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

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Date: Thu, 24 Jan 2019 10:12:58 +0800 (GMT+08:00)
From: =?UTF-8?B?5L2V5YWI6L+b?= <chatinger at 163.com>
To: "r-sig-meta-analysis at r-project.org"
        <r-sig-meta-analysis at 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 at 163.com>
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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