12. SPSS AMOS - Assess Discriminant Validity - Fornell and Larcker Criterion
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Discriminant validity assesses whether constructs meant to be distinct are not highly correlated with each other.
Briefing
Discriminant validity checks whether constructs that are supposed to be distinct in a study are actually empirically distinct—meaning their measures should not correlate too highly. After assessing composite reliability and convergent validity, the next step is to test whether each latent construct’s internal variance (captured by the square root of AVE) exceeds its shared variance with other constructs (captured by the inter-construct correlations). A common benchmark comes from Fornell and Larcker: for each construct, the square root of the AVE should be greater than its correlation with every other latent variable in the model.
In the walkthrough, the model includes three constructs: Authentic Leadership Behavior, Ethical Leadership Behavior, and Life Satisfaction. The process in IBM SPSS AMOS starts by running the model and extracting two ingredients: (1) AVE values for each construct (already computed earlier) and (2) the correlation matrix among the latent constructs. The square root of each AVE is then calculated and placed beside the corresponding correlations. The rule is simple: if the square root of AVE for a construct is lower than any of its correlations with other constructs, discriminant validity is violated.
The initial results show discriminant validity problems specifically for Authentic Leadership Behavior. While the square root of AVE for Ethical Leadership Behavior and Life Satisfaction is higher than their correlations with other constructs, the square root of AVE for Authentic Leadership Behavior is not higher than its correlation with Ethical Leadership Behavior. That mismatch indicates overlapping measurement—statistically, the constructs are not sufficiently distinct.
To address the issue, the method shifts to checking indicator loadings. Items with weak loadings (the transcript flags loadings well below 0.70, even below 0.60) can be removed to improve the construct’s AVE, because AVE reflects how much variance the construct captures from its indicators relative to error. After deleting two problematic indicators (items 3 and 4), the AVE improves and the square root of AVE for Authentic Leadership Behavior rises. Correlations are recalculated as well, and the updated Fornell–Larcker comparisons are rechecked.
Even after removing the low-loading indicators, discriminant validity still fails. The remaining reason is substantive rather than purely statistical: Authentic Leadership Behavior and Ethical Leadership Behavior function as subdimensions of a higher-order construct (servant leadership) in the study. When two constructs are conceptually nested like that, treating them as fully separate constructs can produce unavoidable overlap. The recommended fix in this situation is to merge the two concepts into a higher-order construct rather than forcing discriminant validity through item deletion alone.
Overall, the session ties together a standard Fornell–Larcker test in AMOS with practical troubleshooting: first verify the criterion using AVE and latent correlations, then consider removing weak indicators, and finally—when theory implies relatedness—re-specify the measurement model by combining subdimensions into a higher-order construct.
Cornell Notes
Discriminant validity tests whether latent constructs that should be distinct are actually empirically different. Using the Fornell and Larcker criterion, each construct’s square root of AVE must be greater than its correlations with every other construct. In the AMOS workflow, AVE values are used to compute square roots, and latent correlations are pulled from the estimates/scalars correlation output. The initial check flags a discriminant validity problem for Authentic Leadership Behavior because its square root of AVE is lower than its correlation with Ethical Leadership Behavior. Removing low-loading indicators improves AVE but does not fully resolve the issue, because Authentic and Ethical leadership are treated as subdimensions of a higher-order construct (servant leadership), so merging them is recommended.
What does discriminant validity mean in practice, and why does it matter after convergent validity is already checked?
How does the Fornell and Larcker criterion operationalize discriminant validity?
What exact quantities are needed in AMOS to run the Fornell–Larcker check?
What was the discriminant validity failure in the example model?
Why didn’t deleting low-loading indicators fully solve the discriminant validity issue?
What modeling change is recommended when discriminant validity problems reflect theory, not measurement noise?
Review Questions
- In a Fornell–Larcker table, what specific comparison must hold for each construct to demonstrate discriminant validity?
- If discriminant validity fails, what is the first troubleshooting step mentioned here, and what statistical target does it improve?
- When should item deletion be considered insufficient, and what alternative model adjustment is suggested in this transcript?
Key Points
- 1
Discriminant validity assesses whether constructs meant to be distinct are not highly correlated with each other.
- 2
Fornell and Larcker require the square root of each construct’s AVE to be greater than that construct’s correlations with all other latent constructs.
- 3
In AMOS, discriminant validity checks rely on AVE values and the latent construct correlation matrix from Estimates → Scales and Correlations.
- 4
Low indicator loadings (well below 0.70, even below 0.60 in the transcript) can be removed to raise AVE and improve the Fornell–Larcker comparisons.
- 5
If discriminant validity problems persist due to conceptual nesting (e.g., subdimensions of a higher-order construct), merging constructs into a higher-order model is the recommended fix.
- 6
Authentic Leadership Behavior and Ethical Leadership Behavior were treated as subdimensions of servant leadership, explaining persistent discriminant validity overlap.