i have done mediation analysis according to the standards of preacher and hayes. My c' happens to be less than c with bootstrap at -.063 and no 0 in between the confidence intervals, but in the path c', the p value did not become non-significant. According to B&K this can be assumed as partial mediation, but what does preacher and hayes have to say for this? Does preacher and hayes support partial mediation? And citation will be much appreciated. Thank you.
Jokingly saying, you should ask Preacher and Hayes what they have to say :-) but afaik their steps are just a little bit better than Baron and Kenny, which happened to be heavily criticized and has been deemed outdated by many (eg. Is Baron and Kenny method for mediation now outdated? )
Preacher actually did a paper about partial mediation (but not only). Here is some interesting excerpts:
Importantly, we also extend past work on this topic by questioning the emphasis on the significance of c' after including the proposed mediator, as well as the use of terms such as ‘full’ versus ‘partial’ mediation.
Abandon the emphasis on the significance of c and c'
Or this one:
These findings underscore the importance of avoiding the terms ‘full’ or ‘partial’ when describing mediation.
Rucker, D.D., Preacher, K.J., Tormala, Z.L., Petty, R.E., (2011)., Mediation Analysis in Social Psychology: Current Practices and New Recommendations, Social and Personality Psychology Compass 5/6, 359–371, DOI: 10.1111/j.1751-9004.2011.00355.x
However, I'd like to draw your attention to another paper about whole this mediation story. It's titled 'Mediation myth' and it covers almost all aspects of today's mediation analysis. Nicely written, but with quite nasty (for us) conclusions:
The observation that ab is significant would be taken by many researchers as evidence for mediation. But whether results of significance testing in mediation analysis generally have any meaningful interpretation is a critical question, one that is rarely considered in most mediation studies.
Rex B. Kline (2015). The Mediation Myth, Basic and Applied Social Psychology, 37:4, 202-213, DOI: 10.1080/01973533.2015.1049349