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Your approach to testing mediation appears to conform to the "causal steps approach" described in the classic methods paper by Baron & Kenny (1986). This approach to mediation entails the following steps: Test whether X and Y are significantly associated (the c path); if they are not, stop the analysis; if they are... Test whether X and M are ...


18

What does it mean that ACME (treated) is 0.0808? 0.0808 is the estimated average increase in the dependent variable among the treatment group that arrives as a result of the mediators rather than 'directly' from the treatment. The dependent variable in this example is the probability of sending a message to a congress member, the mediator is the emotional ...


12

I believe the quick one-sentence answer to your question, When is it appropriate to control for variable Y and when not? is the "back-door criterion". Judea Pearl's Structural Causal Model can tell you definitively which variables are sufficient (and when it's necessary) for conditioning, to infer the causal impact of one variable on another. Namely, ...


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Definitions I'll use the $a, b, c, c'$ notation common to simple mediation, as shown here. Assuming there is a positive effect to be mediated (i.e., $c > 0$) and any underlying causal arguments are satisfied then Partial mediation occurs when $0 < c' < c$. Complete mediation occurs when $c' = 0$. Theoretical interest concerns the ...


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Baron and Kenny are indeed outdated, though that does not make them wrong in all cases. The concerns divide into broadly statistical limitations and assumptions which are discussed in the reference your reviewer suggests and in the literature alluded to by @PeterFlom, and broadly non-statistical concerns about the definition and causal identification of ...


7

This is more a discussion of concerns I have firstly with the approach of Baron and Kenny (which has some bearing on your question), and with a number of more recent papers (I haven't seen them all, so my comments may not apply to everything). It may also relate to the 2011 paper you mention, which I have only had the chance to skim through just now. From ...


7

This does suggest a "full" mediation, in which all of the IV's influence is mediated. The ACME being significant shows that the mediating process appears to be present. On the other hand, you don't have evidence that there is an ADE (insignificant result). The reason the total effect is larger than the ACME alone is that the estimate still includes the ...


7

Conditioning (i.e. adjusting) the probabilities of some outcome given some predictor on third variables is widely practiced, but as you rightly point out, may actually introduce bias into the resulting estimate as a representation of causal effects. This can even happen with "classical" definitions of a potential causal confounder, because both the ...


6

Not an expert on this, but the Statistical Mediation Wikipedia Page uses three regressions. In them, you would use an interaction (multiplication). You might also look into Structural Equation Modeling (SEM), which I believe can directly model mediation. R, Stata, and other packages can do SEMs, though it seems to be a bit of an art to me. Also be clear if ...


6

I disagree with discretizing to get rid of collinearity. It doesn't get rid of it, it just pushes it under a rug where it can cause problems while being less visible. "Number of guards" seems like a mediating variable. There is a lot of recent work on mediators, much of it by MacKinnon and his colleagues. E.g. this book but he has also written articles and ...


6

Here are some places to look. I'd especially recommend the work by Kosuke Imai and colleagues. Bullock, John G., and Shang E. Ha. 2011. Mediation Analysis is Harder Than it Looks. In Cambridge Handbook of Experimental Political Science, ed. James N. Druckman, Donald P. Green, James H. Kuklinski, and Arthur Lupia. New York: Cambridge University Press. ...


6

I posted this question in another location and was provided the answer by Terry Jorgenson. Question and answer: I would like to calculate the conditional indirect effects of X on Y given a set of values for the moderator W. Both X and the moderator are continuous. Could you provide some direction for structuring the model syntax? Assuming X and W are ...


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If you want to do a Sobel test for assessing the significance of a mediation, don't do it this procedure is considered old fashioned. From the website of Andrew Hayes (who wrote the SPSS macro for Sobel tests): "If you intend to use this macro merely to implement the "Baron and Kenny" steps to mediation analysis or the Sobel test, I advise you ...


5

I have a comment and hopefully an answer. You use the term "second step", which is a term typically reserved for hierarchical models (e.g., hierarchical regression). Are you certain you are doing mediation analysis? It may help if you describe your question and perhaps how you performed your analyses (e.g., using path analysis, a macro in SPSS). Note that ...


5

The lavaan package is an R package for SEM. You can use it to test for multiple mediation hypothesis, and there is boostrap.


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Moderating variables (aka effect modifier, interacting variable, etc.) alter the effect of another variable. In your example increased stress causes decreased well-being, but this effect is altered in the presence of locus of control. Of course, nothing prevents a moderating variable from having its own direct effect (aka main effect). An example here would ...


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No, "mediation" and "indirect effect" are not synonymous. For example, when analyzing complex causal systems in which any variable in the system at time $t$ contributes causally to every variable in the system at times $>t$, the term "mediator" is largely meaningless, whereas indirect effects may or may not exist due both to the qualitative structure of ...


5

From definitions, I feel that a variable can not simultaneously function as mediator and moderator. Let's try to investigate both effects: Mediaiton Mediation is a hypothesized causal chain in which one variable affects a second variable that, in turn, affects a third variable. The intervening variable, $M$, is the mediator. It mediates the relationship ...


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This is quite straightforward. The reason you have no relationship between $x$ and $y$ using your approach is because of the code: y <- 2.5 + 0 * x + .4 * med + rnorm(100, sd = 1) If you want some relationship between $x$ and $y$ even when ${\rm med}$ is included (that is, you want partial mediation), you would simply use a non-zero value for $b_{32}$...


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A few thoughts come to mind. I hope they are helpful. Lets say you have exposure X, outcome Y, and mediator X. 1) Baron and Kenny is, in my opinion, not a very good way to address mediation, at least not without a lot of thougfulness. The main problem is potential "collider bias" REF. If there are confounders of the Z-Y relationship ( Z <-- C --> Y ), ...


4

Baron and Kenny is distinctly old fashioned these days. They see mediation as a "yes-no" "present-absent" quality; more recent approaches (lots of work by MacKinnon and others) treats it as a continuum. This makes more sense to me.


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The Baron & Kenny approach is somewhat outdated - nowadays it is recommended to use a bootstrapping approach to test for mediation (Preacher & Hayes, 2004). One problem with the B&K approach is, that it is possible to observe a change from a significant $X\rightarrow Y$ path to a nonsignificant $X\rightarrow Y$ path with a very small change in ...


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I guess your supervisor is correct and the model is implying mediations. In general, most of SEM and Path analysis involve some mediation or indirect effects. The whole point, of these models is to say, instead of everything being related to everything, i.e. like in a correlation matrix, is to say that some relations are good enough to explain the whole ...


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Report standardized parameter estimates. These are analogous with some sort of effect size. That's what they do in the paper. (You might also ask your supervisor what they actually want - people sometimes ask for an effect size because they think that things should have effect sizes, but what is meant by an effect size can be complex - and it is not always ...


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This should probably be migrated to StackOverflow since it is about software, but: You could do this in the R package lavaan. In your model, you would first specify models for M1, M2, and Y. We will want to label all the paths, as well. I will label c' as cp, for "c-prime": M1 ~ a1 * X M2 ~ a2 * X + d21 * M1 Y ~ cp * X + b1 * M1 + b2 * M2 The indirect ...


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If I'm understanding right, you may be wanting to do an analysis of covariance (ANCOVA). There is a helpful tutorial here (http://r-eco-evo.blogspot.com/2011/08/comparing-two-regression-slopes-by.html). Specifically, read down to the bottom where comparing slopes and intercepts is discussed. This was achieved through a slightly different version of your ...


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If you are interested in interpreting coefficients and significance/p-values, don't use stepwise regression. See this post. In fact, stepwise regression is basically always a bad idea in this day and age when better model-selection techniques are easily computable. If you want to easily interpret the model and say which coefficients are truly "significant," ...


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This the relation between health message and cookie consumption could be stronger for those who score higher on the impSS as compared to those who don’t score as high although not in exactly the right language, is the central idea of moderation, you are right. Mediation, on the other hand, means that the effect of one independent variable on the ...


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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 ...


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Since you ask this conceptually.... If the results change when you add the mediator, the mediator is doing something, but what? Since the traditional use of the term "mediation" is one that reduces the effect, negative mediation would be one that increases the effect. As for a real world example.... well, I don't have one that's from actual data, but ...


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