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A least squares approach to latent variables extraction in formative-reflective models

Author

Listed:
  • Marco Fattore

    () (Dipartimento di Metodi Quantitativi per l'Economia e le Scienze Aziendali, Università degli Studi di Milano-Bicocca)

  • Matteo Pelagatti

    () (Dipartimento di Statistica, Università degli Studi di Milano-Bicocca)

  • Giorgio Vittadini

    () (Dipartimento di Metodi Quantitativi per l'Economia e le Scienze Aziendali, Università degli Studi di Milano-Bicocca)

Abstract

In this paper, we propose a new least-squares based procedure to extract exogenous and endogenous latent variables in formative-reflective structural equation models. The procedure is a valuable alternative to PLS-PM and Lisrel; it is fully consistent with the causal structure of formative-reflective schemes and extracts both the structural parameters and the factor scores, without identification or indeterminacy problems. The algorithm can be applied to virtually any kind of formative-reflective scheme, with unidimensional and even multidimensional formative blocks. To show the effectiveness of the proposal, some simulated examples are discussed. A real data application, pertaining to customer equity management, is also provided, comparing the outputs of our approach with those of PLS-PM, which may produce inconsistent results when applied to formative-reflective schemes.

Suggested Citation

  • 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.
  • Handle: RePEc:mis:wpaper:20120302
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    References listed on IDEAS

    as
    1. Wilcox, James B. & Howell, Roy D. & Breivik, Einar, 2008. "Questions about formative measurement," Journal of Business Research, Elsevier, vol. 61(12), pages 1219-1228, December.
    2. Diamantopoulos, Adamantios & Riefler, Petra & Roth, Katharina P., 2008. "Advancing formative measurement models," Journal of Business Research, Elsevier, vol. 61(12), pages 1203-1218, December.
    3. 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.
    4. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    5. Ruiz, David Martín & Gremler, Dwayne D. & Washburn, Judith H. & Carrión, Gabriel Cepeda, 2008. "Service value revisited: Specifying a higher-order, formative measure," Journal of Business Research, Elsevier, vol. 61(12), pages 1278-1291, December.
    6. Bruhn, Manfred & Georgi, Dominik & Hadwich, Karsten, 2008. "Customer equity management as formative second-order construct," Journal of Business Research, Elsevier, vol. 61(12), pages 1292-1301, December.
    7. Heungsun Hwang & Yoshio Takane, 2004. "Generalized structured component analysis," Psychometrika, Springer;The Psychometric Society, vol. 69(1), pages 81-99, March.
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    More about this item

    Keywords

    path model; formative-reflective model; least squares; reduced rank regression; PLS-PM;

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