Mediation Analysis

The 0.006 path that was not dead

The structural lesson ended on a puzzle. Competence has essentially no direct effect on loyalty — 0.006, p = 0.84 — while likeability carries 0.34. The obvious reading is that competence is irrelevant.

That reading is wrong, and mediation analysis is how you prove it. An effect can travel entirely through a middleman.

A note on this model. Chapter 8 runs mediation on the full extended model, with the four formative drivers. This lesson keeps the simpler core model (COMP, LIKE, CUSA, CUSL) for teaching clarity, so the magnitudes differ from the book’s. The techniques are identical.

Setting up

A mediator transmits an effect. The indirect effect is the product of the two legs — COMP → CUSA times CUSA → CUSL. The total effect is direct plus indirect. The useful question is never “is there mediation” but which kind.

library(seminr)

corp_rep_sm <- relationships(
  paths(from = c("COMP", "LIKE"), to = c("CUSA", "CUSL")),
  paths(from = c("CUSA"),         to = c("CUSL")))

set.seed(123)
corp_rep_boot <- bootstrap_model(corp_rep_pls_model, nboot = 1000)
corp_rep_boot_summary <- summary(corp_rep_boot, alpha = 0.05)

R practice — save your bootstrap. Bootstrapping is the expensive step. saveRDS(corp_rep_boot, "outputs/corp_rep_boot.rds") means reopening the project tomorrow does not mean waiting on 10,000 resamples again.

1. Are the indirect effects significant?

corp_rep_summary$total_indirect_effects

specific_effect_significance(corp_rep_boot,
                             from = "COMP", through = "CUSA", to = "CUSL",
                             alpha = 0.05)
specific_effect_significance(corp_rep_boot,
                             from = "LIKE", through = "CUSA", to = "CUSL",
                             alpha = 0.05)

specific_effect_significance() bootstraps the product of the two legs directly. This is the correct test — no Sobel approximation, no normality assumption about a product of coefficients.

• COMP through CUSA: 0.082, CI 0.018 to 0.151 — significant
• LIKE through CUSA: 0.214, CI 0.146 to 0.286 — significant

Both indirect paths are real.

2. Are the direct effects significant?

corp_rep_boot_summary$bootstrapped_paths

• LIKE → CUSL: 0.342, significant
• COMP → CUSL: 0.009, CI spans zero — nothing, exactly as before

3. Classify with Zhao, Lynch & Chen (2010)

Forget Baron and Kenny; the field has moved on. The modern typology needs only your two significance tests, plus the sign of the direct × indirect product:

sign(corp_rep_summary$paths["LIKE", "CUSL"] *
     corp_rep_summary$paths["LIKE", "CUSA"] *
     corp_rep_summary$paths["CUSA", "CUSL"])

Applying it:

• COMP — indirect significant, direct not: indirect-only mediation. Competence affects loyalty entirely through satisfaction.
• LIKE — both significant, same sign: complementary mediation. Satisfaction transmits part of likeability’s effect; the rest flows direct.

Why this matters more than the statistics

This is the reason you never delete a predictor because its direct path is flat. Competence drives satisfaction; satisfaction drives loyalty. Skip the mediation analysis and you would have discarded a genuine driver of loyalty on the strength of a 0.006 coefficient.

Managerially the two constructs now have different jobs: competence is a satisfaction lever, likeability is both a satisfaction lever and a direct loyalty lever.

Going further

Chapter 8 of Hair et al. (2026) has the full treatment, including moderated mediation. Next: moderation — when a relationship’s strength depends on a third variable.