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?