Multiple mediation analysis

I have a question about multiple mediation analysis. I had originally designed a study to see if four separate variables (M1, M2, M3 and M4) mediate the relationship between an independent variable X and a dependent variable Y. The four proposed mediators are all distinct constructs measuring separate characteristics. X, Y, M1, M2, M3 and M4 are all continuous variables. My N is 1500-ish.

Using simple linear regression, I initially determined that X is a significant predictor of Y, and that X was also a significant predictor of M1, M2, M3 and M4 individually. Then, according to the methods described by Barron and Kenny, I ran four separate hierarchical regression analyses, regressing X on Y in Step 1, and then adding the proposed mediator (M1, M2, M3 or M4) in Step 2. In each case, at Step 2, M1 (or M2, M3, M4) was a significant predictor of Y, and X was still a significant predictor of Y, but the unstandardized (B) coefficient for X on Y was lower, and so I calculated Sobel's statistic for each of the four models. Sobel's statistic was significant in each case, suggesting a partial mediating effect (this is the specific method I was instructed to use). From this, I concluded that each individual proposed mediator (M1, M2, M3 and M4) had a partial mediating effect on the relationship between X and Y.

My problem is this: I have now been advised to enter all the proposed mediators (M1, M2, M3 and M4) into a single model simultaneously, to overcome the possibility of a high degree of covariance. I have no experience with this type of multiple mediation model and need some guidance. I performed a hierarchical multiple regression on Y by entering X in Step 1, then adding M1, M2, M3 and M4 together in Step 2. In Step 1, X was a significant predictor of Y. In Step 2, X was no longer a significant predictor of Y, M1 was not a significant predictor of Y, but M2, M3 and M4 were all significant predictors of Y. The overall model was significant with an R-squared of 0.10. Is my approach correct? If so, can I say at this point that my model proves that M2, M3 and M4 fully mediate the relationship between X and Y, and that M1 is not a mediator of the relationship between X and Y? Also, how can I calculate a Sobel's statistic for each mediating variable using the B-coefficients and SEs that I have thus obtained, if I even need to?


Omega Contributor
I do not know much about mediation analysis, but recall hearing multiple times that the Barron and Kenny approach may be dated. You may want to look into this. However, this may not mean that the true results are not so sensitive that the B&K approach wouldn't have given you comparable findings.
I agree that there have been several updates and criticisms of the Barron and Kenny method published, but I believe it is still widely employed and is the method I have been instructed to use in this study. I think the results would still be valid.

I am still hopeful that someone might be able to answer my specific question with regards to multiple simultaneous mediation analysis.


Omega Contributor
These look interesting, authors of the first are well known but the approach is novel - though you have continuous variables. Don't recall reading the second approach, but it may be useful.

Am. J. Epidemiol. (2015) 181 (5): 349-356

Am. J. Epidemiol. (2014) 179 (4): 513-518.

I would advice using Andrew Hayes' PROCESS macro for SPSS.
This macro enables you to run models with multiple mediators (running either in series or parallel), and overcomes the limitations associated with the Baron and Kenny method.

It's free to download from his website (do a quick google search). If you are not comfortable with using syntax in SPSS then you can install the dialog box. You'll need to select model 4 (parallel) or model 6 (series) (if my memory serves me right). If you manage to install it and are having some difficulties getting it to run, reply to this thread.
p.s. the B & K is only the most widely employed method because it was originally the simplest to compute with the available computing power, and then increased in popularity and this started a 'oh it's used by everyone, so must be the best method'. But it has many flaws, and just because it is one the most highly cited methods, is not a reason to use it!