Does mediator make the relationship between the independent and dependent variables stronger?

[Meng Yu]

If we believe a variable is a mediator, does it make the relationship between the independent variable and the dependent variable stronger? I used to think it should attenuate the relationship, but just read something saying this. Can anyone please explain?
Thank you.

[Meng Yu]

https://ademos.people.uic.edu/Chapter14.html

According to this source, mediators should attenuate the relationship.

[Meng Yu]

If by adding the variable which was thought to be a mediator, the relationship between the independent and dependent variables becomes stronger, does it mean the mediator is actually a moderator?

[Christopher Bratt]

One might be tempted to believe that a statistical analysis identifies mediation and causality. Usually, it will fail to do so.

This is frequently misunderstood, even in published research. Specifically, without a research design or logic that can identify what comes first, it is not possible for a statistical analysis to identify causality.

Take these three models, they are all equivalent, although very different from a theoretical point of view.

Model 1
A + B → C and A correlates with B

Model 2
A + B → C and A → B

Model 3
A + B → C and B → A

---

Using software for SEM (such as Stata's SEM) will verify that these three models are equivalent; we cannot distinguish between them. For instance, if we use fullblown SEM with latent A, B, and C, model fit will be identical across the three models and the standardised paths between the three variables will be equal across the three models.

So,

A + B → C and A → B

is the same as

A + B → C, A correlates with B

Adding B to the equation, that is, using it as a covariate (or we might say controlling for it), is often assumed to decrease the estimated effect of A (provided A and B are correlated). But sometimes adding B to the equation can increase the estimated effect of A; in this case, the association between A and C increases once we control for B.


Moderation is the same as interaction. You could test for that by:

A + B + A*B → C

[Meng Yu]

Adding B to the equation, that is, using it as a covariate (or we might say controlling for it), is often assumed to decrease the estimated effect of A (provided A and B are correlated). But sometimes adding B to the equation can increase the estimated effect of A; in this case, the association between A and C increases once we control for B.

So, if we can determine A causes B based on theories or it is impossible for B causes A in reality, can we assume adding B to the equation will decrease the estimated effect of A?

If A correlates with B, then it means there is another factor that leads to both A and B. Is that the reason why adding B may increase the estimated effect of A?

[Richard Williams]

Sometimes there are suppressor effects in models. For example, a remedial education program aimed at poor people may reduce the effects of poverty on achievement. If the program is good and you don’t include it in your model, it might appear that poverty has little effect on achievement. But, if you add the program to your model, you may find that poverty has a strong negative effect on achievement, but that effect is somewhat offset by the fact that poor people are more likely to get into the program, and being in the program tends to increase achievement.

[Meng Yu]

Sometimes there are suppressor effects in models.

So if we use A to indicate poverty, B to indicate program, and C to indicate achievement, then A and B are correlated. By adding B to the equation, we increase the estimated effect of A because both A and B are caused by lack of resources. Lack of resources lead to poverty and the necessity to establish the program. By adding B, we add more factors that cause lower achievement. Is this what you mean?

[Richard Williams]

See this handout for a discussion of my example and related examples:

https://www3.nd.edu/~rwilliam/stats2/l35.pdf

[Meng Yu]

Thank you for the handout. The examples read more like the Simpson's paradox to me. I assume the suppressor effects can be handled by adding moderators. But what I was talking about earlier mainly focused on mediating effect.

[Richard Williams]

Maybe there is some confusion on terms. In the nice link you posted earlier,

https://ademos.people.uic.edu/Chapter14.html

it says

Mediation analysis tests a hypothetical causal chain where one variable X affects a second variable M and, in turn, that variable affects a third variable Y. Mediators describe the how or why of a (typically well-established) relationship between two other variables and are sometimes called intermediary variables since they often describe the process through which an effect occurs. This is also sometimes called an indirect effect.

I would say my examples on suppressor effects count as mediators, not moderators. The negative direct effect of poverty is partially offset by the positive indirect effect of poverty positively affecting program participation which in turn positively affects achievement.

I also don't see it as some sort of paradox. Suppressor effects can be a little hard to understand, but I don't see them as paradoxical. The whole reason we set up compensatory programs is to help compensate for some sort of weakness. If we didn't have the compensatory programs, the gaps in achievement between the haves and have nots would be even greater (assuming the programs actually do some good).

Put another way, there is no reason to think that all the direct and indirect effects of a variable must all be positive or all be negative. If they are all positive you'll see weakening of the original effects as more vars get added. But if there is a mix of positives and negatives, the original direct effects may get even stronger as more vars get added.

[Meng Yu]

I see what you mean. I understand the suppressed effect of an independent variable now. So if A causes B, in your case being poor leads to a higher likelihood of being in HeadStart, then by adding B to the equation, the negative effect of A on C becomes stronger because B takes away some of its positive effect.

[Richard Williams]

I see what you mean. I understand the suppressed effect of an independent variable now. So if A causes B, in your case being poor leads to a higher likelihood of being in HeadStart, then by adding B to the equation, the negative effect of A on C becomes stronger because B takes away some of its positive effect.

Yes. For clarity, I might say positive indirect effect.

As a sidelight -- sometimes you see a simple model where income is regressed on sex, and you find women make much less than men. But, then you add a bunch of other variables, e.g. occupational sector, and the direct effect of sex gets much smaller, maybe even goes to zero.

In that case, it would almost certainly be wrong or misleading to say that sex has no effect on income. Much more likely is that it has effects, but they are indirect rather than direct.

Put another way, the model explains (or tries to explain) why and how sex affects income. It does so by affecting other variables, and those variables in turn affect income.

But, some people will make mistakes because they do not understand how indirect effects work, and therefore only look at direct effects.

Also, you'll sometimes hear that women make less than men because women take lower-paying jobs. But, that leaves open the question, why are the jobs lower paying? Perhaps it is because women tend to hold those jobs! (There is some interesting literature that shows that, sometimes, once women start to take over a profession, the prestige and pay of that profession goes down.)

And, of course, if women are in lower-paying jobs, why aren't they going to higher-paying jobs instead? Perhaps there are barriers to entry that keep women out.

So in short, if the direct effect of sex is small, that does not mean that women are not disadvantaged. It may just be that the disadvantages occur before the final outcome.

[Meng Yu]

Thank you for your explanation and examples.

So if the relationship between A and C is positive, and the relationship between A and B is causal and positive, will adding B to the equation reduce the effect of A on C?

[Richard Williams]

When being more careful in my wording, I usually add qualifiers like "If the model is true..."

When C is regressed on A, the total effect of A (direct plus indirect) is attributed entirely to the direct effect.

When B is added to the model, the total effect of A can be divided into its direct and indirect effects.

So yes, if all the direct and indirect effects are positive, then adding B to the model should reduce the estimated direct effect of A.

For more complicated examples, you can see

https://www3.nd.edu/~rwilliam/stats2/l62.pdf

https://www3.nd.edu/~rwilliam/stats2/l63.pdf

https://www3.nd.edu/~rwilliam/stats2/l71.pdf

[Bruce Weaver]

Here are some relevant articles.


Fiedler, K., Schott, M., & Meiser, T. (2011). What mediation analysis can (not) do. Journal of Experimental Social Psychology, 47(6), 1231-1236.

Fiedler, K., Harris, C., & Schott, M. (2018). Unwarranted inferences from statistical mediation tests–An analysis of articles published in 2015. Journal of Experimental Social Psychology, 75, 95-102.

MacKinnon, D. P., Krull, J. L., & Lockwood, C. M. (2000). Equivalence of the mediation, confounding and suppression effect. Prevention science, 1(4), 173-181.