Extended definition
Convergent and discriminant validity are two complementary construct validity criteria used in measurement instrument validation. Convergent validity establishes that items designed to measure the same latent construct correlate strongly — operationally, the construct explains a substantial proportion of variance in its indicators. Discriminant validity establishes that items from theoretically distinct constructs correlate weakly — the construct must be empirically separable from other constructs in the model. Fornell and Larcker (1981) proposed the classical operationalization via Average Variance Extracted (AVE):
where is the standardized factor loading of indicator and the error variance. AVE > 0.50 signals adequate convergent validity; for discriminant validity, each construct’s AVE must exceed the squared correlation with any other construct. Henseler, Ringle, and Sarstedt (2015) proposed the HTMT (Heterotrait-Monotrait ratio of correlations) criterion as a more sensitive alternative in variance-based SEM (PLS-SEM); HTMT < 0.85 (strict) or < 0.90 (liberal) is the recommended threshold.
When it applies
Convergent and discriminant validity apply in any project validating a latent measurement instrument: psychological questionnaire, organizational scale, clinical quality-of-life instrument, educational scale. They are mandatory steps in CFA — after confirming factor structure, AVE and HTMT verify that constructs are empirically robust. In SEM, discriminant validity between factors is a prerequisite for interpreting structural coefficients as effects between distinct constructs. APA and the Standards for Educational and Psychological Testing (AERA/APA/NCME) require evidence of convergent and discriminant validity in instrument development.
When it does not apply
It does not apply in purely formative models (composite indicators) — formative constructs are defined by their indicators, not modeled as causes of them; classical AVE is not appropriate. It does not apply in instruments with single indicators per construct — without multiple items, AVE is not computable. It does not apply as a single test: construct validity is a cumulative process (content, criterion, nomological validity), not a checklist. In purely exploratory research without established theory about the constructs, AVE can be hard to interpret; first stabilize factor structure via EFA. In small samples, AVE estimates have wide CIs and unstable conclusions.
Applications by field
— Psychometrics: standard in scale validation; AVE and HTMT in instruments published in top-tier journals. — Organizational research: validation of engagement, culture, leadership questionnaires via PLS-SEM with HTMT. — Marketing: SEM in consumer behavior models requires convergent and discriminant validation. — Education: validation of cognitive and attitudinal assessment instruments follows AERA/APA/NCME protocol.
Common pitfalls
The first pitfall is relying only on the Fornell-Larcker criterion in modern SEM: Henseler et al. (2015) simulations showed it underdetects discriminant problems in some scenarios; HTMT is more sensitive and widely preferred. The second is confusing Cronbach’s alpha with AVE — Cronbach is reliability (internal consistency); AVE is convergent validity; both are necessary but distinct. The third is interpreting AVE > 0.50 alone as sufficient without checking discriminance: convergent without discriminant suggests collapsed constructs. The fourth is failing to report HTMT in PLS-SEM published post-2015 — top-tier journals today require it. The fifth is interpreting low between-construct correlation as automatic evidence of discriminance: it may reflect weak indicators, not genuinely distinct constructs.