Mediation analysis not producing expected results, probably as consequence of multicollinearity issue

Question

I am using the PROCESS macro to do a basic mediation analysis, with variables X,M, and Y. All are continuous. I know from theory that X and M, and M and Y respectively, should have a relationship. I am certain from the theory that X is causing M, not the other way around. Indeed, in my data when I do a regular linear regression, paths a, b, and c, are all significant. Standardized Betas for the 3 paths are 0.76, -0.17, and 0.16 respectively.

This leads me to expect that when I do a mediation analysis, at least one of paths c' or b should have a significant relationship. However, this is not the case. In the PROCESS results, both the direct and the indirect result are not significant. My suspicion is that X and M are so strongly related (standardized B = 0.76), that both path b and path c' are suppressed by this. Path ab is quite a bit larger than path c', which does point at a strong degree of mediation. However, since path ab is not significant, I don't feel that this result is of any value.

Is my interpretation correct, and is there any way I can deal with this?

Answer 1

First, I think you are placing way too much emphasis on statistical significance. For comparing results, see Andrew Gelman's paper The Difference between "significant" and "not significant" is not, itself, Statistically Significant.

However, since path ab is not significant, I don't feel that this result is of any value.

This is not a good view of statistical significance, especially when your theory is strong. The p value answers a very specific question:

If, in the population from which this sample was randomly drawn, the null hypothesis was true, how likely is it that I'd get a test statistic at least as extreme as the one I got, in a sample the size of the one I have?

That question is not apropos here.

As to how to deal with collinearity, there are various methods, but the one that seems most appropriate here is ridge regression. This method allows some bias in the parameter estimates in order to reduce their variance.