[R-meta] standardized betas transformed to correlation coefficients

[Viechtbauer, Wolfgang (SP)]

Dear Yingkai,

I would strongly caution against using this formula. It was empirically derived and has no proper statistical grounding. In general, one cannot transform a standardized regression coefficient into a correlation coefficient (without any further information about how the x and y variables of interest correlate with all of the other predictors in the model). The one exception is the case where there are are no other predictors in the model, in which case the standardized regression coefficient is exactly equal to the correlation coefficient (and which illustrates that at least in this scenario, the transformation equation would be incorrect as it would incorrectly inflate the 'estimated correlation' when the association is positive).

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Yingkai
Sent: Friday, 21 February, 2020 7:42
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] standardized betas transformed to correlation coefficients

Dear all,

I am confused about how to transform standardized betas  to correlation
coefficients.
Can I used the simple imputation formula proposed by Peterson and Brown
(2005) where r = β + 0.05 λ ?  λ is an indicator variable that equals 1
when β is nonnegative and 0 when β is negative. Is this correct? or
acceptable ?

best,
-- 
Yingkai, Ph.D Candidate
Southwest University, ChongQing, CHINA.