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CBSEM using #SmartPLS4 | 14 | Mediation Analysis using CBSEM Model in SmartPLS4 thumbnail

CBSEM using #SmartPLS4 | 14 | Mediation Analysis using CBSEM Model in SmartPLS4

Research With Fawad·
5 min read

Based on Research With Fawad's video on YouTube. If you like this content, support the original creators by watching, liking and subscribing to their content.

TL;DR

Mediation decomposes X→Y into a direct effect (C′) and an indirect effect through a mediator M (A×B).

Briefing

Mediation analysis hinges on separating an effect into two parts: a direct path from an independent variable to a dependent variable, and an indirect path that runs through a mediator. In practice, the indirect effect is computed as the product of two links—X→M (often labeled A) and M→Y (labeled B)—so the indirect effect equals A×B. The total effect is then the sum of the direct effect (the X→Y relationship when the mediator is included, labeled C′) and the indirect effect (A×B). This decomposition matters because it clarifies *how* influence travels, not just whether it exists.

The transcript lays out mediation types based on which components are statistically significant. Partial mediation occurs when both the indirect effect (A×B) and the direct effect (C′) are significant, meaning some influence flows through the mediator while some still bypasses it. Full mediation is the opposite pattern: the indirect effect is significant, but the direct effect becomes insignificant once the mediator is in the model—indicating the mediator carries the effect. It also distinguishes complimentary mediation (direct and indirect effects move in the same direction, such as both positive) from competitive mediation (direct and indirect effects differ in sign, such as a negative direct effect paired with a positive indirect effect).

For testing mediation, the discussion contrasts the classic Baron and Kenny (1986) four-step approach with later refinements. Baron and Kenny required significance checks on the total effect (X→Y), then on X→M, then on both X→M and M→Y, and finally on the direct and indirect paths together. That framework has been criticized because it relied on unstandardized coefficients and significance testing (including Sobel tests) that can miss mediation when suppressor effects exist or when only the product A×B matters. The transcript highlights a key shift: significance of A or B individually is no longer treated as a requirement, since the indirect effect is the product A×B.

The recommended method uses bootstrapping to test the indirect effect’s confidence interval. Bootstrapping repeatedly resamples the dataset (with replacement) to generate thousands of pseudo-samples (commonly 5,000–10,000; here, 1,000 is used) and then checks whether the indirect effect’s confidence interval excludes zero. This approach directly targets the statistical uncertainty around A×B.

A SmartPLS4 walkthrough then demonstrates the workflow in a single structural model. After ensuring the measurement model is assessed first, the model fit is checked, and bootstrapping is run (CBM bootstrapping with one-tailed testing set because relationships are hypothesized as positive). The results are interpreted through standardized path coefficients and p-values. The indirect effect of organizational commitment (OC) on organizational performance (OP) through collaborative culture (CC) is reported as significant (p < 0.05), with a T statistic consistent with the one-tailed setup. To determine mediation type, the direct effect OC→OP in the presence of CC is also examined: because it remains significant, the transcript concludes partial mediation. It further reports the specific indirect effect magnitude (standardized indirect effect around 0.189) and uses bias-corrected confidence intervals to confirm the indirect effect does not cross zero, supporting the mediation hypothesis. Finally, it notes how to structure reporting in structural equation modeling: measurement model reliability/validity first, then direct effects, then mediation (and moderation if present).

Cornell Notes

Mediation analysis splits the relationship between X and Y into a direct effect (C′) and an indirect effect through a mediator M. The indirect effect is computed as the product of two paths: A (X→M) times B (M→Y), so indirect = A×B. The total effect equals direct + indirect. Partial mediation occurs when both the indirect effect and the direct effect are significant; full mediation occurs when the indirect effect is significant but the direct effect becomes insignificant once M is included. Because indirect effects depend on the product A×B, bootstrapping is used to test significance via confidence intervals that should exclude zero. In SmartPLS4, this is implemented by running CBM bootstrapping after the measurement model is validated, then checking indirect effects and direct effects to classify mediation.

How do direct, indirect, and total effects relate in mediation testing?

Direct effect (C′) is the X→Y relationship *with* the mediator included, so it captures influence that bypasses the mediator. Indirect effect flows through the mediator and equals A×B, where A is X→M and B is M→Y. Total effect is the combined impact: total = direct (C′) + indirect (A×B). In the transcript, C is the total effect when no mediator exists; C′ becomes the direct effect once the mediator is added.

What statistical pattern distinguishes partial mediation from full mediation?

Partial mediation: the indirect effect (A×B) is significant and the direct effect (C′) is also significant, meaning some influence goes through M and some remains direct. Full mediation: the indirect effect is significant but the direct effect is insignificant once M is in the model, meaning the effect of X on Y operates entirely through M. The SmartPLS4 results in the transcript show the indirect effect is significant and the direct OC→OP path remains significant, so the conclusion is partial mediation.

Why did the approach move away from Baron and Kenny’s significance-step logic and Sobel tests?

Baron and Kenny’s method and Sobel-style testing can fail when suppressor effects keep the total effect (C path) nonsignificant or when only the product A×B matters. Later guidance emphasizes that indirect effects depend on the product of A and B, so A or B individually being nonsignificant doesn’t rule out a significant indirect effect. The transcript cites this as a reason to reject Sobel testing for mediation significance.

How does bootstrapping test mediation in a way that matches the math of indirect effects?

Bootstrapping repeatedly draws random samples with replacement from the dataset to create many pseudo-samples (e.g., 1,000 in the walkthrough). For each pseudo-sample, it estimates the indirect effect A×B. Significance is then assessed by checking whether the bias-corrected confidence interval for the indirect effect includes zero. If zero is not in the interval, the indirect effect is treated as significant.

What is the practical SmartPLS4 workflow for mediation analysis described here?

First, validate the measurement model (reliability and validity) before touching mediation. Then build a single structural model that includes X, the mediator M, and Y (rather than running separate models for each link). Check model fit, run CBM bootstrapping with an appropriate number of resamples, and inspect the inner model for path coefficients, p-values, and specific indirect effects. Finally, classify mediation by comparing significance of the indirect effect and the direct effect.

Review Questions

  1. In mediation, what does it mean if the indirect effect’s confidence interval excludes zero but the direct effect is significant?
  2. Why is the indirect effect tested as A×B rather than by requiring A and B to be individually significant?
  3. When reporting mediation results in SmartPLS4, which quantities determine whether mediation is partial or full?

Key Points

  1. 1

    Mediation decomposes X→Y into a direct effect (C′) and an indirect effect through a mediator M (A×B).

  2. 2

    Indirect effect significance should be tested on the product A×B, not on whether A or B alone is significant.

  3. 3

    Total effect equals direct effect plus indirect effect: total = C′ + (A×B).

  4. 4

    Partial mediation occurs when both the indirect effect and the direct effect are significant; full mediation occurs when only the indirect effect is significant.

  5. 5

    Bootstrapping is the preferred method for mediation significance testing because it builds confidence intervals for the indirect effect and avoids Sobel-test limitations.

  6. 6

    In SmartPLS4, mediation is run within one structural model after the measurement model is validated, using CBM bootstrapping and then inspecting specific indirect effects and direct paths.

  7. 7

    Mediation reporting should follow a structured order: measurement model quality first, then direct effects, then mediation results (including effect sizes, p-values, and confidence intervals).

Highlights

Indirect effect is calculated as A×B, where A is the X→M path and B is the M→Y path.
Partial mediation is identified when both the indirect effect and the direct effect remain significant after adding the mediator.
Bootstrapping tests mediation by generating many resamples and checking whether the indirect effect’s confidence interval excludes zero.
The SmartPLS4 example concludes collaborative culture (CC) partially mediates the relationship between organizational commitment (OC) and organizational performance (OP) because both indirect and direct effects are significant.

Mentioned