Abstract
Confirmatory tetrad analysis in PLSSEM (CTAPLS; Gudergan et al., 2008; Hair et al., 2024) allows distinguishing between formative and reflective measurement models. In principal, the analysis follows Bollen and Ting’s (2000) confirmatory approach of testing modelimplied vanishing tetrads in the PLSSEM context.
Description
The use of confirmatory tetrad analysis in PLSSEM (CTAPLS; Gudergan et al., 2008, Hair et al., 2024) allows distinguishing between formative and reflective measurement models. In principal, the analysis follows Bollen and Ting’s (2000) confirmatory approach of testing modelimplied vanishing tetrads in the PLSSEM context with the difference that a bootstrapping procedure is applied to test the significance of the modelimplied tetrads.
Gudergan et al. (2008) and Hair et al. (2024) describe the CTAPLS procedure in detail.
The implemented procedure needs at least 4 manifest variables per construct and can handle a maximum of 25 manifest variables per construct because of the exponentially increasing number of tests if a tetrad is redundant or not.
CTAPLS Settings in SmartPLS
Subsamples
In bootstrapping, subsamples are created with observations randomly drawn from the original set of data (with replacement). To ensure stability of results, the number of subsamples should be large.
For an initial assessment, one may wish to choose a smaller number of bootstrap subsamples (e.g., 500) to be randomly drawn and estimated with the PLSSEM algorithm, since that requires less time. For the final results preparation, however, one should use a large number of bootstrap subsamples (e.g., 19,000).
Note: Larger numbers of bootstrap subsamples increase the computation time.
Do Parallel Processing
This option runs the bootstrapping routine on multiple processors (if your computer device offers more than one core). Using parallel computing will reduce computation time.
Important: The number of processes should not be higher than the number of processors in your computer.
Test Type
Specifies if a onesided or twosided significance test is conducted.
Significance Level
Specifies the significance level of the test statistic.
References

Bollen, K. A., and Ting, K.f. (2000). A Tetrad Test for Causal Indicators, Psychological Methods, 5(1): 322.

Gudergan, S. P., Ringle, C. M., Wende, S., and Will, A. (2008). Confirmatory Tetrad Analysis in PLS Path Modeling, Journal of Business Research, 61(12): 12381249.

Hair, J. F., Sarstedt, M., Ringle, C. M., & Gudergan, S. P. (2024). Advanced Issues in Partial Least Squares Structural Equation Modeling (PLSSEM), 2nd Ed., Thousand Oaks, CA: Sage.
Please always cite the use of SmartPLS!
Ringle, Christian M., Wende, Sven, & Becker, JanMichael. (2024). SmartPLS 4. Bönningstedt: SmartPLS. Retrieved from https://www.smartpls.com