Computational Statistics

, Volume 25, Issue 1, pp 107–120 | Cite as

On the convergence of the partial least squares path modeling algorithm

  • Jörg Henseler
Open Access
Original Paper


This paper adds to an important aspect of Partial Least Squares (PLS) path modeling, namely the convergence of the iterative PLS path modeling algorithm. Whilst conventional wisdom says that PLS always converges in practice, there is no formal proof for path models with more than two blocks of manifest variables. This paper presents six cases of non-convergence of the PLS path modeling algorithm. These cases were estimated using Mode A combined with the factorial scheme or the path weighting scheme, which are two popular options of the algorithm. As a conclusion, efforts to come to a proof of convergence under these schemes can be abandoned, and users of PLS should triangulate their estimation results.


Partial least squares path modeling PLS Convergence 

Mathematics Subject Classification (2000)

62J99 Linear inference, regression 91B82 Statistical methods; economic indices and measures 91E45 Measurement and performance 



The author thanks Christian M. Ringle and Vincenzo Esposito Vinzi for doublechecking the findings by means of experimental versions of their respective PLS path modeling software implementations, SmartPLS and XLSTAT-PLSPM. This paper was initially presented at the 5th International Symposium on Partial Least Squares and Related Methods, Ås, Norway, 5–7 September 2007.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Supplementary material

180_2009_164_MOESM1_ESM.xls (55 kb)
ESM 1 (XLS 55 kb)


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Institute for Management ResearchRadboud University NijmegenNijmegenThe Netherlands

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