# Help interpreting direct vs. indirect effects?

After adding several potential mediators to a regression model, I've found that the coefficient on my main explanatory variable has decreased by over 100% (and is no longer significant). How am I to interpret this finding?

The purpose of my analysis is to measure attenuation in coefficients as potential mediators are added to the regression, so as to assess direct vs. indirect effects.

But when the coefficient on my explanatory variable declines by over 100%, I'm not sure how to present the finding. I can't plausibly say that the mediators explain "over 100%" of the relationship between x and y. How should I think about this finding in terms of direct and indirect effects?

Background: I'm using a logit regression, which makes things complicated. Since the coefficients produced by logit regression (i.e., logged odds) are "non-collapsible" — they can't be compared across models — I'm using an adjusted coefficient that allows comparison across nested models. In Stata, this approach is achieved via the khb adofile. The khb command corrects for the "naive" logit coefficients and produces a measure called "mediation percentage." What I'm finding here is that my mediation percentage sometimes goes above 100%, and I don't know what this might mean.

## 1 Answer

Given you have a non-significant direct effect, you actually don’t know whether the true coefficient of the direct effect is positive or negative, and however there is no evidence that it is not null. Let's first assume it is null then. My interpretation is that your main explanatory variable (let’s call it $X$) has only an effect on your outcome (let’s call it $Y$) through mediators (let’s say $M$). In short, all the effect of $X$ on $Y$ is through mediators. However, if you disregard the issue of statistical significance and just consider the coefficient values, you should conclude that $X$ has a negative direct effect on $Y$, but a positive overall effect, given its indirect effect is higher than its (negative) direct effect.