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

[Zach Simpson]

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> Date: Thu, 24 Jan 2019 10:12:58 +0800 (GMT+08:00)
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> Subject: [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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> 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