We all know it is possible to get path coefficients from correlation matrix (e.g., PATH ANALYSIS I: INTRODUCTION (ecu.edu) ). Using a simple solver on a spreadsheet, it is therefore possible to check the results of any article when a correlation matrix is provided.
The other way around, we can also from structural equation modeling coefficients obtain the correlations when they are not provided in a given article. Can I use this method to obtain correlations before using Hunter and Schmidt's meta-analysis method? Do you know a software to do it effortless because performing it using a spreadsheet is boring?
As far as I have read I have not found any article on what you suggest.
Hi Adrien,
What you may be referring too, but I'm not sure, is to compute partial correlations on the basis of information from regression models. (NB. structural models are systems of equations).
Ariel Aloe (https://www.researchgate.net/profile/Ariel-Aloe) has done a lot of work on this, including cautioning against the use of partial correlations and other indices derived from regression coefficients.
- 10.1080/00221309.2013.853021: Partial effect sizes in MA
- 10.1002/jrsm.1126: inaccuracy of regression results replacing CC
- 10.3758/s13428-018-1123-7: Concealed correlations MA
If you want a quick way to compute a partial correlation from a t-statistic, check Workbook 6 of Meta-Essentials (disclaimer: I co-developed) - see www.meta-essentials.com
Hi Robert,
Thank you for these references. In fact, this is what I mean. However, I am not using the partial correlation directly or indirectly with Peterson and Brown's formula. I use these partial correlations and zero-order correlation between independant variables to calculate all the zero-order correlations. The only things I need to compute all zero-order correlations is
1) zero-order correlations between independant variables,
2) path coefficients.
For instance,
1) if you get the zero order correlation rX1X2 (or the covariance between X1 and X2, and the variances of X1 and X2) ;
2) if you know a and b the path coefficients of this really simple structural equation : Y = a X1 + b X2
Therefore, you can compute the correlations between Y and X1 (rYX1) as well as between Y and X2 (rYX2) since
rYX1 = a + b * rX1X2 and rYX2 = b + a * rX1X2
This is a really simple example, but we could do the same for more complicated structural models using a spreadsheet, couldn't we? I use it to compute all the correlation for these articles because they provide all the informations required:
Article An analysis of the relation between resilience and reduced a...
Article A Defining Aspect of Human Resilience in the Workplace: A St...
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