Convergence of the error in Hanafi-Wold's procedure on the PLS-PM task

Authors

  • Abderrahim Sahli Mathematics, Statistics, and Applications Laboratory, Faculty of sciences, Mohammed V University in Rabat, Morocco
  • Zouhair El Hadri Mathematics, Statistics, and Applications Laboratory, Faculty of sciences, Mohammed V University in Rabat, Morocco
  • Mohamed Hanafi Research unit in Statistics, Sensometrics and Chemometrics, Oniris VetAgroBio, Nantes, France

DOI:

https://doi.org/10.19139/soic-2310-5070-2223

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.

Downloads

Published

2025-05-17

Issue

Vol. 14 No. 2 (2025)

Section

Research Articles

License

Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
    2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
    3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).

How to Cite

Convergence of the error in Hanafi-Wold’s procedure on the PLS-PM task. (2025). Statistics, Optimization & Information Computing, 14(2), 469-485. https://doi.org/10.19139/soic-2310-5070-2223