[R-meta] Can correlation coefficients be used as moderator in meta-regression model when effect size is also from correlation coefficient

[Mike Cheung]

Hi Xianjin,


Yes, effect sizes can be used as predictors, and even mediators provided
that you have a good theory. One issue in yi ~ temperature.r +
precipitation.r + ph.r is that temperature.r, precipitation.r, and ph.r are
assumed measured with the same precision, which is not true in a
meta-analysis. A better approach is to use the “true” effect sizes as the
predictors. Here are some discussions on how to do it.


StackExchange discussion:

https://stats.stackexchange.com/questions/58310/can-i-incude-an-effect-size-as-an-independent-variable-in-a-meta-regression/58534#58534


Section 5.6 Extensions: mediation and moderation models on the effect sizes
in Cheung (2015) Meta-Analysis: A Structural Equation Modeling Approach:

https://books.google.com.sg/books?id=Pw7QBwAAQBAJ&pg=PA140&lpg=PA140&dq=%225.6+Extensions:+mediation+and+moderation+models+on+the+effect+sizes%22&source=bl&ots=zDiS8mnCN4&sig=ACfU3U11T2b31X3uGWHRcydSQays6Joy6w&hl=en&sa=X&ved=2ahUKEwiKjdLF8ozgAhUQbo8KHarBDaUQ6AEwAHoECAAQAQ#v=onepage&q=%225.6%20Extensions%3A%20mediation%20and%20moderation%20models%20on%20the%20effect%20sizes%22&f=false


R code for the above analyses:

https://htmlpreview.github.io/?https://github.com/mikewlcheung/metaSEM-book/blob/master/metaSEMbook.html#mediation-and-moderation-models


Best,

Mike

On Fri, Jan 25, 2019 at 7:47 AM Zach Simpson <zpsimpso using gmail.com> wrote:

> > -----Original Message-----
> > Date: Thu, 24 Jan 2019 10:12:58 +0800 (GMT+08:00)
> > From: =?UTF-8?B?5L2V5YWI6L+b?= <chatinger using 163.com>
> > To: "r-sig-meta-analysis using r-project.org"
> >         <r-sig-meta-analysis using r-project.org>
> > Subject: [R-meta] Can correlation coefficients be used as moderator in
> >         meta-regression model when effect size is also from correlation
> >         coefficient
> > Message-ID: <a6bd718.dbc7.1687da1bc95.Coremail.chatinger using 163.com>
> > Content-Type: text/plain; charset="utf-8"
> >
> >
> >
> > Hi,
> >
> >
> > I'm doing a meta-analysis on how soil microbial biomass (SMB) changes
> with elevational gradients globally. Now I have a problem in
> meta-regression. Hope someone can give me a hand.
> > In the meta-analysis, we collected data from 72 elevational transects.
> As SMB were from two different measuring methods (i.e. PLFAs and CFE) with
> different units. So the Pearson correlation coefficients betweeen SMB and
> elevation were calculated and then used as the effect size. As the
> correlation coefficient is unitless; therefore, data from PLFAs and CFE
> could be compared directly. If SMB increase with elevation, effect size was
> positive; conversely, effect size was negative.
> > The problem is in the moderator analysis. We hope to know which
> environmental factor (e.g. soil carbon concentration, temperature,
> precipitation, soil pH etc.) was most associated with SMB. As our response
> variable is the r effect size between elevation and SMB, the Pearson
> correlation coefficients between elevation and these environmental factors
> (i.e. MAT, MAP, SOC, TN, C:N, soil pH) were used as explanatory variables
> in the meta-regression model. The model in rma function is like this ( yi ~
> temperature.r + precipitation.r + ph.r, random = ~ 1|Transect ID, …), where
> 'temperature.r' is the correlation coefficient between temperature and
> elevation in each transect, the same meanings to 'precipitation.r' and
> 'ph.r'. And results of the meta-regression are reasonable.
> > However, I have not read such an approach in any literature, which makes
> me unconfident. So my question is do you think my way of using correlation
> coefficient as moderator is reasonable?
> >
> >
> > Best,
> >
> > Xianjin
> >
> > Xianjin He
> > Post-doc in Sun Yat-sen University
> > Guangzhou, China
>
>
> Hey Xianjin,
>
> [I'm no expert but I'm currently pulling together a meta-analysis
> myself and so I thought I'd share my thoughts.]
>
> I think yours is a tricky situation since you mentioned:
>
> > We hope to know which environmental factor (e.g. soil carbon
> concentration, temperature, precipitation, soil pH etc.) was most
> associated with SMB.
>
> Therefore, you're wanting to use those moderators to explain variance
> in SMB, rather than explain variance in the correlation between SMB
> and elevation. But maybe it does make sense: the effect size (SMB
> dependence on elevation) may be related to the effects of moderators
> (as driven by elevation). I would just worry about whether the primary
> data come from areas where the main source of moderator variances is
> from elevation and not some other variable.
>
> Also, you could consider transforming the correlations into Fisher's z
> to account for how correlations become skewed at higher magnitudes
> (i.e., make a more statstically ideal effect size). More detail is in:
>
> Rosenberg MS, Rothstein HR, Gurevitch J (2013) Effect sizes:
> conventional choices and calculations. In: Handbook of Meta-analysis
> in Ecology and Evolution. pp 61–71
>
> That's just my 2 cents. Hopefully someone more knowledgeable shares
> some insight.
>
> Cheers and good luck with the analysis,
> Zach Simpson
> Lincoln University, New Zealand
>
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