and Behavioral Statistics*, *36*(3),
   - Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014).
   Design-comparable effect sizes in multiple baseline designs: A general
   modeling framework. *Journal of Educational and Behavioral Statistics*,
   *39*(5), 368-393.
   - Stapleton, L. M., Pituch, K. A., & Dion, E. (2015). Standardized
   effect size measures for mediation analysis in cluster-randomized
trials. *The
   Journal of Experimental Education*, *83*(4), 547-582.
   - Feingold, A. (2009). Effect sizes for growth-modeling analysis for
   controlled clinical trials in the same metric as for classical
analysis. *Psychological
   Methods*, *14*(1), 43.

One of my students and I have also developed an R package for estimating
standardized mean differences from multilevel models fitted with nlme::lme()
Kind Regards,

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