[R-meta] Calculating effect sizes from standardized regression coefficients in Metafor

[Viechtbauer, Wolfgang (NP)]

Dear Katrin,

I am not sure I fully understand your question. I think you are referring to escalc() with measure "PCOR", which calculates partial correlation coefficients (from things like the corresponding t-statistics of the regression coefficients), but your phrasing (that this "calculates effect size from partial correlations") is confusing me.

If you want to meta-analyze standardized regression coefficients and have the corresponding standard errors, then one can of course also meta-analyze those directly. However, note that the standard errors of standardized regression coefficients are typically not computed in the most accurate way (i.e., the standard errors one obtains by fitting a regression model to standardized variables ignore that the variances used to standardize the variables are estimated). See, for example:

Jones, J. A., & Waller, N. G. (2013). Computing confidence intervals for standardized regression coefficients. Psychological Methods, 18(4), 435-453. https://doi.org/10.1037/a0033269

If you have the full correlation matrix of the variables in each regression model, one can compute more appropriate standard errors, but this is unlikely to be the case in practice.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Wolf, Katrin via R-sig-meta-analysis
>Sent: Tuesday, 11 July, 2023 12:33
>To: r-sig-meta-analysis using r-project.org
>Cc: Wolf, Katrin
>Subject: [R-meta] Calculating effect sizes from standardized regression
>coefficients in Metafor
>
>Dear colleagues,
>
>I am currently struggling with dealing with standardized regression coefficients
>(as indicator of the relationship between two variables of interest) in my meta-
>analysis with Metafor. Due to literature research, standardized regression
>coefficients can be used for meta-analysis when corresponding standard errors are
>also taken into account. Due to Metafor manual from 2023, it is possible to
>calculate effect size from partial correlations under consideration of t-
>statistics, sample size, number of predictors in regression model and R^2. Do I
>interpret correctly that this is another approach?
>I am sure there is a lot of experience with handling beta weights in Metafor. I
>would appreciate any information on this topic.
>
>Kind regards,
>Katrin
>
>---
>Dr. Katrin Wolf, Dipl.-Psych.
>Wissenschaftliche Mitarbeiterin
>
>Otto-Friedrich-Universit�t Bamberg
>Lehrstuhl Fr�hkindliche Bildung und Erziehung
>96045 Bamberg