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

[何先进]

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

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