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On the Relationships among Latent Variables and Residuals in PLS Path Modeling: the Formative-Reflective Scheme


  • Giorgio Vittadini
  • Simona Caterina Minotti
  • Marco Fattore
  • Pietro Giorgio Lovaglio


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.

Suggested Citation

  • Giorgio Vittadini & Simona Caterina Minotti & Marco Fattore & Pietro Giorgio Lovaglio, 2005. "On the Relationships among Latent Variables and Residuals in PLS Path Modeling: the Formative-Reflective Scheme," Working Papers 20061101, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica, revised Oct 2006.
  • Handle: RePEc:mis:wpaper:20061101

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    References listed on IDEAS

    1. 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.
    2. Arnold Wollenberg, 1977. "Redundancy analysis an alternative for canonical correlation analysis," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 207-219, June.
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    Cited by:

    1. Marco Fattore & Matteo Pelagatti & Giorgio Vittadini, 2012. "A least squares approach to latent variables extraction in formative-reflective models," Working Papers 20120302, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica.
    2. repec:eee:csdana:v:120:y:2018:i:c:p:84-97 is not listed on IDEAS

    More about this item


    Latent Variables; Partial Least Squares; PLS Path Modeling; Redundancy Analysis; LISREL Model;

    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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