30. SEMinR Lecture Series - How to Solve Convergent and Discriminant Validity Issues

Convergent and discriminant validity problems in reflective measurement models can often be fixed inside SEMinR by tightening the measurement first—then cleaning the data and re-checking HTMT—rather than treating validity as a one-shot diagnostic. The core workflow starts before analysis: each construct should have enough indicators (at least four to six), items must be easy to understand, and statements should not overlap conceptually, because overlapping wording is a common driver of discriminant validity failures.

For convergent validity, the practical lever is outer loadings and the downstream reliability/AVE metrics. Indicators with weak factor loadings are candidates for removal, but the decision should be tied to improvement in composite reliability and average variance extracted (AVE), not loading thresholds alone. While loadings above 0.70 are often treated as desirable, social science datasets frequently produce weaker outer loadings; SEMinR guidance in the transcript emphasizes caution. Items should be deleted only when doing so meaningfully increases composite reliability and AVE (with AVE expected to exceed recommended cutoffs). If reliability and AVE are already above targets, items with loadings below 0.70 may still be retained as long as they remain reasonably strong (the transcript notes a practical range where loadings above 0.40 need not be removed if overall validity metrics are already acceptable). In R, the process is implemented by inspecting the SEMinR summary outputs for reliability, AVE, and the specific indicators with low outer loadings, then iterating the model after deletions.

Discriminant validity is then addressed through HTMT, cross-loadings, and—when needed—data quality checks. HTMT values above the required limit signal trouble between specific construct pairs (the transcript gives an example where four constructs show issues, with LG and SC among the problematic pairings). When HTMT flags a problem, one recommended diagnostic is to compute response standard deviations per construct and remove respondents with extremely low variability (the transcript uses a threshold of standard deviation below 0.25). The rationale is straightforward: near-zero standard deviation suggests respondents did not read or did not answer properly. After deleting those problematic cases, HTMT is re-run; the transcript reports that validity metrics improve significantly.

Next comes cross-loading review. If an item cross-loads on two constructs and the difference between its primary loading and the competing loading is less than 0.10, that indicator is a candidate for removal. The transcript illustrates this by comparing cross-loadings between specific constructs (e.g., LG vs RC, and LG vs RC again through different indicator pairs), using spreadsheet comparisons to identify where the loading differences fall below the 0.10 guideline.

If HTMT still fails, the transcript outlines escalation steps. Bootstrapped HTMT with bias-corrected confidence intervals can confirm whether discriminant validity is supported (the key check is whether a “1” appears between the interval bounds). If discriminant validity issues persist even after confidence-interval checks, one fallback is to collapse theoretically distinct dimensions into a single higher-order measure when correlations in the 0.8–0.9 range are repeatedly reported in the literature. If none of the remedies work, additional data collection may be necessary. Finally, the transcript notes that sampling quirks can drive multicollinearity-like behavior; dropping highly colinear independent variables may help when discriminant validity problems are tied to model structure rather than measurement quality.