# Discriminant Validity Assessment and Heterotrait-monotrait Ratio of Correlations (HTMT)

## Abstract

The purpose of the discriminant validity assessment is to verify that a reflective construct exhibits stronger relationships with its own indicators than with those of any other construct in the PLS path model (Hair et al., 2022).

## Brief Description

Discriminant validity assessment has become a generally accepted prerequisite for analyzing relationships between reflectively measured constructs. In the context of variance-based structural equation modeling, such as partial least squares structural equation modeling (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- the analysis of cross-loadings are considered outdated methods for assessing discriminant validity.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 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 reflectively measured constructs.

**HTMT bootstrapping:**If you like to obtain the HTMT_Inference results, you need to run the bootstrapping procedure. After choosing the -> 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", you should use the option one-tailed. Thereby, you can test in accordance with Franke & Sarstedt (2019) if 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. Verify if the upper bound of "Confidence intervals bias corrected" is below the critical HTMT value.

**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 and 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. For further details on this version (i.e., HTMT+) see the Appendix of the OPEN ACCESS article by Ringle et al. (2023).

## Literature

- Hair, J. F., Hult, G. T. M., Ringle, C. M., and Sarstedt, M. (2022).
**A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM).**, 3rd Ed., Thousand Oakes, CA: 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., 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. - Ringle, C.M., Sarstedt, M., Sinkovics, N., and Sinkovics, R.R. (2023).
**A Perspective on Using Partial Least Squares Structural Equation Modelling in Data Articles**,*Data in Brief*, 48: 109074. - More literature ...