[R-sig-ME] effect sizes in lmer

[Steven J. Pierce]

Josh,

Check out the following paper in addition to the other suggestions folks
here are making. Baguley provides a useful critique of standardized effect
sizes. If your variables are measured in inherently meaningful units, there
is utility in understanding what the parameter estimates actually tell you
in terms of simple effect size. 

Baguley, T. (2009). Standardized or simple effect size: What should be
reported? British Journal of Psychology, 100(3), 603-617. doi:
10.1348/000712608X377117

As an additional thought, an interaction is just a situation where the
effect size of one bivariate relationship (say slope of x as predictor of y)
depends on some other variable (for example z). Consider reporting all the
conditional effect sizes that describe the set of relationships rather than
some overall effect size. For example, what is the effect of x on y when z =
1, when z = 2, etc. Interpreting those conditional effects would be more
scientifically informative about the phenomenon under study than an overall
effect size, which is often too abstract a quantity for people to actually
understand. I suspect there are in fact situations where the same value for
the overall effect size could have drastically different implications
depending on what is happening with the various conditional effects. 


Steven J. Pierce, Ph.D.
Associate Director
Center for Statistical Training & Consulting (CSTAT)
Michigan State University
E-mail: pierces1 at msu.edu
Web: http://www.cstat.msu.edu 

-----Original Message-----
From: Joshua Hartshorne [mailto:jkhartshorne at gmail.com] 
Sent: Sunday, October 13, 2013 9:32 AM
To: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] effect sizes in lmer

Hi Henrik,

I'm not sure if I follow your reply. Using fixef will give me 24 effects,
including the intercept. An ANOVA would give 7. What I need to report are
the 7 ANOVA-style effects, not the 24 me-style ones.

To make this more concrete, I have 4 types of stimuli, two different types
of tests, and 3 conditions. What the readers are going to want to know is
whether there is an omnibus interaction. Fixef reports 6 omnibus
interactions -- one for every level of the interaction. I will also need to
report the lower-level interactions and main effects. (Doesn't matter
whether these are truly interpretable in the face of a significant
higher-order interaction: It's standard practice to report them.)

I can measure the significance of the ANOVA-style omnibus interaction by
using model comparison. But that doesn't give me an effect size exactly.
(One suggestion I heard recently was to use the change in AIC as an effect
size.)

Any ideas?

Josh

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