Does It Work Through What You Think? Test The Mechanism

How it works

Mediation is estimated with three ordinary least squares regressions on the same rows and the same covariate set: the mediator on the predictor gives the a path; the outcome on both the predictor and the mediator gives the b path and the direct path c-prime; the outcome on the predictor alone gives the total path c. The indirect effect is a times b, and its 95% confidence interval is a percentile bootstrap — rows resampled with replacement, both regressions refitted on each resample, and the 2.5th and 97.5th percentiles of the resulting products reported, from a fixed seed so the interval is reproducible. The Sobel normal-theory test is computed and reported alongside, with its weakness stated. Moderation is estimated with a single interaction model, and the predictor's conditional slope is evaluated at the mean of the moderator and one standard deviation either side (or within each level of a categorical moderator), each with a standard error from the model's covariance matrix.

Use it when you have a specific third variable in mind and want to know whether the predictor-outcome association runs through it (mediation) or varies across it (moderation), and you want the uncertainty on that claim rather than just a point estimate.

Not a substitute for a randomised experiment or a designed causal study — on observational data the decomposition describes associations under assumptions the data cannot check. Not for a binary mediator or outcome, not for several mediators at once, and not for repeated measures on the same unit, which violate the independence the standard errors assume.

What data do you need?

One row per unit, with the predictor, the intermediate step, and the outcome measured on it. For example, marketing spend, site traffic, and revenue per customer:

Minimum 30 rows · Best with 200-20,000 rows

What's in the report?

Standard-library analysis: does a predictor relate to an outcome through a third variable, or does its relationship with the outcome depend on one? Map a predictor, an outcome, and either a mediator or a moderator (plus optional covariates). Mediation splits the total association into the direct path and the indirect path that runs through the mediator — the a, b, c and c-prime paths with standard errors, the indirect effect a×b with a percentile bootstrap confidence interval, the proportion mediated where it is interpretable, the Sobel test reported alongside with its weakness stated, and the whole path diagram as a table. Moderation fits the interaction model and reports the conditional slope of the predictor at low, mean and high values of the moderator (or within each moderator level). Every narrative states, in your own column names, the assumption set a causal reading would rest on.