Interpretation of path analysis [direct, indirect and total effect]

[Mohammed Kasbar]

Dear Statalist respected users,

I am doing path analysis using SEM and I estimated 3 different models. In the first model, I have one causal variable X, one mediator M and the outcome variable Y.
In the second model, I have one causal variable X, 2 mediators M1 and M2 [2 different paths], and outcome variable Y.
The third model is non-recursive in which I used an instrumental variable (IV) that influences the causal variable X, a mediator M and I allowed for the reverse causality between X and Y.

I am quite confused in interpreting the indirect effect (ab) (the product of multiplying the coefficient (a) of the impact of X on M and the coefficient (b) of the impact of M on Y).

(a) is negative and significant: this comes in accordance with theory.
(b) is positive and significant: this contradicts the theory.

the product (ab) is negative and statistically significant

direct effect (C') is positive and significant.

total effect (C) is negative and insignificant.

Results are robust in the three models, the indirect effect is negative and significant, the direct effect is positive and significant and the total effect is insignificant.

My research question is to see if there is a mediation effect from M on the relationship between X and Y.

the interpretation of (b) coefficient is my problem, I am not sure if I can say that X reduces M given the negative association between X and M, then the reduced M improves Y [given the positive association]?
according to theory, the increase in M should deteriorate Y and vice versa.

Thanks a lot for your interest.

I am looking forward to hearing from you.

Kind regards,
Mohammed

[Mohammed Kasbar]

Update:

The question in other words: does the interpretation of b depend on a?
for example, the negative association between X and M means that the increase in X causes reduction in M. Then, the increase in the reduction of M increases Y. Can I draw this conclusion?

thank you

[Mohammed Kasbar]

I do appreciate if someone can help. Thank you

[Phil Bromiley]

I've been off so let me try to answer your questions. We read the statistical results as results, even if they don't agree with theory. In the future, you'll increase your chances of a useful answer by following the FAQ on asking questions. For example, I'm not sure which of the 3 models you're discussing and what C means.

So, as I see it you have something like:
y = b * m + c * x
m= a * x

The interpretation of b as influence of m on y doesn't depend on a. But the interpretation of the influence of x on y depends on a, b, and c. A negative, statistically significant b in consistent with concluding m reduces y. The parameter a tells us about the influence of x on m. But (assuming you've done it right) the statistically insignificant value on (a*b) + c indicates the direct effect of x on y may counteract the indirect effect resulting in a small total effect.

Think about it simply. A one unit increase in x increases m by a. That a increase in m increases y by a * b. And, the direct effect of x on y is c so the total is (a*b) + c.

There is a massive literature on mediation. Some work by Myles Shaver claims that you may want to allow for possible correlations of the errors in the two equations.

[Mohammed Kasbar]

Phil Bromiley
Thanks a lot for your contribution. This is really helpful.