Qualitatively negligible, but sufficiently strong evidence for indirect effects during mediation analysis in brms

Modeling
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1

Hello, I’m conducting a mediation analysis with ordinal outcomes, using brms.

My model contains:
X → M → Y where M is the mediating variable, and Y is the ordinal outcome variable.

X: a continuous variable, repeated measures within-patient
Y: an ordinal variable (rating 1 to 3), repeated measures within-patient
M: a continuous mediating variable, repeated measures within-patient

So, with “mu” as the random intercept for “patient”, the model could look like:

(1) Y = c*X + mu (for c, the total effect)
(2) M = a*X + mu (for a)
(3) Y = c'*X + b*M + mu (for b and c’, the direct effect)

The indirect effect, according to the product of coefficients (PC) approach, would be a*b.

First, model fit diagnostics looks reasonable.
Second, the range for coefficients a, b and the direct and total effects are ~0.05 in magnitude, which I think also makes sense, in the context of our data.

But the indirect effect is 0.001, the the CI barely excluding 0. This looks like I should interpret my model as having sufficient evidence for a mediation effect; however the effect looks so small. It’s also true that we have a large sample size, about 500 measurements per patient, with 40 patients total, which might be skewing the results. How should we report this mediation effect? Are there approaches, other than CI, to make a comment about the strength of effects, and describe it as potentially existing but negligible?

Thank you so much!

2

If the indirect effect is in the same direction as the total effect, perhaps it would be useful to report the proportion of the total effect that is mediated (which in this case would be ~0%).

3

Thank you so much. And if it were the opposite direction in a different model, it would just be interpretable as a suppression effect, no matter how seemingly negligible?

4

In that case, mediated-effect/direct-effect might be a useful way to convey how much of the direct effect is being suppressed? In both cases you’d make it clear that ignoring the mediation pathway would not have a meaningful impact on the expected outcome.

5

Ok makes sense, thank you! I guess it’s already qualitatively obvious how small the effect size is, and not to over interpret it. I’ll be careful on how I describe this, thank you for your suggestion.