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

[Viechtbauer, Wolfgang (NP)]

Hi Katrin,

For "PCOR" (partial correlations), you need to know the t-statistic (or the corresponding p-value), sample size, and the number of predictors (unless you already know the partial correlation directly, but this is quite rare). For "SPCOR", you also need the R^2 from the model.

If you go that route, then I would recommend using "ZPCOR" for the Fisher r-to-z transformed partial correlation coefficients. So yes, this is option 1.

Another option - if you already have the standardized regression coefficients and corresponding standard errors - is to directly meta-analyze those.

It is difficult to say which option is better in general, but option 1 does not suffer from the problem that I explained in my other post (about the standard errors of standardized regression coefficients -- although to what extent this is really a problem is context specific).

Best,
Wolfgang

>-----Original Message-----
>From: Wolf, Katrin [mailto:katrin.wolf using uni-bamberg.de]
>Sent: Thursday, 13 July, 2023 8:45
>To: Viechtbauer, Wolfgang (NP); R Special Interest Group for Meta-Analysis
>Subject: AW: Calculating effect sizes from standardized regression coefficients
>in Metafor
>
>Dear Wolfgang,
>
>Thank you very much for your response! Please let me summarize to check if I
>understood correctly. As I could also see from the correspondence with Rasheda,
>there are two possible ways for dealing with regression coefficients:
>1. Using escalc with "PCOR" (under consideration of t-statistics, sample size,
>number of predictors and variance explained)
>2. directly meta-analyze beta coefficients as effect size (yi) in one of the rma-
>commands. In this case vi would be variance of beta coefficient meaning square of
>SE?
>    (I am going to check the paper you mentioned regarding the standard errors.)
>
>Is one of these approaches better than the other - considering the fact that I
>aim at aggregating effect sizes from different kind of measures: regression
>coefficients, correlation coefficients (Fisher’s r-to-z transformed correlation
>coefficient) and group mean differences (standardized mean difference)?
>
>Best,
>Katrin
>
>-----Ursprüngliche Nachricht-----
>Von: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
>Gesendet: Mittwoch, 12. Juli 2023 16:57
>An: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-
>project.org>
>Cc: Wolf, Katrin <katrin.wolf using uni-bamberg.de>
>Betreff: RE: Calculating effect sizes from standardized regression coefficients
>in Metafor
>
>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