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Hi I am trying a mediation analysis (using library("mediation") in R)

My model has 3 predictors and one mediator (n=455), but I am only interested in predictor 1. There is some collinerarity between predictor 1 and 2 - 0.383444 (Pearson). No collinerarity between predictor 3 and the others. The Mediator is correlated with IV1 and slightly with IV2. Predictors, Mediator and dependent variable are all continuous.

lm(DV ~ IV1 + IV2 + IV3 , data = data)

Only IV2 is significant, R2 = 0.050

lm(DV ~ Mediator + IV1 + IV2 + IV3 , data = data)

Mediator and IV2 is significant, R2 = 0.056

I have a much bigger dataset with n = 1200, but unfortunately I don't have Mediator information available for them. If I do a linear regression to predict DV with this dataset, IV1 and IV2 are both highly significant, the standardized beta meaningful.

  1. With this information can I investigate the mediating effect of the mediator on IV1 with my small dataset with 455 subjects (using the mediate()-Function of the "mediation"-package in R) , even though the dataset itself is too small to show a significant effect of IV1 on the DV?

  2. Also, I was wondering whether my mediator might mediate IV2-effect. The correlation between IV1 and the mediator is higher than between IV2 and the mediator though.

I am thankful for any ideas.

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  • $\begingroup$ I am a bit confused as to why you interpret separate OLS regressions for a mediation analysis, instead of using likelihood ratio tests for the direct and indirect effects for the mediation paths. If you do I would say 1) Yes 2) Definitely try it, I wouldn't rely on bivariate correlations between IV1, IV2 and the mediator alone, as they don't take into account the error structure. I would also try bootstrapping the tests and comparing the results to the ones you already did to see if the problem of missing data is not affecting your error normality assumptions. $\endgroup$ – Chris Novak Dec 11 '15 at 14:29
  • $\begingroup$ Thanks for the suggestion. I try the bootstrapping to look at error normality. Though I had hoped it didn't change to much as the residual standard error is almost the same. I am not so familiar with likelihood ratio test. $\endgroup$ – Annamarie Dec 14 '15 at 10:02
  • $\begingroup$ I haven't used the "mediation" package but in any structural equation package (e.g. "lavaan") you can test for the direct and indirect effects separately. Also maybe try a model with both V1 and V2 having a mediated effect on DV. $\endgroup$ – Chris Novak Dec 18 '15 at 9:09
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Partly, this is an issue of not relying too much on significance tests.

But, in addition, it's a question of how you define mediation. If you define it as reducing an effect, then you can't reduce something that doesn't exist. But if you define it as changing an effect, then even a near-zero relationship can be mediated by another variable.

However, it may be best to not get hung up on exact definitions and, instead, look at what is going on in your data. Adding a variable to a model where nothing is significant (or important or large) can definitely change those relationships and that can be important to capture, regardless of whether you call it mediation or not.

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  • $\begingroup$ Thankyou for your comment @Peter Flom. In my case I define mediation as in explainig the effect of IV1 on DV, which I observe in the large dataset. To make it clearer: DV is cognition. The mediator are changes in the brain. These changes in the brain are mainly influenced by IV1 (disease) and also by IV2 (age). I try to investigate whether the effect of IV1 (disease) on DV (cognition) is MEDIATED through these brain changes. $\endgroup$ – Annamarie Dec 14 '15 at 9:20
  • $\begingroup$ Then you should ask if the effect is large enough to be mediated. $\endgroup$ – Peter Flom Dec 14 '15 at 11:32

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