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I am interested in testing a simple mediation model with one IV, one DV, and one mediator. The indirect effect is significant as tested by the Preacher and Hayes SPSS macro, which suggests the mediator does serve to statistically mediate the relationship.

When reading about mediation I have read things such as "Note that a mediational model is a causal model." - David Kenny. I can certainly appreciate the use of mediation models as causal models, and indeed, if a model is theoretically sound, I can see this as very useful.

In my model, however, the mediator (a trait considered to be a diathesis for anxiety disorders) is not caused by the independent variable (symptoms of an anxiety disorder). Rather, the mediator and independent variables are related, and I believe the association between the independent variable and the dependent variable can be explained largely by variance between the IV-mediator-DV. In essence I am trying to demonstrate that previous reports of the IV-DV relationship can be explained by a related mediator that is not caused by the IV.

Mediation is useful in this case because it explains how the IV-DV relationship can be statistically explained by the IV-Mediator-DV relationship. My problem is the question of causation. Could a review come back and tell us that the mediation is not appropriate because the IV does not in fact cause the mediator (which I would have never argued in the first place)?

Does this make sense? Any feedback on this matter would be greatly appreciated!

Edit: What I mean to say is that X is correlated with Y not because it causes Y, but because Z causes Y (partially) and because X and Z are highly correlated. A bit confusing, but that is it. The causal relationships in this instance are not really in question and this manuscript is not so much about causation. I simply seek to demonstrate that variance between X and Y can be explained by variance between Z and Y. So basically, that X is correlated indirectly to Y through Z (the "mediator" in this case).

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2 Answers 2

up vote 10 down vote accepted

A. "Mediation" conceptually means causation (as Kenny quote indicates). Path models that treat a variable as a mediator thus mean to convey that some treatment is influencing an outcome variable through its effect on the mediator, variance in which in turn causes the outcome to vary. But modeling something as a "mediator" doesn't mean it really is a mediator--this is the causation issue. Your post & comment in response to Macro suggest that you have in mind a path analysis in which a variable is modeled as a mediator but isn't viewed as "causal"; I'm not quite seeing why, though. Are you positing that the relationship is spurious--that there is some 3rd variable that is causing both the "independent variable" and the "mediator"? And maybe that both the "independent variable" & the "mediator" in your analysis are in fact mediators of the 3rd variable's influence on the outcome variable? If so, then a reviewer (or any thoughtful person) will want to know what the 3rd variable is & what evidence you have that it is responsible for spurious relationships between what are in fact mediators. This will get you into issues posed by Macro's answer.

B. To extend Macro's post, this is a notorious thicket, overgrown with dogma and scholasticism. But here are some highlights:

  1. Some people think that you can only "prove" mediation if you experimentally manipulate the mediator as well as the influence that is hypothesized to exert the causal effect. Accordingly, if you did an experiment that manipulated only the causal influence & observed that its impact on the outcome variable was mirrored by changes in the mediator, they'd so "nope! Not good enough!" Basically, though, they just don't think observational methods ever support causal inferences & unmanipulated mediators in experiments are just a special case for them.

  2. Other people, who don't exclude causal inferences from observational studies out of hand, nevertheless believe that if you use really really really complicated statistical methods (including but not limited to structural equation models that compare the covariance matrix for the posited mediating relationship with those for various alternatives), you can effectively silence the critics I just mentioned. Basically this is Baron & Kenny, but on steroids. Empirically speaking, they haven't silenced them; logically, I don't see how they could.

  3. Still others, most notably, Judea Pearl, say that the soundness of causal inferences in either experimental or observational studies can never be proven w/ statistics; the strength of the inference inheres in the validity of the design. Statistics only confirm the effect causal inference contemplates or depends on.

Some readings (all of which are good, not dogmatic or scholastic):

Last but by no means least, part of a cool exchange between Gelman & Pearl on causal inference in which mediation was central focus: http://andrewgelman.com/2007/07/identification/

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Thank you for your reply. I will try to elaborate my method. Literature has determined X relates to Y, Z relates to Y, and that X relates to Z. No one has previously considered the possibility that X related to Y due to its relationship with Z. By doing a mediation analysis I hoped to demonstrate that the relationship between X and Y can be explained by the relationship between X and Z. Basically, that variance shared between X and Y is due to overlapping variance between X and Z (and Y). Theoretically, I wish to suggest that Z (rather than X) should be considered in theoretical models. –  Behacad Jul 21 '11 at 17:08
    
What I am still not quite sure of is what you mean by "the possibility that X is related to Y due to its relationship with Z." Are you saying that relationship between X & Y is spurious? That Z causes both? Or alternatively that X is a mediator of Z's influence on Y? Others might disagree--we can enter the thicket-- but this is where I think Pearl comes in. Mediation analysis can't tell you which of these is true: X -> Z -> Y; Z -> X, Z -> Y; or Z -> X -> Y. All could "fit"; causal inference depends on assumptions extrinsic to statistical model here. –  dmk38 Jul 21 '11 at 17:26
    
What I mean to say is that X is correlated with Y not because it causes Y, but because Z causes Y and because X and Z are highly correlated. A bit confusing, but that is it. The causal relationships in this instance are not really in question. I simply seek to demonstrate that variance between X and Y can be explained by variance between Z and Y. So basically, that X is correlated indirectly to Y through Z. Perhaps my whole problem is calling this "mediation" while I should be referring to this phenomenon as confounding. Perhaps McKinnon, Krull and Lockwood (2000) will help. –  Behacad Jul 21 '11 at 17:28
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As McKinnon, Krull and Lockwood suggest, mediation and confounding are statistically identical. Conceptually is how they differ. "Unlike the mediational hypothesis, confounding does not necessarily imply a causal relationship among the variables. In fact, at least one definition of a confounder effect specifically requires that the third variable not be an "intermediate" variable..." - dionysus.psych.wisc.edu/Lit/Topics/Statistics/Mediation/…. –  Behacad Jul 21 '11 at 17:32
    
The "confounder" is the 3rd variable that causes the spurious correlation. So in your case, Z is the confounder--if it is causing both X and Y, and thus defeating the inference X->Y. But you seem to want to say a "correlation" between X and Z "explains" the relationship between X and Y and thus rules out X causes Y. You need more than that. You need a causal inference about the relationship between Z and X that rules out X->Y. Otherwise the Z-X correlation could still be consistent with X->Y. E.g., X might mediate Z's impact on Y. Simple correlations aren't "explaining" as much as you hope. –  dmk38 Jul 21 '11 at 18:04

Causality and Mediation

  • A mediation model makes theoretical claims about causality.
    • The model proposes that the IV causes the DV and that this effect is totally or partially explained by a chain of causality whereby the IV causes the MEDIATOR which in turn causes the DV.
  • Support for a mediational model does not prove the proposed causal pathway.
    • Statistical tests of mediation are typically based on observational studies. The range of alternative causal interpretations is large (e.g., third variables, alternative directions, reciprocity, etc.)
    • I am typically not persuaded by arguments (if any) presented by researchers who propose causal claims implied in mediation models.
  • Support for a mediational model may provide evidence to supplement other sources of evidence when building an argument for a causal claim. In summary, correlation does not prove causation, but it can provide supplementary evidence.
  • Despite the limitations of tests of mediation in observational studies, (a) mediation models are good for getting researchers thinking about causal pathways, and (b) there are better and worse ways to write up mediation models, where better ways acknowledge nuances in interpretation and provide thorough theoretical discussion of the evidence both for the proposed causal pathway and alternative causal pathways (see this page of tips that I prepared).
  • @dmk38 has provided some excellent references and additional discussion.

Showing that a variable explains the prediction of another variable

  • Based on your description, mediation does NOT appear to be aligned with your research question. As such I would avoid using the language of mediation in your analyses.
  • As I understand it, your research question is concerned with whether the prediction of one variable (lets call it X1 instead of IV) on the DV is explained by a second variable (lets call it X2 instead of MEDIATOR). You may also be making causal claims like X2 causes DV but X1 is only correlated with X2 and does not cause DV.
  • There are several statistical tests that might be suitable for testing this research question:
    • Compare zero-order (X1 with DV) with semi-partial correlations (X1 partialling out X2 with DV). I imagine the interesting element would be the degree of reduction and not so much the statistical significance (although of course you would want to get some confidence intervals on that reduction).
    • Or similarly, compare incremental R-square of a hierarchical regression where you add X2 in block 1 and X1 in block 2 with the R-square of a model with just X1 predicting DV.
    • I imagine you could also draw a path diagram that aligned with your causal assumptions (e.g., double headed arrows between X1 and X2 and a single headed arrow between X2 and DV.
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(+1), very clear and to the point. –  NRH Jul 22 '11 at 9:06
    
I think you nailed it. Although dmk38's answer is great in theoretical terms about the underlying problem, here are the soultions. I would also go with partical correlation or hierarchical regression to show that there must be a third variable causing the effect. The language of mediation is completely misleading in this context as it is inherently causal. –  Henrik Jul 22 '11 at 10:02
    
Thank you very much, that is helpful. The "causal" relationships are quite complicated given the nature of the constructs I am studying (e.g., two types of traits that influence each other over a life time), which muddies up the water some more. Thanks again! –  Behacad Jul 22 '11 at 19:06

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