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I am doing a linear regression analysis and have the problem as stated above. When only the independent variable (IV) and the dependent variable (DV) are included in my model, I get this:

  Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.58751    0.01147  51.202  < 2e-16 ***
IV       0.27696    0.06564   4.219 3.13e-05 ***

Adding a control variable (CV) to the regression, leads to this:

             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.508030   0.092986  -5.464 8.92e-08 ***
IV      0.134419   0.057986   2.318    0.021 *  
CV        0.049427   0.004173  11.845  < 2e-16 ***

I checked the variance inflation factors, which are both 1.050193 (they are identical, does that mean anything?). So multicollinearity doesn't seem to be the problem.

Then I thought of Mediation (Baron & Kenny). Because the IV gets insignificant, when adding the CV, the CV seems to be the mediator. I checked this using the lavaan package:

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)
  Y ~                                                 
    X          (c)    0.134    0.058    2.328    0.020
  M ~                                                 
    X          (a)    3.038    0.725    4.191    0.000
  Y ~                                                 
    M          (b)    0.049    0.004   11.896    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .Y                 0.021    0.002   13.229    0.000
   .M                 3.468    0.262   13.229    0.000

Defined Parameters:
                   Estimate  Std.Err  z-value  P(>|z|)
    direct            0.134    0.058    2.328    0.020
    indirect          0.150    0.038    3.953    0.000
    total             0.285    0.067    4.262    0.000
    prop_mediated     0.528    0.128    4.118    0.000

Now to my problem: to me this doesn't make sense. To me I cannot construct an explanation for this result (X->M->Y).

Is there anything else I can check, a test I can do? The data is archival, so remeasuring, or measuring something like measuring X before M is not possible.

I am looking forward to your replies!

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  • $\begingroup$ Just a small note, I don't know which way you entered the variables in lavaan but based on "Because the IV gets insignificant, when adding the CV", shouldn't CV be the probable mediator and not IV? $\endgroup$
    – Sointu
    Commented May 9 at 17:48
  • $\begingroup$ Are you sure? I read again about the steps for Mediation according to Baron & Kenny, and it looks to me that if you have a significant relationship between x and y and then you add another variable (lets call it z), and the coefficent of z becomes significant and x becomes insignificant, shouldn't z be the mediator? On the one hand I am pretty sure of this, on the other hand maybe you are right, and this is where my problem is coming from $\endgroup$
    – user9011032
    Commented May 9 at 18:12
  • $\begingroup$ Yes, it is as you explain in this comment, but I read your original as if you had it the other way around: "Because the IV gets insignificant, when adding the CV, my independent variable seems to be the mediator and my CV seems to be the IV/X" - so it sounds like you made CV the X and original IV the mediator, although related to your comment example, your CV would be "z" and IV would remain as "x", right? $\endgroup$
    – Sointu
    Commented May 9 at 18:16
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    $\begingroup$ Thanks, I made a mistake in the original post! I changed it. $\endgroup$
    – user9011032
    Commented May 9 at 18:25

1 Answer 1

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What you have described is mediation, right on the nose. So, you have it. Not only does the IV go from significant to not (which isn't really a good test of anything, as Andrew Gelman showed in an article called "the difference between `significant' and 'not significant' is not, itself, statistically significant" but the paraemeter estimate got a lot closer to 0. The mediation analysis you did confirms that it is mediation (there are some newer approaches to mediation, but that probably won't matter).

You haven't told us what the variables are, but just that it "doesn't make sense" for there to be mediation. Well, that might be very good. I mean, it could be that the data is wrong, or that you created errors bringing it from the archive, or something like that. But maybe you've discovered something new. That should thrill you.

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  • $\begingroup$ More a question than an answer: is it impossible for some reason, or unlikely, given all the results, that the CV variable is not a mediator but a confounder? If you cannot imagine why or how there would be mediation, why do you seem to rule out confounding? $\endgroup$
    – BenP
    Commented May 11 at 13:58
  • $\begingroup$ @BenP You put this as a comment on my answer, I think you meant it as a comment on the question $\endgroup$
    – Peter Flom
    Commented May 11 at 14:24
  • $\begingroup$ Yes correct @PeterFlom, sorry! But on the other hand, maybe you could give me an answer as well. I mean, since we do not know the exact meaning of the variables involved, you must have had a reason to call it "mediation" based on the analyses done. $\endgroup$
    – BenP
    Commented May 11 at 14:26
  • $\begingroup$ It's mediation because the effect of the IV changed a lot when the mediator was added. $\endgroup$
    – Peter Flom
    Commented May 11 at 14:31
  • $\begingroup$ But could that not be the case too for a confounder, so that the uncontrolled effect of X is at least in part spurious? $\endgroup$
    – BenP
    Commented May 11 at 14:34

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