CBSEM using #SmartPLS4 | 10 | Understand and Interpret Discriminant Validity

TL;DR

Discriminant validity tests whether constructs meant to be distinct are not overly correlated in the measurement model.

Briefing Cornell Notes

Briefing

Discriminant validity—whether constructs that should be distinct are actually empirically different—can be tested in covariance-based structural equation modeling using SmartPLS4 by applying two complementary checks: the Fornell–Larcker criterion and the Heterotrait–Monotrait (HTMT) ratio. The practical payoff is straightforward: if constructs overlap too much, the measurement model becomes unreliable, and any conclusions drawn from the structural paths risk being misleading.

The Fornell–Larcker approach (proposed in 1981) compares within-construct variance to shared variance between constructs. For each latent variable, the square root of its Average Variance Extracted (AVE) should be greater than its correlations with every other latent variable in the model. In simple terms, a construct’s “own” variance must dominate the variance it shares with other constructs. SmartPLS4 operationalizes this by running the CBSEM algorithm, then producing a matrix where the diagonal entries represent √AVE for each construct, while off-diagonal cells contain inter-construct correlations. In the example with three constructs (CC, OC, and OP), CC passes the test because √AVE(CC) exceeds both corr(CC, OC) and corr(CC, OP). OC also passes when √AVE(OC) is compared against its correlations with the other constructs—especially corr(OC, CC) and corr(OC, OP). OP passes as well: √AVE(OP) is larger than corr(OP, CC) and corr(OP, OC). With these comparisons satisfied, discriminant validity is supported under Fornell–Larcker.

Because Fornell–Larcker has faced criticism for being insensitive to some discriminant validity problems, the transcript then shifts to a more modern method: HTMT. The HTMT ratio examines the correlation of indicators across different constructs (heterotrait) relative to the correlation of indicators within the same construct (monotrait). Put differently, it asks whether cross-construct relationships are meaningfully smaller than within-construct relationships. Following guidance attributed to Hensler and colleagues, HTMT values below 0.90 indicate discriminant validity for reflective constructs.

In the SmartPLS4 workflow, HTMT is computed by selecting the HTMT option and reviewing pairwise ratios between constructs. The example reports that the HTMT ratio for CC vs. OC is below 0.90, CC vs. OP is below 0.90, and OC vs. OP is also below 0.90. Ratios involving the same construct (e.g., OC vs. OC) are not meaningful because they equal 1 by definition. With both Fornell–Larcker comparisons and HTMT thresholds met, the measurement model is treated as having no discriminant validity issues, and the constructs are considered empirically distinct.

Overall, the transcript provides a clear SmartPLS4 checklist: run the CBSEM algorithm, verify √AVE exceeds inter-construct correlations using Fornell–Larcker, then confirm reflective discriminant validity using HTMT with a 0.90 cutoff.

Cornell Notes

Discriminant validity checks whether constructs that should be distinct are not overly correlated in the measurement model. Two methods are used in SmartPLS4 for CBSEM: Fornell–Larcker and HTMT. Fornell–Larcker requires that the square root of each construct’s AVE (diagonal √AVE) is greater than that construct’s correlations with every other construct. HTMT uses a ratio of heterotrait (between-construct) correlations to monotrait (within-construct) correlations; for reflective constructs, HTMT values below 0.90 indicate discriminant validity. In the worked example with constructs CC, OC, and OP, both criteria are satisfied, supporting the conclusion that the constructs are empirically distinct.

What does discriminant validity mean in survey-based structural equation modeling, and why does it matter?

Discriminant validity is the degree to which measures that are supposed to represent different constructs are empirically distinct rather than highly correlated. In social-science survey research, constructs can overlap conceptually, so statistical checks help confirm that each construct has a distinct identity. If discriminant validity fails, the measurement model may blur constructs, undermining confidence in structural relationships.

How does the Fornell–Larcker criterion test discriminant validity in SmartPLS4?

Fornell–Larcker compares within-construct variance to shared variance. For each latent variable, the square root of AVE (√AVE) must be greater than the correlations between that construct and every other latent variable in the model. In SmartPLS4, this is read from the Fornell–Larcker matrix: diagonal cells show √AVE, while off-diagonal cells show inter-construct correlations. The transcript’s example checks CC vs. OC and CC vs. OP, then OC vs. CC and OC vs. OP, and finally OP vs. CC and OP vs. OC.

What is the key rule for interpreting HTMT, and what does HTMT actually compare?

HTMT (Heterotrait–Monotrait ratio) compares cross-construct indicator correlations to within-construct indicator correlations. It effectively asks whether indicators from different constructs (heterotrait) correlate less than indicators within the same construct (monotrait). For reflective constructs, the transcript uses a threshold: HTMT values below 0.90 indicate discriminant validity. Pairwise HTMT ratios are evaluated between different constructs; same-construct ratios are not informative because they equal 1.

Why might Fornell–Larcker be questioned, and what does HTMT add?

Recent research has questioned how sensitive Fornell–Larcker is at detecting discriminant validity issues. HTMT is presented as a more modern approach because it uses a ratio grounded in indicator-level correlations (heterotrait vs. monotrait), which can better capture problems where constructs appear distinct at the latent level but not at the indicator level.

In the example with CC, OC, and OP, what evidence supports discriminant validity?

Evidence comes from two checks. First, Fornell–Larcker: √AVE for each construct (CC, OC, OP) is larger than that construct’s correlations with the other two constructs. Second, HTMT: each pairwise HTMT ratio (CC–OC, CC–OP, OC–OP) is reported as less than 0.90. Together, these results support the claim that the constructs are distinct and the model has no discriminant validity issues.

Review Questions

In the Fornell–Larcker matrix, which values must be compared for each construct, and what inequality must hold?
How does HTMT differ from Fornell–Larcker in what it measures (indicator-level logic vs. latent-level comparisons)?
What HTMT cutoff is used for reflective constructs in the transcript, and how are pairwise ratios interpreted?

Key Points

1
Discriminant validity tests whether constructs meant to be distinct are not overly correlated in the measurement model.
2
Fornell–Larcker requires √AVE for each latent variable to be greater than its correlations with all other latent variables.
3
In SmartPLS4, Fornell–Larcker is checked using the diagonal √AVE values versus off-diagonal inter-construct correlations.
4
HTMT evaluates heterotrait (between-construct) correlations relative to monotrait (within-construct) correlations.
5
For reflective constructs, HTMT values below 0.90 indicate discriminant validity.
6
Using both Fornell–Larcker and HTMT provides a stronger basis for concluding constructs are empirically distinct.

Highlights

Fornell–Larcker: √AVE of a construct must exceed its correlations with every other construct in the model.

HTMT: a heterotrait-to-monotrait ratio below 0.90 signals discriminant validity for reflective constructs.

SmartPLS4 workflow: run the CBSEM algorithm, then verify discriminant validity via the Fornell–Larcker matrix and HTMT pairwise ratios.

In the CC/OC/OP example, both criteria are satisfied, supporting distinct constructs with no discriminant validity issues.

Topics

Mentioned

SmartPLS4
CBSEM
AVE
HTMT