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On the relationships among latent variables and residuals in PLS path modeling: The formative-reflective scheme


  • Vittadini, Giorgio
  • Minotti, Simona C.
  • Fattore, Marco
  • Lovaglio, Pietro G.


A new approach for the estimation and the validation of a Structural Equation Model with a formative-reflective scheme is presented. The basis of the paper is a proposal for overcoming a potential deficiency of PLS Path Modeling. In the PLS approach the reflective scheme assumed for the endogenous latent variables is inverted; moreover, the model errors are not explicitly taken into account for the estimation of the endogenous latent variables. The proposed approach utilizes all the relevant information in the formative manifest variables providing solutions which respect the causal structure of the model. The estimation procedure is based on the optimization of the redundancy criterion. The new approach, entitled Redundancy Analysis approach to Path Modeling is compared with both traditional PLS Path Modeling and LISREL methodology, on the basis of real and simulated data.
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Suggested Citation

  • Vittadini, Giorgio & Minotti, Simona C. & Fattore, Marco & Lovaglio, Pietro G., 2007. "On the relationships among latent variables and residuals in PLS path modeling: The formative-reflective scheme," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5828-5846, August.
  • Handle: RePEc:eee:csdana:v:51:y:2007:i:12:p:5828-5846

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    References listed on IDEAS

    1. Arnold Wollenberg, 1977. "Redundancy analysis an alternative for canonical correlation analysis," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 207-219, June.
    2. Tenenhaus, Michel & Vinzi, Vincenzo Esposito & Chatelin, Yves-Marie & Lauro, Carlo, 2005. "PLS path modeling," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 159-205, January.
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    Cited by:

    1. Pasquale Dolce & Vincenzo Esposito Vinzi & Natale Carlo Lauro, 2018. "Non-symmetrical composite-based path modeling," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 759-784, September.
    2. Fattore, Marco & Pelagatti, Matteo & Vittadini, Giorgio, 2018. "A least squares approach to latent variables extraction in formative–reflective models," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 84-97.
    3. Ned Kock, 2015. "PLS-based SEM Algorithms: The Good Neighbor Assumption, Collinearity, and Nonlinearity," Information Management and Business Review, AMH International, vol. 7(2), pages 113-130.

    More about this item

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity


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