Hayes (2017) p. 18 states
[T]here is a growing chorus of quantitative social scientists who reject the regression-based orientation I outline here on the grounds that linear modeling and statistical adjustment simply don’t do the job many people claim it does.
As far as I can tell, nowhere does Hayes specifically outline exactly what these grounds for rejection are, or whether they are valid.
Searching on the internet it's easy for me to find criticisms of the related Baron and Kenny method, and there is a related question on this site "Is Baron and Kenny method for mediation now outdated?". However, Hayes (2017) claims to present methods that are advanced over Baron and Kenny's methods. As he puts it on p. 146,
Statistical mediation analysis has changed since the publication of Baron and Kenny (1986). The heyday of the causal steps “criteria to establish mediation” approach is over. Also disappearing in the 21st century is a concern about whether a process can be labeled as complete or partial mediation. Modern mediation analysis emphasizes an explicit estimation of the indirect effect, inferential tests of the indirect effect that don’t make unnecessary assumptions, and an acknowledgment that evidence of a statistically significant association between X and Y is not necessary to talk about and model intervening variable processes (in which case the concepts of complete and partial mediation simply don’t make sense).
So what I'm hoping for here is a clear explanation of the reasons many researchers reject the regression-based orientation for mediation, i.e. the reasons they reject Hayes's and other regression-oriented approaches, and not just the Baron and Kenny approach. Are these reasons valid?
Hayes, A. F. (2017). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach. Guilford publications.
