Multi-group Convergent Validity

Metric invariance (equal loadings) is a necessary prerequisite because it ensures you are comparing loadings that are on a common scale. However, it is not sufficient: even with constrained-equal loadings, the per-group AVE can still fall below 0.50 if item error variances are large in one group. Always compute and report AVE separately for each group after establishing metric invariance.

This indicates differential convergent validity: the scale captures the construct more weakly in the low-AVE group. Inspect individual loadings in that group to identify which items underperform. If a few items are consistently weak in a specific group, consider whether those items are culturally or contextually less relevant there, and report the limitation explicitly rather than pooling groups as if convergent validity is equal.

HTMT primarily tests discriminant validity, but low HTMT values also provide indirect evidence for convergent validity by confirming that constructs are well-differentiated. It should complement, not replace, AVE. Use both together: AVE verifies that each construct is well-captured by its own items, while HTMT confirms it is distinct from other constructs.

As a practical minimum, 100–150 cases per group is often cited for multi-group CFA to yield stable loading and fit estimates. With fewer cases, loading standard errors widen, AVE estimates become unreliable, and chi-square difference tests lose power. Power analysis using Monte Carlo simulation is the most principled approach when planning sample sizes.

Partial metric invariance — where at least two items per factor have equal loadings — allows limited cross-group comparisons for those items, but global AVE comparisons are compromised because the unconstrained loadings differ across groups. Report partial invariance transparently and restrict convergent validity claims to the invariant items.