Discriminant Validity Assessment and Heterotrait-monotrait Ratio of Correlations (HTMT)
Discriminant validity assessment verifies that a reflectively measured construct is empirically distinct from the other constructs in a PLS path model — that is, that it exhibits stronger relationships with its own indicators than with those of any other construct (Hair et al., 2022). It has become a generally accepted prerequisite for analyzing relationships between reflectively measured constructs in variance-based structural equation modeling, such as PLS-SEM.
Why the HTMT Criterion Replaced Older Approaches
In the context of PLS-SEM, the Fornell-Larcker criterion and the analysis of cross-loadings are considered outdated methods for assessing discriminant validity. Henseler, Ringle and Sarstedt (2015) demonstrated through a simulation study that these approaches do not reliably detect the lack of discriminant validity in common research situations. These authors therefore propose an alternative approach, based on the multitrait-multimethod matrix, to assess discriminant validity: the heterotrait-monotrait ratio of correlations (HTMT). Henseler, Ringle and Sarstedt (2015) substantiate this approach’s superior performance by means of a Monte Carlo simulation study, in which they compare the new approach to the Fornell-Larcker criterion and the assessment of (partial) cross-loadings. Finally, they provide guidelines on how to handle discriminant validity issues in variance-based structural equation modeling.
Henseler, Ringle and Sarstedt (2015) provide detailed explanations of the HTMT criterion for discriminant validity assessment in variance-based structural equations modeling. Also see the Appendix of the open-access article by Ringle et al. (2023) for some HTMT improvements, such as HTMT+.
Discriminant Validity Assessment in SmartPLS
When running the PLS and PLSc algorithm in SmartPLS, the results report includes discriminant validity assessment outcomes in the "Quality Criteria" section:
- the Fornell-Larcker criterion,
- cross-loadings, and
- the HTMT criterion results.
We recommend using the HTMT criterion to assess discriminant validity. If the HTMT value is below 0.90, discriminant validity has been established between two reflectively measured constructs.
HTMT Bootstrapping
If you want to obtain the HTMT_Inference results, you need to run the bootstrapping procedure. After choosing Calculate -> Bootstrapping in SmartPLS, the start dialog opens. It is important that you select "Complete (slower)" under the "Amount of results" option in the bootstrapping start dialog. Under "Test type", use the option one-tailed. This lets you test, in accordance with Franke & Sarstedt (2019), whether the HTMT value is significantly below the critical value of 0.9 to establish discriminant validity. In the bootstrapping results report, locate the bootstrapped HTMT criterion results in the "Quality Criteria" section, and verify whether the upper bound of "Confidence intervals bias corrected" is below the critical HTMT value.
HTMT Computation in SmartPLS (HTMT+)
In SmartPLS 3.2.1 and later versions, the HTMT criterion computation differs from the equation given by Henseler, Ringle and Sarstedt (2015). Instead of using the correlations between indicators directly, SmartPLS uses the absolute value of the correlation between indicators. For example, using 0.1, 0.2, and -0.3 results in an average correlation of 0 and causes problems in the original HTMT equation; using their absolute values (0.1, 0.2, and 0.3) instead results in an average correlation of 0.2. As a consequence, the HTMT criterion is normed between 0 and 1 in SmartPLS, and no issues result from negative correlations. For further details on this version (i.e., HTMT+), see the Appendix of the open-access article by Ringle et al. (2023).
Frequently Asked Questions
What is discriminant validity in PLS-SEM?
Discriminant validity means that a reflectively measured construct is empirically distinct from the other constructs in the model. It is established when a construct exhibits stronger relationships with its own indicators than with the indicators of any other construct.
Why shouldn't I use the Fornell-Larcker criterion or cross-loadings anymore?
Henseler, Ringle and Sarstedt (2015) showed, via a Monte Carlo simulation, that the Fornell-Larcker criterion and the analysis of cross-loadings do not reliably detect a lack of discriminant validity in common research situations. The HTMT criterion performs substantially better and is therefore recommended instead.
What HTMT value indicates discriminant validity?
If the HTMT value is below 0.90, discriminant validity has been established between two reflectively measured constructs. See also the SmartPLS threshold overview for the full green/black/red cut-off ranges used in SmartPLS reports.
How do I test whether HTMT is significantly below the threshold?
Run the bootstrapping procedure with "Complete (slower)" selected under "Amount of results" and "one-tailed" selected under "Test type". Then check, in accordance with Franke & Sarstedt (2019), whether the upper bound of the bias-corrected confidence interval for HTMT is below the critical value of 0.9.
How does SmartPLS's HTMT computation differ from the original formula?
Since SmartPLS 3.2.1, SmartPLS uses the absolute values of indicator correlations rather than their raw values (HTMT+). This norms the HTMT criterion between 0 and 1 and avoids the problems that negative correlations can cause in the original HTMT equation of Henseler, Ringle and Sarstedt (2015).
Related SmartPLS Methods
- Result color thresholds in SmartPLS reports
- Confirmatory composite analysis (CCA)
- Confirmatory tetrad analysis in PLS (CTA-PLS)
- Bootstrapping
- PLS-SEM algorithm
References
- Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2027). A primer on partial least squares structural equation modeling (PLS-SEM) (4th ed.). Sage.
- Franke, G. R., & Sarstedt, M. (2019). Heuristics versus statistics in discriminant validity testing: A comparison of four procedures. Internet Research, 29(3), 430–447.
- Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity in variance-based structural equation modeling. Journal of the Academy of Marketing Science, 43(1), 115–135.
- Ringle, C. M., Sarstedt, M., Sinkovics, N., & Sinkovics, R. R. (2023). A perspective on using partial least squares structural equation modelling in data articles. Data in Brief, 48, Article 109074.
- More literature ...
Cite correctly
Please always cite the use of SmartPLS!
Ringle, Christian M., Wende, Sven, & Becker, Jan-Michael. (2024). SmartPLS 4. Bönningstedt: SmartPLS. Retrieved from https://www.smartpls.com
