[R-sig-ME] question on lme4

[Phillip Alday]

Dear Belinda,

(Partial) R^2 is a rather challenging concept for mixed models. Intuitively, correlation (r) is difficult for multilevel models -- do you want the average of all within-group correlations, the overall correlation or something else entirely?  Neither one is "right" or "wrong" but rather answer subtly different questions.This only gets harder when we consider things like Simpson's paradox or models with crossed (whether partially or fully) or nested groups. 

This is discussed a bit on the FAQ:

https://rawgit.com/bbolker/mixedmodels-misc/master/glmmFAQ.html#how-do-i-compute-a-coefficient-of-determination-r2-or-an-analogue-for-glmms

The betas (coefficients) are themselves effect sizes -- after all they describe how big a change in the dependent/response variable (i.e. effect) you can expect per unit change in the predictor. If you want them to standardised effect sizes, then you can simply standardise your predictors (which is often recommended practice anyway because it puts all your predictors on the same scale and makes some aspects of model fitting easier) and you'll have an effect size in terms of standard deviations, i.e. similar to Cohen's d. The confidence intervals on the coefficients are then also confidence intervals on your effect size. 

This is easy to do in R by the way: simply change

y ~ x1 * x2 

to

y ~ scale(x1) * scale(x2) 

(And make sure to do the same thing for the relevant parts of your random-effect structure.)

Best,
Phillip

PS: Ben Bolker is one of the maintainers of lme4, but this mailing list thankfully -- for his sake -- isn't a hotline to him. It's just a collection of people interested in mixed models, especially in R.


> On 15 Feb 2017, at 00:54, Belinda Pletzer <belinda.pletzer at gmail.com> wrote:
> 
> Dear Dr. Bolker,
> 
> I am writing to you with a question regarding linear mixed effects models
> in R, since you are listed as the maintainer for the lme4 package. I've
> been using both nlme and the lme4 package for my models and have now for
> the second time encountered a reviewer who insisted on the calculation of
> standardized effect sizes like d, r or beta for the fixed effects in my
> model.
> 
> I've already spent hours on the internet trying to figure out a way to do
> so, but all I found were some approximations to calculate R²-like measures
> for the whole model, but not for each effect separately and as far as I
> understood all the literature I've found, it is not advisable to attemt the
> calculation of standardized effect sizes in lme's, but I might be mistaken.
> 
> Do you know of any way to do something like that with your package, or
> could you otherwise point me towards someone who knows an other way or
> towards some literature that might help in responding to this reviewer?
> 
> Thanks a lot in advance!
> 
> Best regards,
> Belinda Pletzer
> 
> 	[[alternative HTML version deleted]]
> 
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