### Indirect Effects

**From ****Melanie Wall, University of Minnesota:**

I am teaching a course in latent variable modeling (to biostatistics and other public health students) and was yesterday introducing path analysis concepts including direct and indirect effects.

I showed them how to calculate indirect effects by taking the product of direct paths. Then a student asked about how to interpret the indirect effect and I gave the answer that I always give, that the indirect effect *ab* (in the following simple model) is the effect that a change in *x* has on *Z* through its relationship with *Y*.

After chewing on this for a second, the student asked the following:

**Student:** "The interpretation of the *b* path is: *b* is the increase we would see in *Z* given a unit increase in *Y* while holding *X* fixed, right?"

**Me:** "That's right"

**Student:** "Then what is being held constant when we interpret an indirect effect?"

**Me:** "Not sure what you mean"

**Student:** "You said the interpretation of the indirect effect *ab* is: *ab* is the increase we would see in *Z* given a one unit increase in *X* through its causal effect on *Y*. But since *b* (the direct effect from *Y* to *Z*) requires *X* to be held constant how can it be used in a calculation that is also requiring *X* to change one unit"

**Me:** "Hmm. Very good question, I'm not sure I have a good answer for you. In the case where the direct path from *X* *Z* is zero I think we have no problem since the relationship between *Y* and *Z* then has nothing to do with *X*. But you are right, here if "*c*" is non-zero then we must interpret *b* as the effect of *Y* on *Z* when *X* is held constant. I understand that this sounds like it conflicts with the interpretation of the *ab* indirect effect where we are examining what a change in *X* will cause. How about I get back to you. As I have told you before, the calculations here aren't hard, its trying to truly understand what your model means that's hard."