[R-meta] multiple correlation meta-analysis as in Cheung & Chan (2002)

[Catia Oliveira]

Hello,

I am interested in running a similar study to that conducted by Mike
Cheung (The role of perceived behavioral control in predicting human
behavior: A
meta-analytic review of studies on the theory of planned behavior)
where the multiple correlations estimates (square root of R2) were
tracked to determine whether a set of predictors have explanatory
power when one has been accounted for. This will be done across
datasets, so I would have to pool all the multiple correlations
estimates using the same variables (e.g. all studies with 2 predictors
X ~ A + B and all studies with 3 predictors X ~ A + B + C). Could I
still use the Hunter and Schmidt approach used by Mike Cheung to
aggregate the multiple correlations estimates? If so, how can I then
compare the size of the R2 based on the number of predictors (e.g., is
the multiple correlations estimates for 3 predictors sig higher than
for 2)?

Thank you,

Catia