[R-meta] meta-analysis on different association-indicators with metafor

[Viechtbauer, Wolfgang (SP)]

Dear Katrin,

This is a tricky issue. First of all, do all of these types of coefficients estimate the same underlying association? Probably not. One could approach this empirically and code the coefficient type to see whether it actually makes a difference.

But one should definitely not treat all of the coefficients as if they were Pearson product-moment correlation coefficients. To start with, the sampling variance of each of these types of coefficients is different. 

For (semi)partial correlations, see:

Aloe, A. M. (2014). An empirical investigation of partial effect sizes in meta-analysis of correlational data. Journal of General Psychology, 141, 47–64.

Aloe, A. M., & Becker, B. J. (2012). An effect size for regression predictors in meta-analysis. Journal of Educational and Behavioral Statistics, 37, 278–297.

Aloe, A. M., & Thompson, C. G. (2013). The synthesis of partial effect sizes. Journal of the Society for Social Work and Research, 4, 390–405.

For standardized regression coefficients, see:

Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized regression coefficients. Psychometrika, 76(4), 670-690.

Jones, J. A., & Waller, N. G. (2015). The normal-theory and asymptotic distribution-free (adf) covariance matrix of standardized regression coefficients: Theoretical extensions and finite sample behavior. Psychometrika, 80(2), 365-378.

As for the other two types, no references come to mind.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Wolf, Katrin
Sent: Friday, 03 August, 2018 15:31
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] meta-analysis on different association-indicators with metafor

Dear all,

I'm struggling how to treat different indicators of the association that I want to examine in my meta-analysis, which are
- correlations (this is clear to me)
- partial correlations (I assume controlling for covariates can be considered as a moderator)
- standardised regression coefficients from various regression models
- betas from propensity score matching
- standardised coefficients from SEMs

Can all standardised Betas be treated the same way referring to calculating effect sizes?

Thank you very much in advance for your help,
Katrin