Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-12T20:20:24.183Z Has data issue: false hasContentIssue false
  • English
  • Français

Global Least Squares Path Modeling: A Full-Information Alternative to Partial Least Squares Path Modeling

Published online by Cambridge University Press:  01 January 2025

Heungsun HwangOpen the ORCID record for Heungsun Hwang[Opens in a new window] and
Gyeongcheol ChoOpen the ORCID record for Gyeongcheol Cho[Opens in a new window]
Heungsun Hwang*
Affiliation:
McGill University
Gyeongcheol Cho
Affiliation:
McGill University
*
Correspondence should be made to Heungsun Hwang, Department of Psychology, McGill University, 2001 McGill College Avenue, MontrealQC H3A 1G1, Canada. Email: heungsun.hwang@mcgill.ca
Get accessRights & Permissions [Opens in a new window]

Abstract

Partial least squares path modeling has been widely used for component-based structural equation modeling, where constructs are represented by weighted composites or components of observed variables. This approach remains a limited-information method that carries out two separate stages sequentially to estimate parameters (component weights, loadings, and path coefficients), indicating that it has no single optimization criterion for estimating the parameters at once. In general, limited-information methods are known to provide less efficient parameter estimates than full-information ones. To address this enduring issue, we propose a full-information method for partial least squares path modeling, termed global least squares path modeling, where a single least squares criterion is consistently minimized via a simple iterative algorithm to estimate all the parameters simultaneously. We evaluate the relative performance of the proposed method through the analyses of simulated and real data. We also show that from algorithmic perspectives, the proposed method can be seen as a block-wise special case of another full-information method for component-based structural equation modeling—generalized structured component analysis.

Keywords

partial least squares path modelingfull-informationsingle optimization criterionalternating least squaresblock-wise generalized structured component analysiscomponent-based structural equation modelingregularized generalized canonical correlation analysisLohmöller’s algorithmWold’s algorithm

Information

Type
Theory and Methods
Information
Psychometrika , Volume 85 , Issue 4 , December 2020, pp. 947 - 972
Copyright
Copyright © 2020 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

Electronic Supplementary material The online version of this article (https://doi.org/10.1007/s11336-020-09733-2) contains supplementary material, which is available to authorized users.

References

Addinsoft, S. (2009). XLSTAT 2009. Addinsoft. Paris, France: Addinsoft.Google Scholar
Anderson, E. W., & Fornell, C.Foundations of the American customer satisfaction index.Total Quality Management, (2000). 11(7), 869–88210.1080/09544120050135425.CrossRefGoogle Scholar
Anderson, E. W., Fornell, C., & Lehmann, D. R.Customer satisfaction, market share, and profitability: Findings from Sweden.Journal of Marketing, (1994). 58(3), 53–6610.2307/1252310.CrossRefGoogle Scholar
Bollen, K. A., Kirby, J. B., Curran, P. J., Paxton, P. M., & Chen, F.Latent variable models under misspecification two-stage least squares (2SLS) and maximum likelihood (ML) estimators.Sociological Methods and Research, (2007). 36(1), 48–8610.1177/0049124107301947.CrossRefGoogle Scholar
Boyd, S., Boyd, S. P., & Vandenberghe, L. Convex optimization, (2004). Cambridge, England:Cambridge University Press 10.1017/CBO9780511804441.CrossRefGoogle Scholar
Chin, W. W.(1998). The partial least squares approach for structural equation modeling. Marcoulides, G. A. Modern methods for business research,Mahwah, NJ, US:Erlbaum 295–336.Google Scholar
Chin, W. W. (2001). PLS-Graph User’s Guide Version 3.0. Soft Modeling Inc.Google Scholar
Cho, G., & Choi, J. Y.(2020). An empirical comparison of generalized structured component analysis and partial least squares path modeling under variance-based structural equation models. Behaviormetrika, 47(1), 243–272.CrossRefGoogle Scholar
Cho, G., Jung, K., & Hwang, H.(2019). Out-of-bag prediction error?: A cross validation index for generalized structured component analysis. Multivariate Behavioral Research,.CrossRefGoogle ScholarPubMed
Cho, G., Sarstedt, M., & Hwang, H. (2020). A comparative evaluation of factor- and component-based structural equation modeling methods under (in)consistent model specifications. Manuscript Submitted for Publication.Google Scholar
Coolen, H., & de Leeuw, J. (1987). Least squares path analysis with optimal scaling. Paper presented at the fifth international symposium of data analysis and informatics.Google Scholar
de Leeuw, J., Young, F. W., & Takane, Y.(1976). Additive structure in qualitative data: An alternating least squares method with optimal scaling features. Psychometrika, 41(4), 471–503.CrossRefGoogle Scholar
Dijkstra, T. K. (2010). Latent variables and indices: Herman Wold’s basic design and partial least squares. In V. Esposito Vinzi, W. W. Chin, J. Henseler, & H. Wang (Eds.), Handbook of Partial Least Squares: Concepts, Methods and Applications (pp. 23–46). Berlin, Heidelberg: Springer. https://10.1007/978-3-540-32827-8_2.CrossRefGoogle Scholar
Dijkstra, T. K. (2017). A perfect match between a model and a mode. In Partial least squares path modeling: Basic concepts, methodological issues and applications (pp. 55–80). Berlin, Germany: Springer-Verlag. https://10.1007/978-3-319-64069-3_4.CrossRefGoogle Scholar
Dijkstra, T. K., & Henseler, J.(2015). Consistent partial least squares path modeling. MIS Quarterly, 39(2), 297–316.CrossRefGoogle Scholar
Efron, B.(1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7(1), 1–26.CrossRefGoogle Scholar
Fomby, T. B., Johnson, S. R., & Hill, R. C. (2012). Advanced econometric methods. Advanced Econometric Methods. Berlin, Germany: Springer. https://10.1007/978-1-4419-8746-4.CrossRefGoogle Scholar
Fornell, C.(1992). A national customer satisfaction barometer: The Swedish experience. Journal of Marketing, 56(1), 6–21.CrossRefGoogle Scholar
Fornell, C., Johnson, M. D., Anderson, E. W., Cha, J., & Bryant, B. E.(1996). The American customer satisfaction index: Nature, purpose, and findings. Journal of Marketing, 60(4), 7.CrossRefGoogle Scholar
Gifi, A. (1990). Nonlinear multivariate analysis. Retrieved from: Wiley. https://www.wiley.com/en-us/Nonlinear+Multivariate+Analysis-p-9780471926207.Google Scholar
Hair, J. F., Hult, GTM, Ringle, C. M., Sarstedt, M., & Thiele, K. O.(2017). Mirror, mirror on the wall: a comparative evaluation of composite-based structural equation modeling methods. Journal of the Academy of Marketing Science, 45(5), 616–632.CrossRefGoogle Scholar
Hanafi, M.(2007). PLS path modelling: Computation of latent variables with the estimation mode B. Computational Statistics, 22(2), 275–292.CrossRefGoogle Scholar
Hwang, H., Cho, G., Jung, K., Falk, C., Flake, J., Jin, M. J., & Lee, S. H. (in press). An approach to structural equation modeling with both factors and components: Integrated generalized structured component analysis. Psychological Methods.Google Scholar
Hwang, H., & Takane, Y.(2004). Generalized structured component analysis. Psychometrika, 69(1), 81–99.CrossRefGoogle Scholar
Hwang, H., & Takane, Y.(2014). Generalized structured component analysis: A component-based approach to structural equation modeling,New York, NY:Chapman and Hall/CRC Press.CrossRefGoogle Scholar
Hwang, H., Takane, Y., & Jung, K.(2017). Generalized structured component analysis with uniqueness terms for accommodating measurement error. Frontiers in Psychology, 8,21375723672.CrossRefGoogle ScholarPubMed
Hwang, H., Takane, Y., & Tenenhaus, A.(2015). An alterantive estimation procedure for partial least squares path modeling. Behaviormetrika, 42(1), 63–78.CrossRefGoogle Scholar
Johnson, M. D., Gustafsson, A., Andreassen, T. W., Lervik, L., & Cha, J.(2001). The evolution and future of national customer satisfaction index models. Journal of Economic Psychology, 22(2), 217–245.CrossRefGoogle Scholar
Jöreskog, K. G.(1970). Estimation and testing of simplex models. British Journal of Mathematical and Statistical Psychology, 23(2), 121–145.CrossRefGoogle Scholar
Jöreskog, K. G.(1978). Structural analysis of covariance and correlation matrices. Psychometrika, 43(4), 443–477.CrossRefGoogle Scholar
Jöreskog, K. G., Wold, H.(1982). The ML and PLS techniques for modeling with latent variables: Historical and comparative aspects. Wold, H., & Jöreskog, K. G. Systems under indirect observation: Causality, structure, prediction, part I,Amsterdam, Netherlands:North Holland 263–270.Google Scholar
Karatzoglou, A., Smola, A., Hornik, K., & Zeileis, A.(2004). kernlab - An S4 package for kernel methods in R. Journal of Statistical Software, 11(9), 1–20.CrossRefGoogle Scholar
Krämer, N. (2007). Analysis of high dimensional data with partial least squares and boosting. Technische Universität Berlin, Fakultät IV - Elektrotechnik und Informatik: Technische Universität Berlin, Berlin. https://10.14279/depositonce-1539.CrossRefGoogle Scholar
Lohmöller, J. B. (1984). LVPLS Program Manual-Version 1.6. Zentralarchiv fur Empirische Sozialforschung. Koln: Universitat zu Koln.Google Scholar
Lohmö ller, J. B. (1989). Latent variable path modeling with partial least squares. New York, NY: Springer-Verlag. https://10.1007/978-3-642-52512-4.CrossRefGoogle Scholar
McDonald, R. P.(1996). Path analysis with composite variables. Multivariate Behavioral Research, 31(2), 239–270.CrossRefGoogle ScholarPubMed
Noonan, R., Wold, H.(1982). PLS path modeling with indirectly observed variables: A comparison of alternative estimates for the latent variable. Jöreskog, K. G., & Wold, H. Systems under indirect observation: Causality, structure, prediction, part II,Amsterdam, Netherlands:North Holland 75–94.Google Scholar
Rigdon, E. E.(2012). Rethinking partial least squares path modeling: In praise of simple methods. Long Range Planning, 45(5–6), 341–358.CrossRefGoogle Scholar
Rigdon, E. E., Sarstedt, M., & Ringle, C. M.(2017). On comparing results from CB-SEM and PLS-SEM: Five perspectives and five recommendations. Marketing ZFP, 39(3), 4–16.CrossRefGoogle Scholar
Ringle, C. M., Wende, S., & Will, A. (2005). SmartPLS 2.0 (beta). Hamburg, Germany: SmartPLS. Retrieved from http://www.smartpls.com.Google Scholar
Rönkkö, M., McIntosh, C. N., Antonakis, J., & Edwards, J. R.(2016). Partial least squares path modeling: Time for some serious second thoughts. Journal of Operations Management, 47–48,9–27.CrossRefGoogle Scholar
Sarstedt, M., Hair, J. F., Ringle, C. M., Thiele, K. O., & Gudergan, S. P.(2016). Estimation issues with PLS and CBSEM: Where the bias lies!. Journal of Business Research, 69(10), 3998–4010.CrossRefGoogle Scholar
ten Berge, JMF(1993). Least squares optimization in multivariate analysis,Leiden, Netherlands:DSWO Press.Google Scholar
Tenenhaus, A., Guillemot, V.(2017). RGCCA: Regularized and sparse generalized canonical correlation analysis for multiblock data. R Package Version, 2(1), 2.Google Scholar
Tenenhaus, A., & Tenenhaus, M.(2011). Regularized generalized canonical correlation analysis. Psychometrika, 76(2), 257.CrossRefGoogle Scholar
Tenenhaus, M.(2008). Component-based structural equation modelling. Total Quality Management and Business Excellence, 19(7–8), 871–886.CrossRefGoogle Scholar
Tenenhaus, M., Tenenhaus, A., & Groenen, PJF(2017). Regularized generalized canonical correlation analysis: A framework for sequential multiblock component methods. Psychometrika, 82(3), 737–777.CrossRefGoogle ScholarPubMed
Vinzi, V. E., Trinchera, L., & Amato, S. (2010). PLS path modeling: From foundations to recent developments and open issues for model assessment and improvement. In V. Esposito Vinzi, W. W. Chin, J. Henseler, & H. Wang (Eds.), Handbook of Partial Least Squares: Concepts, Methods and Applications (pp. 47–82). Berlin, Heidelberg: Springer. https://10.1007/978-3-540-32827-8_3.CrossRefGoogle Scholar
Wold, H.(1966). Estimation of principal components and related models by iterative least squares. Krishnajah, P. R. Multivariate analysis,NewYork, NY:Academic Press 391–420.Google Scholar
Wold, H.(1973). Nonlinear iterative partial least squares (NIPALS) Modelling: Some current developments. Krishnaiah, P. R. Multivariate analysis-III,New York, NY:Academic Press 383–407.CrossRefGoogle Scholar
Wold, H.(1982). Soft modeling: The basic design and some extensions. Jöreskog, K. G., & Wold, H. Systems under indirect observation: Causality, structure, prediction, part II,Amsterdam, Netherlands:North Holland 1–54.Google Scholar
Wold, H.(1985). Partial least squares. Kotz, S., & Johnson, N. L. Encyclopedia of Statistical Sciences,New York, NY:Wiley 581–591.Google Scholar
Supplementary material: File

Hwang and Cho supplementary material

Hwang and Cho supplementary material
Download Hwang and Cho supplementary material(File)
File 875.4 KB