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Regularized Generalized Structured Component Analysis

Published online by Cambridge University Press:  01 January 2025

Heungsun Hwang
Heungsun Hwang*
Affiliation:
McGill University
*
Requests for reprints should be sent to Heungsun Hwang, Department of Psychology, McGill University, 1205 Dr. Penfield Avenue, Montreal, QC, H3A 1B1, Canada. E-mail: heungsun.hwang@mcgill.ca
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Abstract

Generalized structured component analysis (GSCA) has been proposed as a component-based approach to structural equation modeling. In practice, GSCA may suffer from multi-collinearity, i.e., high correlations among exogenous variables. GSCA has yet no remedy for this problem. Thus, a regularized extension of GSCA is proposed that integrates a ridge type of regularization into GSCA in a unified framework, thereby enabling to handle multi-collinearity problems effectively. An alternating regularized least squares algorithm is developed for parameter estimation. A Monte Carlo simulation study is conducted to investigate the performance of the proposed method as compared to its non-regularized counterpart. An application is also presented to demonstrate the empirical usefulness of the proposed method.

Keywords

generalized structured component analysismulti-collinearityridge-type regularizationalternating regularized least squares

Information

Type
Theory and Methods
Information
Psychometrika , Volume 74 , Issue 3 , September 2009 , pp. 517 - 530
Copyright
Copyright © 2009 The Psychometric Society

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Footnotes

The author wishes to thank Yoshio Takane for his valuable comments on an earlier version of this paper. The author is also grateful for Claes Fornell who generously provided the ACSI data. Finally, the author is indebted to the Editor, Associate Editor, and three anonymous reviewers for their constructive comments that improved the quality and readability of the paper.

References

Belsley, D.A., Kuh, E., Welsch, R.E. (1980). Regression diagnostics: identifying influential data and sources of collinearity, New York: WileyCrossRefGoogle Scholar
Chin, W.W. (1998). Issues and opinion on structural equation modeling. Management Information Systems Quarterly, 22, 7–16CrossRefGoogle 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, 471–503CrossRefGoogle Scholar
Efron, B. (1982). The jackknife, the bootstrap and other resampling plans, Philadelphia: SIAMCrossRefGoogle 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, 7–18CrossRefGoogle Scholar
Grapentine, T. (2000). Path analysis vs. structural equation modeling. Marketing Research, 12, 12–20Google Scholar
Grewal, R., Cote, J.A., Baumgartner, H. (2004). Multicollinearity and measurement error in structural equation models: Implications for theory testing. Marketing Science, 23, 519–529CrossRefGoogle Scholar
Hastie, T., Tibshirani, R., Friedman, J. (2001). The elements of statistical learning: data mining, inference, and prediction, New York: SpringerCrossRefGoogle Scholar
Hoerl, A.F., Kennard, R.W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12, 55–67CrossRefGoogle Scholar
Hwang, H. (2007). VisualGSCA. Available at http://www.psych.mcgill.ca/perpg/fac/hwang/VisualGSCA.html.Google Scholar
Hwang, H., Takane, Y. (2004). Generalized structured component analysis. Psychometrika, 69, 81–99CrossRefGoogle Scholar
Hwang, H., DeSarbo, S.W., Takane, Y. (2007). Fuzzy clusterwise generalized structured component analysis. Psychometrika, 72, 181–198CrossRefGoogle Scholar
Hwang, H., Takane, Y., Malhotra, N.K. (2007). Multilevel generalized structured component analysis. Behaviormetrika, 34, 95–109CrossRefGoogle Scholar
Jagpal, H.S. (1982). Multicollinearity in structural equation models with unobserved variables. Journal of Marketing Research, 19, 431–439CrossRefGoogle Scholar
Jöreskog, K.G., Goldberger, A.S. (1975). Estimation of a model with multiple indicators and multiple causes of a single latent variable. Journal of the American Statistical Association, 10, 631–639Google Scholar
Kaplan, D. (1994). Estimator conditioning diagnostics for covariance structure models. Sociological Methods Research, 23, 200–229CrossRefGoogle Scholar
ten Berge, J.M.F. (1993). Least squares optimization in multivariate analysis, Leiden: DSWOGoogle Scholar
Takane, Y., Hwang, H. (2007). Regularized linear and kernel redundancy analysis. Computational Statistics and Data Analysis, 52, 394–405CrossRefGoogle Scholar
Takane, Y., Hunter, M., & Hwang, H. (2004). An improved method for generalized structured component analysis. Paper presented at the International Meeting of the Psychometric Society, Pacific Grove, California, USA, June 2004.Google Scholar
Temme, D., Kreis, H., & Hildebrandt, L. (2006). PLS path modeling—A software review (SFB 649 discussion paper). Humboldt University, Berlin, Germany.Google Scholar
Tenenhaus, M. (2008). Component-based structural equation modelling. Total Quality Management and Business Excellence, 19, 871–886CrossRefGoogle Scholar
Velicer, W.F., Jackson, D.N. (1990). Component analysis versus common factor analysis: some issues in selecting appropriate procedure. Multivariate Behavioral Research, 25, 1–28CrossRefGoogle ScholarPubMed