I am trying to hand calculate the standard error for the a path in a moderated mediation model where the moderator modifies the a path. For example:
Mediator = X + Moderator + X*M
I gather that the a path would be calculated like so (with coefficients from the above model):
X + (X*M * Moderator)
How would I calculate the standard error in this case? I am not having any luck finding the answer so far.
In response to the request for more information, I am updating the question.
Say I think that the coping mediates the relationship between gender and depression but that this mediation effect depends on age. I run 2 regressions:
Outcome = Coping
Estimate Std. Error t value Pr(>|t|) (Intercept) 4.2063 0.1529 27.513 < 2e-16 *** Age 0.6621 0.2739 2.417 0.01714 * Gender 0.6853 0.2189 3.131 0.00218 ** Age*Gender -0.8737 0.3726 -2.345 0.02065 *
Outcome = Depression, with Coping
Estimate Std. Error t value Pr(>|t|) (Intercept) 5.19472 0.31975 16.246 < 2e-16 *** Coping -0.59130 0.07054 -8.382 1.1e-13 *** Age -0.37615 0.21850 -1.721 0.087717 . Gender -0.66654 0.17728 -3.760 0.000263 *** Age*Gender 0.20956 0.29682 0.706 0.481535
I believe that I would need to calculate the indirect and total effects (conditional on Age = 45) with the following:
indirect = 0.6853*-0.59130 + 45*-0.8737*-0.59130 total = indirect + -0.66654 + 45*0.20956
How would I calculate the SE for the (a) path to Coping through Age*Gender and/or how would I calculate the SE for these conditional indirect and total effects?