[R-meta] meta-analytic models with overdispersed data

[Viechtbauer Wolfgang (SP)]

If you take the absolute value of a d value, then its sampling distribution is no longer (approximately) normal, but actually (approximately) a folded normal distribution (https://en.wikipedia.org/wiki/Folded_normal_distribution). Not sure why you think it would be a negative binomial distribution -- that is a discrete distribution, so it can't apply. Also, I don't see how 'overdispersion' is the issue here.

Regardless, if you really want to meta-analyze absolute d values, rma() or similar functions are not really applicable. I don't know of any 'out of the box' solutions for this, but one could just do maximum likelihood estimation directly.

Best,
Wolfgang

-- 
Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry and    
Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 MD    
Maastricht, The Netherlands | +31 (43) 388-4170 | http://www.wvbauer.com    

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On Behalf Of Dave Daversa
Sent: Thursday, July 27, 2017 13:07
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] meta-analytic models with overdispersed data

Hi all:

I have read numerous websites and searched online forums for help with the
following meta-analysis question but still am not clear what the answer
is.

My study is concerned with the magnitudes of effects (using hedges d as a
measure of effect size).  So, I have taken the absolute value of the effect
size to use as my response variables in random effects models (rma
function).  However, t*he "absolute" effect sizes are not normally
distributed (rather a negative binomial distribution).  I presume that the
model run via rma() is not appropriate*, given assumptions of normality of
the data?

I have read discouraging remarks about log-transforming effect sizes for
meta-analysis...

I understand that bootstrapping can be done to estimate confidence
intervals for the data, but what model to use to estimate mean effect sizes
is still unclear to me.

If you can provide any answers and/or point me to references to clarify how
I model overdispersed data for meta-analysis, it would be a great help.

Many thanks for your time and assistance.

-- 
****************************************************************
*David Daversa, PhD*

*Postdoctoral Researcher*

*Institute for Integrative Biology, University of
Liverpoolddaversa at gmail.com <ddaversa at gmail.com>ddaversa at liv.ac.uk
<ddaversa at wustl.edu>*
https://eegid.wordpress.com/post-doctoral-researchers/dave-daversa/
<http://www.zoo.cam.ac.uk/zoostaff/manica/drdaversa.htm>