Simple mediation analysis in PROCESS 4.2 in SPSS. The outcome variable is binary, the mediator is continuous and the IV is binary

Question

In the first model, the IV (X) significantly predicts the mediator (M).

In the second model, the mediator significantly predicts the outcome variable (Y) but the IV (X) does not predict the outcome variable (Y).

In the third model, the direct effect of X on Y is non-significant. The indirect effect of X on Y is significant.

EDIT EDIT

In the old times of the Sobel Test, the first regression model would show a significant relationship between the IV and the outcome. Then, in the next model, when the mediator was added, it could be seen if the IV's effect decreased as a result of this and whether its effect was still significant. This would show us whether there was mediation and if it was partial or complete.

PROCESS does not show this first IV and outcome relationship. PROCESS also does not compute a total effect when the outcome is binary. So I went back to the old times and ran a logistic regression for this relationship. I ran a linear regression for the IV to mediator relationship. And then I ran another logistic regression adding both the IV and the mediator as predictors of the binary outcome. Then I did a Sobel Test. However, I was told that a Sobel Test can only be done with an outcome which is continuous. I am baffled by this as I have seen a published paper which did exactly what I did above on a binary outcome.

Answer 1

There is some debate about terminology and method in mediation analysis. I'm not sure what PROCESS does (I don't know SPSS well at all) but here are my thoughts:

First, stop paying so much attention to significant, not significant, and what changes from one to the other when comparing models. See Andrew Gelman's article "the difference between 'significant' and 'not significant' is not, itself, statistically significant". Look at effect sizes and how they change.

When you write it up, you can, if you like, avoid using the term "mediation" and just say what happened. How you should say this would depend on the sophistication of your audience. For a less statistically schooled audience, I like using actual predictions, rather than just parameter estimates and their standard errors and p values.

Second (and here's where definitions come in) to me, "mediation" means that adding the mediator to the model makes meaningful changes to the relationship between the IV and the DV. The data analyst (perhaps in consultation with a substantive matter expert) can decide what is meaningful. And, to me, either a large increase or decrease could be called "mediation". But, whatever you call it, such a relationship is important to look at.