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

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.