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effect sizes in lme/ multi-level models

2 messages · Leo Gürtler, Spencer Graves

Leo Gürtler
# 
Dear alltogether,

I am searching for a way to determine "effect size" in multi-level 
models by using lme().
Coming from Psychology, for ordinary OLS there are measures (for 
meta-analysis, etc.) like

CohensD <- (mean_EG - mean_CG) / SD_pooled

or

(p)eta^2 <- SS_effect / (SS_effect + SS_error)

I do not intend to lead a discussion of the usefulness of such measures 
as long as the standards of psychological journals (e.g. as defined by 
the APA) order them.
However, I wondered how to determine measures of effect size in lme. 
Pinheiro&Bates (2000) do not touch that topic.
I assume that as long as a grouping structure is present, the formular 
of CohensD (see above) has to be corrected to give respect to the 
grouping structure. Is there any equivalent measure like eta^2, 
partial-eta^2, etc.?

Can anybody help me with formulas, R code or some references?

Thank you very much,

thanks in advance,

leo g??rtler
4 days later
Spencer Graves
# 
The "eta^2" you describe looks something like an R^2 (or maybe a 
partial R^2), and CohensD looks like a Student's t, at least to me.  The 
problem with generalizing these to multi-level models is deciding which 
components of variance to include where.  If you can answer that, I 
think you can find all the pieces you need by trying 
'methods(class="lme")'.  I just got 32 items on that list, but you might 
get a different number unless you have exactly the same packages (and 
versions) attached as I did just now.  From this list of 32, I suggest 
you look first at "fixef", "ranef", and "VarCorr".

	  hope this helps.
	  spencer graves
Leo G??rtler wrote: