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Consistent Partial Least Squares for Nonlinear Structural Equation Models

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  • Theo Dijkstra
  • Karin Schermelleh-Engel

Abstract

Partial Least Squares as applied to models with latent variables, measured indirectly by indicators, is well-known to be inconsistent. The linear compounds of indicators that PLS substitutes for the latent variables do not obey the equations that the latter satisfy. We propose simple, non-iterative corrections leading to consistent and asymptotically normal (CAN)-estimators for the loadings and for the correlations between the latent variables. Moreover, we show how to obtain CAN-estimators for the parameters of structural recursive systems of equations, containing linear and interaction terms, without the need to specify a particular joint distribution. If quadratic and higher order terms are included, the approach will produce CAN-estimators as well when predictor variables and error terms are jointly normal. We compare the adjusted PLS, denoted by PLSc, with Latent Moderated Structural Equations (LMS), using Monte Carlo studies and an empirical application. Copyright The Psychometric Society 2014

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  • Theo Dijkstra & Karin Schermelleh-Engel, 2014. "Consistent Partial Least Squares for Nonlinear Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 585-604, October.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:4:p:585-604
    DOI: 10.1007/s11336-013-9370-0
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    References listed on IDEAS

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    1. Kan, Raymond, 2008. "From moments of sum to moments of product," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 542-554, March.
    2. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    3. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    4. Andreas Klein & Helfried Moosbrugger, 2000. "Maximum likelihood estimation of latent interaction effects with the LMS method," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 457-474, December.
    5. Lu, Irene R.R. & Kwan, Ernest & Thomas, D. Roland & Cedzynski, Marzena, 2011. "Two new methods for estimating structural equation models: An illustration and a comparison with two established methods," International Journal of Research in Marketing, Elsevier, vol. 28(3), pages 258-268.
    6. Kenneth Bollen, 1996. "An alternative two stage least squares (2SLS) estimator for latent variable equations," Psychometrika, Springer;The Psychometric Society, vol. 61(1), pages 109-121, March.
    7. Karin Schermelleh-Engel & Christina Werner & Andreas Klein & Helfried Moosbrugger, 2010. "Nonlinear structural equation modeling: is partial least squares an alternative?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(2), pages 167-184, June.
    8. Wynne W. Chin & Barbara L. Marcolin & Peter R. Newsted, 2003. "A Partial Least Squares Latent Variable Modeling Approach for Measuring Interaction Effects: Results from a Monte Carlo Simulation Study and an Electronic-Mail Emotion/Adoption Study," Information Systems Research, INFORMS, vol. 14(2), pages 189-217, June.
    9. Theo Dijkstra & Jörg Henseler, 2011. "Linear indices in nonlinear structural equation models: best fitting proper indices and other composites," Quality & Quantity: International Journal of Methodology, Springer, vol. 45(6), pages 1505-1518, October.
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    Cited by:

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    4. Ismael Moya-Clemente & Gabriela Ribes-Giner & Odette Pantoja-Díaz, 2020. "Identifying environmental and economic development factors in sustainable entrepreneurship over time by partial least squares (PLS)," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-17, September.
    5. Becker, Jan-Michael & Ismail, Ida Rosnita, 2016. "Accounting for sampling weights in PLS path modeling: Simulations and empirical examples," European Management Journal, Elsevier, vol. 34(6), pages 606-617.
    6. Jörg Henseler, 2018. "Partial least squares path modeling: Quo vadis?," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(1), pages 1-8, January.
    7. Muharman Lubis & Muhammad Azani Hasibuan & Rachmadita Andreswari, 2022. "Satisfaction Measurement in the Blended Learning System of the University: The Literacy Mediated-Discourses (LM-D) Framework," Sustainability, MDPI, vol. 14(19), pages 1-29, October.
    8. Majid Ghasemy, 2022. "Estimating models with independent observed variables based on the PLSe2 methodology: a Monte Carlo simulation study," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(6), pages 4129-4159, December.
    9. Fengju Xu & Taslima Akther, 2019. "A Partial Least-Squares Structural Equation Modeling Approach to Investigate the Audit Expectation Gap and Its Impact on Investor Confidence: Perspectives from a Developing Country," Sustainability, MDPI, vol. 11(20), pages 1-21, October.
    10. Éva Berde & Emese Kovács & Muyassar Kurbanova, 2023. "The two‐sided paradox of ageism during the COVID‐19 pandemic: The cases of Hungary, Tunisia and Uzbekistan," Regional Science Policy & Practice, Wiley Blackwell, vol. 15(3), pages 606-625, April.

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