[R-sig-ME] effect sizes in lmer

[Ben Bolker]

Joshua Hartshorne <jkhartshorne at ...> writes:

> 
> 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 sympathize with this point of view but it also worries me ("oh,
this doesn't make sense, but in my field we do it anyway ...")
 
> 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.)

  I would go ahead and use -2*log-likelihood difference (deviance 
difference). This is
asymptotically chi-squared distributed, and is the analogue of the
F statistic in an ANOVA table, so if the F-statistic is what you 
define as "the effect size" in an ANOVA context then by extension
it makes sense to use the log-likelihood diff.