Discriminant Validity Assessment and Heterotrait-monotrait Ratio of Correlations (HTMT)
The discriminant validity assessment has the goal to ensure that a reflective construct has the strongest relationships with its own indicators (e.g., in comparison with than any other construct) in the PLS path model (Hair et al., 2017).
Discriminant validity assessment has become a generally accepted prerequisite for analyzing relationships between latent variables. For variance-based structural equation modeling, such as partial least squares,
- the Fornell-Larcker criterion and
- the examination of cross-loadings are the dominant approaches for evaluating discriminant validity.
Henseler, Ringle and Sarstedt (2015) show by means of 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) demonstrate 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.
See Henseler, Ringle and Sarstedt (2015) for detailed explanations of the HTMT criterion for discriminant validity assessment in variance-based structural equations modeling.
Discriminant Validity Assessment in SmartPLS
When running the PLS and PLSc algorithm in SmartPLS, the results report includes discriminant validity assessment outcomes, in the section “Quality Criteria”. The following results are provided:
- 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 reflective constructs.
If you like to obtain the HTMT_Inference results, you need to run the bootstrapping routine. When starting the bootstrapping routine, it is important that you select the option “Complete Bootstrapping”. Then, in the bootstrapping results report, you find the bootstrapped HTMT criterion results in the section “Quality Criteria”.
Please note: In SmartPLS 3.2.1 and later version, the HTMT criterion computation differs from the equation given by Henseler, Ringle and Sarstedt (2015). Instead of using the correlations between indicators, SmartPLS uses the absolute value of the correlation between indicators. For example, when instead of using 0.1, 0.2 and -0.3, which results in an average correlation of 0 an causes problems in the original HTMT equation, SmartPLS uses 0.1, 0.2 and 0.3, which results in an average correlation of 0.2. In consequence, the HTMT criterion is normed between 0 and 1 in SmartPLS and no issues result from negative correlations.
- HTMT - A New Criterion to Assess Discriminant Validity
- HTMT - Assessing Discriminant Validity in SmartPLS 3
- Corporate Reputation Model
Hair, J. F., Hult, G. T. M., Ringle, C. M., and Sarstedt, M. (2017). A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)., 2^nd^ Ed., Thousand Oakes, CA: Sage.
- Henseler, J., Ringle, C. M., and 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.