effect sizes in lme/ multi-level models

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effect sizes in lme/ multi-level models

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 gürtler

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Re: effect sizes in lme/ multi-level models

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 Gürtler wrote:

> 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 gürtler
>

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