Skip to main content
SpringerLink
Log in

Estimation of generalized structured component analysis models with alternating least squares

  • Original Paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

Abstract

This paper presents a new algorithm estimating structural equation models by using the generalized structured component analysis (GSCA) formulation. In GSCA models, the latent variables are composites. The weights are estimated in conjunction with the other model parameters, optimizing a genuine least squares criterion. The new algorithm is designed for three subclasses often used in applications. Linear regressions are alternated for different sets of parameters according to the nonlinear manner in which the parameters are incorporated in the model. The new algorithm is compared with two existing ones by using different examples from the literature, as well as simulations. On the average the proposed algorithm produces better criterion values compared to the other two ones.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Bayol M-P, de la Foye A, Tellier C, Tenenhaus M (2000) Use of PLS path modelling to estimate the European Consumer Satisfaction Index (ECSI) model. Stat Appl 12(3):361–375

    Google Scholar 

  • Becker J-M, Rai A, Rigdon E (2013) Predictive validity and formative measurement in structural equation modeling: embracing practical relevance. In: Proceedings of the international conference on information systems (ICIS). URL http://scholarworks.gsu.edu/cgi/viewcontent.cgi?article=1000&context=marketing_facpub. Accessed 15 June 2016

  • Bergami M, Bagozzi RP (2000) Self-categorization, affective commitment and group self-esteem as distinct aspects of social identity in the organization. Br J Soc Psychol 39:555–577

    Article  Google Scholar 

  • Gefen D, Rigdon EE, Straub D (2011) An update and extension to SEM guidelines for administrative and social science research. MIS Q 35:2:iii+A7

    Google Scholar 

  • Gudergan SP, Ringle CM, Wende S, Will A (2008) Confirmatory tetrad analysis in PLS path modeling. J Bus Res 61:1238–1249

    Article  Google Scholar 

  • Henseler J (2010) A comparative study on parameter recovery of three approaches to structural equation modeling: a rejoinder. SSRN eLibrary Manuscript no. 1585305

  • Hoaglin DC, Mosteller F, Tukey JW (1983) Understanding robust and exploratory data analysis. Wiley, Hoboken

    MATH  Google Scholar 

  • Hwang H, Takane Y (2004) Generalized structured component analysis. Psychometrika 69:81–99

    Article  MathSciNet  MATH  Google Scholar 

  • Hwang H (2011) GeSCA. http://www.sem-gesca.org/index.php. Accessed 26 Jan 2016

  • Jöreskog KG, Van Thillo M (1972) LISREL: a general computer program for estimating a linear structural equation system involving multiple indicators of unmeasured variables. Educational Testing Service, Princeton

    Google Scholar 

  • Jöreskog KG, Sörbom D (1979) Advances in factor analysis and structural equation models. Abt Books, Cambridge

    MATH  Google Scholar 

  • Lohmöller J-B (1984) LVPLS—program manual. Zentralarchiv für empirische Sozialforschung, Universität Köln

  • Lohmöller J-B (1989) Latent variables path modeling with partial least squares. Physica, Heidelberg

    Book  MATH  Google Scholar 

  • R Core Team (2015) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/

  • Ringle C M, Götz O, Wetzels M, Wilson B (2009) On the use of formative measurement specifications in structural equation modeling: a Monte Carlo simulation study to compare covariance-based and partial least squares model estimation methodologies. Munich Personal RePEc Archive Paper No. 15390. http://mpra.ub.uni-muenchen.de/15390/. Accessed 1 Apr 2015

  • Rönkkö M (2016) matrixpls: Matrix-based partial least squares estimation. R package version 1.0.1

  • Schlittgen R, Ringle CM, Sarstedt M, Becker J-M (2016) Segmentation of PLS path models by iterative reweighted regressions. J Bus Res 69:4583–4592

    Article  Google Scholar 

  • Tenenhaus M (2008) Component-based structural equation modelling. Total Qual Manag Bus Excell 19(7–8):871–886

    Article  Google Scholar 

  • Wold H (1973) Nonlinear iterative partial least squares (NIPALS) modelling—some current developments. In: Krishnajah PR (ed) Multivariate analysis, vol 3. Academic, New York, pp 383–407

    Google Scholar 

  • Wold H (1982) Models for knowledge. In: Gani J (ed) The making of statisticians. Springer, Berlin, pp 89–212

    Google Scholar 

  • Wright S (1921) Correlation and causation. J Agric Res 20:557–585

    Google Scholar 

  • Wright S (1934) The method of path coefficients. Ann Math Stat 5:161–215

    Article  MATH  Google Scholar 

Download references

Acknowledgements

I would like to express my sincere gratitude to two anonymous referees whose remarks and recommendations helped to improve considerably former versions of the paper.

Author information

Authors and Affiliations

  1. Institute of Statistics and Econometrics, University of Hamburg, Von-Melle-Park 5, 20146, Hamburg, Germany

    Rainer Schlittgen

Authors
  1. Rainer Schlittgen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rainer Schlittgen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Schlittgen, R. Estimation of generalized structured component analysis models with alternating least squares. Comput Stat 33, 527–548 (2018). https://doi.org/10.1007/s00180-017-0723-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-017-0723-5

Keywords

Search

Navigation