[R-sig-ME] Effect Size in lme

[Doran, Harold]

IMHO, this is a worthless endeavor. The statistic you note below is typical in meta-analysis where you want to find a linear relationship between two continuous variables. There was a big push in my field (education) to always publish some form of a standardized effect size alongside all results.

I always thought this was just plain silly since the linear model itself gives a more natural measure of an effect. That is, isn't that what the effect of some covariate is anyway? I never found it reasonable to then convert this to some standardized coefficient (no longer on the metric used for the analysis) to aid in the interpretation. I think it does exactly the opposite. You now have some number that is not on the same metric as the original variable that is supposed to help you think more about the original variable? 

When I want to think about variability of some variable, I prefer the standard deviation and not the variance since the sd is on the same scale as the metric of interest and it is therefore directly interpretable.

With that said, with mixed effects models, I think this issue is a bit more complex. I don't mean to open a can of worms, (but I'm sure I will) what is the right DF for the mixed effects model anyhow? The fixed effects do not follow a known distribution, although many treat them as though they follow an F distribution for convenience.  

-----Original Message-----
From: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Patrick Onyango
Sent: Monday, March 08, 2010 5:52 PM
To: Ben Bolker
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] Effect Size in lme

Dear Ben,
Many thanks.

Thanks for clarifying: yes, I am interested in effect size with  
respect to biological significance of my findings.  In addition to  
the suggestions you have provided, which I hope to talk to you some,  
would you recommend using the following formula, from Nakagawa &  
Cuthill (2007) Biol. Rev. 82, 591-605: partial correlation  
coefficient, r = the t value divided by the square of the sum of the  
t value squared and its corresponding degrees of freedom?

Here is the equation:


I am not quite sure how to interpret, with respect to the kind of  
effect I am looking for, the parameter estimates and the other values  
that you suggested. Are there resources you can recommend. In the  
meantime, I will check in P & B 2000 as well as in West et al. 2007.

Thanks,
Patrick

On Mar 8, 2010, at 4:39 PM, Ben Bolker wrote:

> Patrick Onyango wrote:
>> All,
>> I have been asked to provide effect sizes for results I obtained from
>> lme. Does anyone know how to handle this?
>>
>> Many thanks already.
>> Patrick
>
>   There are a lot of definitions of "effect size".  If the request is
> simply to indicate the practical relevance of the effects (i.e.
> 'biological' significance), I would just quote the parameter estimates
> (with standard errors), and the standard deviations of the random
> effects ...
>
> -- 
> Ben Bolker
> Associate professor, Biology Dep't, Univ. of Florida
> bolker at ufl.edu / people.biology.ufl.edu/bolker
> GPG key: people.biology.ufl.edu/bolker/benbolker-publickey.asc

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