A least squares approach to latent variables extraction in formative-reflective models
AbstractIn 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.
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Bibliographic InfoPaper provided by Università degli Studi di Milano-Bicocca, Dipartimento di Statistica in its series Working Papers with number 20120302.
Length: 16 pages
Date of creation: 04 Mar 2012
Date of revision:
path model; formative-reflective model; least squares; reduced rank regression; PLS-PM;
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- 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.
- 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.
- 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.
- Diamantopoulos, Adamantios & Riefler, Petra & Roth, Katharina P., 2008. "Advancing formative measurement models," Journal of Business Research, Elsevier, vol. 61(12), pages 1203-1218, December.
- 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.
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