# [R-meta] Aggregating results from multiple reg. models in metafor

Viechtbauer, Wolfgang (SP) wolfg@ng@viechtb@uer @ending from m@@@trichtuniver@ity@nl
Mon May 7 13:02:52 CEST 2018

```Indeed, the partial correlation coefficient is esp. advantageous, since we only need to know the test statistic (i.e., t-test) of the regression coefficient of interest, the sample size of the study, and the number of predictors in the regression model in order to compute the partial correlation coefficient and its sampling variance. See help(escalc) and see the section on "Partial and Semi-Partial Correlations".

However, if the same variables are used across datasets, then there is no need to go to a standardized measure. One can just meta-analyze the regression coefficients directly. You will also need the standard error of the coefficients, but hopefully those are also available (or they can be back-calculated if you have the CI for the coefficients, or the p-values, or the test statistics). The square of the standard errors are the sampling variances. You can then meta-analyze the coefficients with standard meta-analytic methods, that is:

rma(coef, stderror^2, data=dat)

where 'coef' is the variable in 'dat' giving the regression coefficients and 'stderror' is the variable with the corresponding standard errors.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On Behalf Of Jens Schüler
Sent: Monday, 07 May, 2018 11:53
To: j.briggs; r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] Aggregating results from multiple reg. models in metafor

Hi Jeffrey,

I am not sure if this exactly what you are looking for but I came across the
practice of using partial correlations in a number of published
meta-analysis in management journals e.g.
Marano, V., Arregle, J. L., Hitt, M. A., Spadafora, E., & van Essen, M.
(2016). Home country institutions and the internationalization-performance
relationship: A meta-analytic review. Journal of Management, 42(5),
1075-1110.

If I have understood the practice correctly, you have to calculate partial
correlation coefficients from the regression estimates. The "challenge"
though is that the regression models, from which the correlations are to be
calculated from, have to be similar or the results are prone to bias.

Aloe published a couple of papers on that:
Aloe, A. M., & Thompson, C. G. (2013). The synthesis of partial effect
sizes. Journal of the Society for Social Work and Research, 4(4), 390-405.
Aloe, A. M. (2014). An empirical investigation of partial effect sizes in
meta-analysis of correlational data. The Journal of general psychology,
141(1), 47-64.

Best
Jens

-----Ursprüngliche Nachricht-----
Von: R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org> Im
Auftrag von j.briggs
Gesendet: Montag, 7. Mai 2018 10:04
An: r-sig-meta-analysis at r-project.org
Betreff: [R-meta] Aggregating results from multiple reg. models in metafor

Dear all,
I would like to aggregate results from different multiple regression models
(same variables different datasets/studies). After reading Lipsey and Wilson
(2001, p. 67) this seems somewhat more complex. I was wondering about the
most suitable way to do this using the metafor package?

Best,
Jeffrey

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