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References

Scientific foundations

Every metric, every threshold and every method in OpenPLS can be traced back to a specific publication. Here are the most important ones.

Textbooks & primers

Standard works for PLS-SEM methodology and application.

  1. 2022
    Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M.
    A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)
    3rd edition, Sage Publications, Thousand Oaks, CA
    The de-facto standard for PLS-SEM practice. Source for the thresholds OpenPLS reports.
  2. 2024
    Hair, J. F., Sarstedt, M., Ringle, C. M., & Gudergan, S. P.
    Advanced Issues in Partial Least Squares Structural Equation Modeling
    2nd edition, Sage Publications
    Advanced topics: PLSpredict, FIMIX segmentation, moderation, IPMA — the roadmap for the OpenPLS engine.
  3. 2021
    Henseler, J.
    Composite-Based Structural Equation Modeling: Analyzing Latent and Emergent Variables
    Guilford Press, New York
    Methodological basis for formative (Mode B) constructs and composite-based SEM.

Algorithmic foundations

The original publications behind the PLS algorithm and its variations.

  1. 1982
    Wold, H.
    Soft modeling: The basic design and some extensions
    In K. G. Jöreskog & H. Wold (Eds.), Systems under Indirect Observation, Part II (pp. 1–54). North-Holland
    Herman Wold’s original formulation of the PLS path algorithm.
  2. 1989
    Lohmöller, J.-B.
    Latent Variable Path Modeling with Partial Least Squares
    Physica-Verlag, Heidelberg
    Complete formal treatment. Source for the PCA and centroid inner-weighting schemes.
  3. 2010
    Esposito Vinzi, V., Chin, W. W., Henseler, J., & Wang, H. (Eds.)
    Handbook of Partial Least Squares: Concepts, Methods and Applications
    Springer, Berlin
    Methodological compendium covering the entire PLS family.

Quality criteria & model assessment

Thresholds and validity criteria OpenPLS reports automatically.

  1. 2015
    Henseler, J., Ringle, C. M., & Sarstedt, M.
    A new criterion for assessing discriminant validity in variance-based structural equation modeling
    Journal of the Academy of Marketing Science, 43(1), 115–135
    Introduction of the heterotrait-monotrait ratio (HTMT). The 0.85 / 0.90 thresholds in OpenPLS reports come from this paper.
  2. 2005
    Tenenhaus, M., Vinzi, V. E., Chatelin, Y.-M., & Lauro, C.
    PLS path modeling
    Computational Statistics & Data Analysis, 48(1), 159–205
    Definition of the Goodness-of-Fit (GoF) index for PLS-SEM, which OpenPLS reports for every model.
  3. 2013
    Henseler, J., & Sarstedt, M.
    Goodness-of-fit indices for partial least squares path modeling
    Computational Statistics, 28(2), 565–580
    Critical discussion of the GoF and contribution to alternative fit indices (SRMR, d_ULS).
  4. 2015
    Dijkstra, T. K., & Henseler, J.
    Consistent partial least squares path modeling
    MIS Quarterly, 39(2), 297–316
    Basis for DG-ρ (rho_A) as a consistent reliability estimate.
  5. 2019
    Hair, J. F., Risher, J. J., Sarstedt, M., & Ringle, C. M.
    When to use and how to report the results of PLS-SEM
    European Business Review, 31(1), 2–24
    Reporting recommendations — defines the structure of the OpenPLS PDF reports.

Extensions & specialised techniques

Bootstrap, multi-group analysis, formative models, predictive assessment.

  1. 2016
    Streukens, S., & Leroi-Werelds, S.
    Bootstrapping and PLS-SEM: A step-by-step guide to get more out of your bootstrap results
    European Management Journal, 34(6), 618–632
    Thresholds and recommendations for bootstrap iterations — the OpenPLS default of 5,000 matches this standard.
  2. 2016
    Henseler, J., Ringle, C. M., & Sarstedt, M.
    Testing measurement invariance of composites using partial least squares (MICOM)
    International Marketing Review, 33(3), 405–431
    Foundation for multi-group analysis (MGA) in OpenPLS.
  3. 2016
    Shmueli, G., Ray, S., Velasquez Estrada, J. M., & Chatla, S. B.
    The elephant in the room: Predictive performance of PLS models
    Journal of Business Research, 69(10), 4552–4564
    PLSpredict — on the OpenPLS engine roadmap.
  4. 2001
    Diamantopoulos, A., & Winklhofer, H. M.
    Index construction with formative indicators: An alternative to scale development
    Journal of Marketing Research, 38(2), 269–277
    Construction guide for formative (Mode B) constructs.

Classic application models

Models available as sample cases in OpenPLS.

  1. 1989
    Davis, F. D.
    Perceived usefulness, perceived ease of use, and user acceptance of information technology
    MIS Quarterly, 13(3), 319–340
    Technology Acceptance Model (TAM) — sample case in OpenPLS.
  2. 2003
    Venkatesh, V., Morris, M. G., Davis, G. B., & Davis, F. D.
    User acceptance of information technology: Toward a unified view
    MIS Quarterly, 27(3), 425–478
    UTAUT — sample-case template for acceptance research.
  3. 1996
    Fornell, C., Johnson, M. D., Anderson, E. W., Cha, J., & Bryant, B. E.
    The American Customer Satisfaction Index: Nature, purpose, and findings
    Journal of Marketing, 60(4), 7–18
    ACSI model — integrated as an example for customer-satisfaction PLS models.

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