14. SEMinR Lecture Series. Discriminant Validity Assessment in R

Discriminant validity is the make-or-break check for reflective measurement models: it tests whether each construct is empirically distinct from every other construct in the structural model. In practice, constructs must not only “work” internally, but also avoid measuring the same underlying concept as their neighbors. The lecture frames discriminant validity as the fourth step after indicator reliability, construct reliability, and convergent validity, and then walks through how to assess it in R using the seminR workflow.

A traditional approach comes from Fornell and Larcker, which compares the square root of a construct’s AVE (average variance extracted) against the correlations between that construct and all other constructs. The rule is straightforward: the square root of AVE for a construct should exceed its inter-construct correlations, implying that within-construct variance dominates shared variance. But the session warns that this criterion can miss problems—especially when indicator loadings across constructs differ only slightly (for example, when loadings fall in a narrow band like 0.65 to 0.85). Henseler and colleagues (2015) are cited for showing that the Fornell–Larcker criterion performs poorly in such cases, so it’s treated as unreliable and something to avoid even if it remains common.

As a more dependable alternative, the lecture emphasizes HTMT (heterotrait–monotrait ratio of correlations). The logic is built from indicator pairs: correlations between indicators measuring the same construct are “monotrait” and should be high, while correlations between indicators measuring different constructs are “heterotrait” and should be low. Discriminant validity problems show up when HTMT values are too large. Henseler et al. propose a threshold of 0.90 for constructs that are conceptually very similar (e.g., cognitive satisfaction, affective satisfaction, and loyalty), while a more conservative cutoff of 0.85 is recommended when constructs are more distinct.

The practical workflow in seminR starts by extracting HTMT results from a summary object (e.g., using the stored PLS estimation results). The lecture then demonstrates that HTMT values below 0.85 (or below 0.90 for highly similar constructs) support discriminant validity. It also notes a follow-up requirement: HTMT should be tested statistically against 1 (or against the chosen threshold) using bootstrap confidence intervals. That means running bootstrapping (the example uses 1,000 samples for speed, though 10,000 is recommended), extracting the bias-corrected confidence intervals, and checking whether the interval includes the critical value. If 1 falls outside the confidence interval, the null hypothesis that HTMT ≥ 1 is rejected, supporting discriminant validity.

Finally, the session adds cross-loading as another check. Each indicator should load highest on its own parent construct compared with all other constructs. The lecture illustrates this with an example where indicators for “vision” load strongly on vision rather than on development, rewards, collaborative culture, or organizational performance, and the same pattern holds for the other constructs.

The takeaway is a layered assessment strategy: rely on HTMT (with thresholds and bootstrap-based confidence intervals), use cross-loadings as a sanity check, and treat Fornell–Larcker as less trustworthy—particularly when constructs have similar indicator loading patterns. The session closes by recapping the broader reflective measurement evaluation steps and pointing ahead to formative model assessment next.