Discriminant validity and common method bias

Discriminant validity asks whether each construct is empirically distinct from the others. If trust and performance expectancy correlate at 0.95, respondents do not distinguish between them, and a path between them, or between each and intention, is hard to interpret. Reviewers check this carefully, and the criteria have changed in the last decade.

HTMT: the recommended criterion

The heterotrait–monotrait ratio (Henseler, Ringle and Sarstedt, 2015) compares the average correlation between items of different constructs with the average correlation between items of the same construct. If constructs are distinct, items correlate much more within than across constructs, and HTMT is well below 1. Thresholds are 0.85 for conceptually distinct constructs and 0.90 for conceptually similar ones (such as different dimensions of satisfaction).

The highest value is 0.544 (BI and UB), far below 0.85. A stricter test uses the bootstrap: the upper bound of the 95% (or one-sided 95%) confidence interval should be below the threshold. The HTMT confidence interval table shows the largest upper bound at 0.632, so discriminant validity is clearly established.

Fornell–Larcker and cross-loadings

The Fornell–Larcker criterion requires the square root of each construct’s AVE (diagonal) to exceed its correlations with all other constructs. For BI, √AVE = 0.918 and its highest correlation is 0.484 with PE, so the criterion holds for every construct. Cross-loadings require each indicator to load higher on its own construct than on any other; here, the lowest own loading (0.814) is far above the highest cross-loading (0.473, BI1 on UB).

Both older criteria are still reported by many authors, but simulation studies show that they often fail to detect real discriminant validity problems in PLS-SEM, especially when loadings are similar. Report HTMT as the main criterion; add Fornell–Larcker if your target journal expects it.

What if HTMT is too high?

• Check the item wording: do items of two constructs ask essentially the same thing?
• Look for items with high cross-loadings and consider removing them if content validity allows.
• Consider whether the two constructs should be merged into one, or modelled as dimensions of a higher-order construct.
• Never simply ignore the problem; explain how you resolved it.

Common method bias

When all constructs are measured with the same questionnaire at the same time, part of the correlation between them may come from the method itself (for example, a general tendency to agree). Reviewers often ask how you addressed this common method bias (CMB). Prevent it in the design (separate the measurement of predictors and outcomes in time, guarantee anonymity, vary scale formats), and test for it afterwards.

Harman’s single factor test puts all items into one unrotated factor. If a single factor explains more than 50% of the variance, CMB may be a problem. In the example, one factor explains 45.2% (principal axis factoring: 39.8%), and a single-factor CFA fits poorly (CFI = .727, RMSEA = .171), so there is no dominant method factor. The test is widely reported but weak: it detects only severe bias.

A more sensitive check in PLS-SEM is the full collinearity assessment (Kock, 2015): regress a random dummy variable on all constructs and check the VIF values; values above 3.3 suggest that the model may be contaminated by CMB. In the course model, the structural VIF values are all below 1.17 (Lesson 6), which is reassuring. A marker variable, a theoretically unrelated construct included in the questionnaire, is the strongest post-hoc approach.

Reporting

Discriminant validity was assessed with the HTMT criterion. All HTMT values were below 0.85 (maximum 0.544 for BI and UB), and the upper bounds of the 95% bootstrap confidence intervals were below 0.85 (maximum 0.632). The Fornell–Larcker criterion was also met. Harman’s single factor test (45.2% of variance) and full collinearity VIFs below 3.3 indicated that common method bias was not a serious concern.