I did research and the studies suggest controlling for the effects of covariates on all endogenous variables, including mediator variables, to improve model accuracy and reliability.
I want to confirm my understanding and I have a question. I am doing a path analysis and I have identified 3 covariates that I need to include along with my other exogenous variables. Do I control for the effects of these covariates on all of the endogenous variables (including a mediator variable) in the model, or just for the effects on the dependent variable?
References
Kuroki, M., & Miyakawa, M. (2003). Covariate selection for estimating the causal effect of control plans by using causal diagrams. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65. https://doi.org/10.1111/1467-9868.00381.
Tygert, M. (2021). Controlling for multiple covariates. ArXiv, abs/2112.00672.
Xu, Z., Hong, Y., & Jin, R. (2016). Nonlinear general path models for degradation data with dynamic covariates. Applied Stochastic Models in Business and Industry, 32, 153-167. https://doi.org/10.1002/ASMB.2129.
This topic recently came up on the SEMNET listserv and multiple folks, including Paul Sacco, John Antonakis, and Holger Steinmetz, shared the following helpful references at least some of which I believe are relevant to your question:
Bernerth, J. B., & Aguinis, H. (2016). A critical review and best‐practice recommendations for control variable usage. Personnel Psychology, 69(1), 229-283.
Carlson, K. D., & Wu, J. (2012). The illusion of statistical control: Control variable practice in management research. Organizational Research Methods, 15(3), 413-435.
Cinelli, C., Forney, A., & Pearl, J. (2021). Cinelli, C., Forney, A., & Pearl, J. (2021). A crash course in good and bad controls. Sociological Methods & Research, 1-34.
Ding, P., VanderWeele, T., & Robins, J. (2017). Instrumental variables as bias amplifiers with general outcome and confounding. Biometrika, 104(2), 291-302. https://doi.org/10.1093/biomet/asx009
Elwert, F., & Winship, C. (2014). Endogenous selection bias: The problem of conditioning on a collider variable. Annual Review of Sociology, 40, 31-53. https://doi.org/10.1146/annurev-soc-071913-043455
Mändli, F., & Rönkkö, M. 2023. To omit or to include? Integrating the frugal and prolific perspectives on control variable use. Organizational Research Methods. https://doi.org/10.1177/10944281231221703
Steiner, P. M., & Kim, Y. (2016). The mechanics of omitted variable bias: Bias amplification and cancellation of offsetting biases. Journal of Causal Inference, 4(2).
Steinmetz, H., & Block, J. (2022). Meta-analytic structural equation modeling (MASEM): new tricks of the trade. Management Review Quarterly. https://doi.org/10.1007/s11301-022-00293-6
Wysocki, A. C., Lawson, K. M., & Rhemtulla, M. (2022). Statistical control requires causal justification. Advances in Methods and Practices in Psychological Science, 5(2), 25152459221095823.
Christian Geiser Thanks for your comments. I will be honest that my citations were from a manuscript review where the reviewer was less than enthused by our approach to covariate adjustment. I struggle with the fact that we have moved on from "everything but the kitchen sink" approach to statistical control, but now there is little consensus or rules of thumb about covariates. Dipping my toe into the DAGs world to see if I can better include covariates in a principled way.
Hey Paul, if you allow me to self-cite a figure that I published in the 2022 tricks of the trade paper. IMHO this is based on graph theory and should (if i did not overlook anything) base a basis for the decision what to do with a potential control variable.
Best,
Holger
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