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Baron and Kenny outlined several steps to aid in determining if a mediational analysis is appropriate to test a particular hypothesis. The very first step was "Show that the initial [independent] variable is correlated with the outcome [dependent]". This is referred here as an "effect to be mediated" ($X\rightarrow Y$).

Since then, however, several authors have highlighted that an effect to be mediated is not necessary (e.g., "Reconsidering Baron and Kenny: Myths and Truths about Mediation Analysis"). At first I found this difficult to conceptualize, but now I understand the rationale. Perhaps it is best to consider it in the context of a mediational model in which the independent variable is positively associated with one mediator and negatively associated with another other, leading to a total effect of near 0 (e.g., $X$ causes $Z$, $Z$ causes $Y$, $X$ has a negative effect on $P$, $P$ has a negative effect on $Y$). Despite the lack of a total effect, mediation could be statistically significant for both mediators.

From a statistical viewpoint this makes sense to me, and indeed I have even explained it to a few others; however, I have trouble understanding this from a logical or even philosophical standpoint. Start by considering that mediational models are inherently causal. How can a mediational model be theoretically possible without "an effect to be mediated"? Cause is defined by one thing leading to change in another. If changes in $X$ are not associated with changes in $Y$, how could mediation conceivably be present? In other words, if changes in $X$ lead to concurrent changes in mediators that lead to no effect on the dependent variables, how could this possibly be considered causation? What might be needed is a special instance in which changes in $X$ lead only to changes in certain mediators and leads to a total effect, but this seems like a different topic.

Consider this example in a universe in which only four variables exist (i.e., all possible mediators are present):

  • Intelligence ($X$) causes perceived need to have a healthy lifestyle ($Z$, mediator 1), which leads to weight loss ($-1Y$)

  • Intelligence causes increased attraction to video games ($A$, mediator 2), which leads to weight gain ($+1Y$).

  • Increasing or decreasing intelligence does not change weight

Thoughts?

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From a cursory skim of the paper, I'm guessing two things could be at issue. First, the noise can always swamp the signal, even if there is perfect mediation ($X\rightarrow Z\rightarrow Y$), such that it's possible that there is an effect, but that it isn't 'significant'. That is, there is a type II error. The second issue is that, in a case with partial mediation and an independent causal force, it is possible for the direct effect from $X$ to $Y$ to be perfectly counteracted by the mediated effect, such that the total effect of $X$ on $Y$ is exactly 0, and could never be shown to be significant even with infinite data. These, I think, should resolve your philosophical anxiety; there is nothing crazy about these possibilities (although I find the second to be very unlikely in general). So you don't necessarily require two mediators, nor, for that matter, do you really need the other causal force, you could be left with just noise.

For what it's worth, philosophers continue to debate the nature of causality, it's not at all clear to me that there is an accepted definition of causality that is so narrow as to exclude the kinds of situations under discussion.

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Your example seems to me to answer your question with a "yes".

Perhaps the way to think about it is to say that there is always a relationship between any two variables: The relationship may be strong or weak, significant or not, meaningful or sill, but it's there. Thus, there is always an effect to be mediated.

The question of mediation (like most statistical questions) then becomes both substantive and statistical. Substantively, it must make sense. Ideally, it will have evidence behind it. Statistically, everything mediates everything else, it's just a question of how strong the mediation is.

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  • $\begingroup$ This is too strong a claim for me. I'm OK with the claim that the network of causal forces / variables is fully connected, ie there is some causal path that will connect any 2 variables, but there could very well be true nulls in an experiment, eg. $\endgroup$ – gung - Reinstate Monica Aug 4 '12 at 1:08
  • $\begingroup$ How could there be exactly true nulls? I agree that the null could be very close to true. $\endgroup$ – Peter Flom - Reinstate Monica Aug 4 '12 at 12:29
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    $\begingroup$ What I mean is that although any two variables that researchers would want to investigate are likely to be causally related somehow, if there isn't a direct causal connection from $A$ to $B$, then in an experimental setting, where $A$ is manipulated & the effect on $B$ is tested, the null will be true. As a ridiculous example, imagine an experiment that wanted to determine if the speed of a cue ball at time1 will influence the speed of the 8 ball at time2, but that the cue & 8 balls are on different pool tables. That would be an exactly true null. $\endgroup$ – gung - Reinstate Monica Aug 4 '12 at 14:55
  • $\begingroup$ Well, let's look at your ridiculous example. Would the null be exactly true? Logically, of course it is true. But if we somehow had a "population" of pairs of pool tables (all the pool tables in the world?) then would the relationship be exactly 0? I don't think it would. Maybe R^2 would be 0.000002 or something, but that's not 0. But that doesn't show causality, of course. Of course, you are right that in that the null would be farther from 0 in any reasonable pair of variables. $\endgroup$ – Peter Flom - Reinstate Monica Aug 4 '12 at 15:02
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    $\begingroup$ I think the independent manipulation of $A$ would make the null exactly true. However, w/ observational research, you're right that the null would definitely be false: if you went to some random pool halls, & measured how fast (hard) people hit the cue ball on 1 table, & how fast object balls (eg 8 balls) rolled on another table, there is no question they would be correlated b/c patrons at the same pool hall would be more similar to each other than to patrons at a pool hall somewhere else in the world, even though there would still be no direct causal connection b/t the different balls. $\endgroup$ – gung - Reinstate Monica Aug 4 '12 at 15:14

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