My question is general to mediation but perhaps best illustrated with example. I have the following situation from marketing - TV GRPs drives Paid Search clicks, and I suspect both of these independently drive visits to the marketer's website. I assume that there is no other independent variable that makes sense in the model.
- I regress site visits on TV GRPs and end up with a significant coefficient - this is the total effect of the IV TV GRP's on site visits - easy
- I regress Paid Search clicks on TV GRPs and again see the relationship is strong. From my business knowledge, I know the relationship is causal.
- I regress site visits on TV GRP's and PS clicks jointly. I see that the coefficient on PS clicks is highly significant and that on TV GRP's is mildly significant.
What does this mean? Since there is correlation (more specifically, a causal relationship between IV TV GRP's and mediator PS clicks), one cannot expect the regression coefficients in the third regression above to be unique or interpretable. There are infinite ways of combining TV GRP's and PS clicks to yield the outcome variable that are all equivalent since all we require is for the total effect of TV GRP's and the total value of the intercept term to more-or-less equal the coefficient and intercept from the first regression. There is no other variable that could possibly force a certain value for the coefficient of the mediator. How then do we conclude what the direct and indirect effect of TV GRPs on site visits are?