Convergence of the error in Hanafi-Wold's procedure on the PLS-PM task
Keywords:
Partial Least Squares Path Modelling, Hanafi-Wold’s procedure, SLM’s procedure, Lohmöller’s procedure
Abstract
Partial least squares path modeling is a statistical method that facilitates examining intricate dependence relationships among various blocks of observed variables, each characterized by a latent variable. The computation of latent variable scores is a pivotal step in this method and it is accomplished through an iterative procedure. Within this paper, we investigate and tackle convergence challenges related to Hanafi-Wold's procedure in computing components for the PLS-PM algorithm. Hanafi-Wold's procedure, as well as alternative procedure, demonstrate the property of monotone convergence when mode B is considered for all blocks combined with centroid or factorial schemes. However, the absence of proof regarding the convergence of the error towards zero in Hanafi-Wold's procedure is a limitation compared to alternative procedure, which possesses this convergence property. Therefore, this paper aims to establish the convergence of the error towards zero in Hanafi-Wold’s procedure.References
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squares path modeling, Computational Statistics, vol. 36, pp. 603–614, 2021. https://doi.org/10.1007/s00180-
020-01015-w
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Computational Statistics, vol. 37, no. 5, pp. 2437–2470, 2022. https://doi.org/10.1007/s00180-022-01204-9
[5] J. Henseler, On the convergence of the partial least squares path modeling algorithm, Computational
Statistics, vol. 25, no. 1, pp. 107–120, 2010. https://doi.org/10.1007/s00180-009-0164-x
[6] K. G. Jöreskog, A general method for the analysis of covariance structure, Biometrika, vol. 57, pp. 239–251,
1970.
[7] H. Latan, J. F. Hair Jr, R. Noonan, and M. Sabol, Introduction to the partial least squares path modeling:
Basic concepts and recent methodological enhancements, in Partial Least Squares Path Modeling: Basic
Concepts, Methodological Issues and Applications, Springer, 2023, pp. 3–21.
[8] S. Petter, and Y. Hadavi, Use of partial least squares path modeling within and across business disciplines,
in Partial Least Squares Path Modeling: Basic Concepts, Methodological Issues and Applications, Springer,
2023, pp. 55–79.
[9] S. Venturini, M. Mehmetoglu, and H. Latan, Software packages for partial least squares structural equation
modeling: An updated review, in Partial Least Squares Path Modeling: Basic Concepts, Methodological
Issues and Applications, Springer, 2023, pp. 113–152.
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2, K. G. Jöreskog and H. Wold (Eds.), North Holland, Amsterdam, pp. 1–54, 1982.
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(Eds.), John Wiley Sons, New York, pp. 581–591, 198
Published
2025-05-17
How to Cite
Sahli, A., Zouhair El Hadri, & Mohamed Hanafi. (2025). Convergence of the error in Hanafi-Wold’s procedure on the PLS-PM task. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2223
Issue
Section
Research Articles
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