When I learn about the meta-analytic structural equation modeling using TSSEM method, I find some different opinions regarding missing data:
In Jak, S. (2015). Meta-Analytic Structural Equation Modelling. Springer International Publishing., The author indicated that 'Similar to the GLS approach, selection matrices are needed to indicate which study included which correlation coefficients. Note however, that in TSSEM, the selection matrices filter out missing variables as opposed to missing correlations in the GLS-approach, and is thus less flexible in handling missing correlation coefficients'.
While in Cheung, M. W.-L. (2021, January 22). Meta-Analytic Structural Equation Modeling. Oxford Research Encyclopedia of Business and Management. Retrieved 28 Jan. 2021, from https://oxfordre.com/business/view/10.1093/acrefore/9780190224851.001.0001/acrefore-9780190224851-e-225., the author indicated that 'Instead of using the GLS as in Becker’s approach, the TSSEM approach uses FIML estimation. FIML is unbiased and efficient in handling missing data (correlation coefficients in MASEM) ···'.
Based on what I described above, I feel confused about what kind of missing data can TSSEM handle, the missing variables? or the missing correlation coefficients? or both can be handled using different methods?
Then my understanding is that the two authors described the ways to handle missing data in TSSEM from different corners, Dr.Jak emphasize on using selection matrices to filter out missing variables; While Dr.Cheung emphasize on using ML to interpolate missing correlation coefficients. But I am not sure whether my understanding on it is right or not, So I sincerely invite you to answer my question, thank you!
Zhenwei Dai
2021.8.28
See these links:
Article Meta-Analytic Structural Equation Modeling: A Two-Stage Approach.
Conference Paper A Primer: Meta-Analytic Structural Equation Modeling
https://cran.r-project.org/web/packages/metaSEM/vignettes/metaSEM.pdf
https://cran.r-project.org/web/packages/metaSEM/vignettes/Examples.html
Cheung, M.W.-L. (in press). Issues in solving the problem of effect size heterogeneity in meta-analytic structural equation modeling: A commentary and simulation study on Yu, Downes, Carter, and O’Boyle (2016). Journal of Applied Psychology.
Cheung, M. W.-L. (2021, January 22). Meta-Analytic Structural Equation Modeling. Oxford Research Encyclopedia of Business and Management. Retrieved 28 Jan. 2021, from https://oxfordre.com/business/view/10.1093/acrefore/9780190224851.001.0001/acrefore9780190224851-e-225.
I don't have access to the 2021 article by Cheung. To my understanding, the quoted section in Jak (2015) was talking about fixed-effects TSSEM proposed by Cheung and Chan in 2005. Fixed-effects TSSEM indeed cannot handle missing correlations as in GLS *in the past*. See the paper by Jak and Cheung in 2018 on how to solve this problem for fixed-effects TSSEM:
Article Accounting for Missing Correlation Coefficients in Fixed-Effects MASEM
Maybe Cheung (2021) is talking about random-effects TSSEM in the quoted section. Random-effects TSSEM use a different approach in stage 1. You can check Chaper 7, section 7.4, of Cheung (2015): Meta‐Analysis: A Structural Equation Modeling Approach:
https://www.wiley.com/en-kg/Meta+Analysis%3A+A+Structural+Equation+Modeling+Approach-p-9781119993438
Hope this helps.
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