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Generalized Structured Component Analysis

Published online by Cambridge University Press:  01 January 2025

Heungsun Hwang  and
Yoshio Takane
Heungsun Hwang*
Affiliation:
HEC Montreal
Yoshio Takane
Affiliation:
McGill University
*
Requests for reprints should be addressed to: Heungsun Hwang, HEC Montreal, Department of Marketing, 3000 Chemin de la Cole Ste-Calherine, Montreal, Quebec, H3T 2A7, CANADA. Email: heungsun.hwang@hec.ca
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Abstract

We propose an alternative method to partial least squares for path analysis with components, called generalized structured component analysis. The proposed method replaces factors by exact linear combinations of observed variables. It employs a well-defined least squares criterion to estimate model parameters. As a result, the proposed method avoids the principal limitation of partial least squares (i.e., the lack of a global optimization procedure) while fully retaining all the advantages of partial least squares (e.g., less restricted distributional assumptions and no improper solutions). The method is also versatile enough to capture complex relationships among variables, including higher-order components and multi-group comparisons. A straightforward estimation algorithm is developed to minimize the criterion.

Keywords

Path analysis with componentspartial least squaresalternating least squares
Type
Theory And Methods
Information
Psychometrika , Volume 69 , Issue 1 , March 2004 , pp. 81 - 99
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

The work reported in this paper was supported by Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the second author. We wish to thank Richard Bagozzi for permitting us to use his organizational identification data and Wynne Chin for providing PLS-Graph 3.0.

References

Allen, N. J., & Meyer, J. P. (1990). The measurement and antecedents of affective, continuance and normative commitment to the organization. Journal of Occupational Psychology, 63, 1–18CrossRefGoogle Scholar
Beaton, A. E., & Tukey, J. W. (1974). The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data. Technometrics, 16, 147–185CrossRefGoogle Scholar
Bergami, M., & Bagozzi, R. P. (2000). Self-categorization, affective commitment and group self-esteem as distinct aspects of social identity in the organization. British Journal of Social Psychology, 39, 555–577CrossRefGoogle ScholarPubMed
Bock, R. D., & Bargmann, R. E. (1966). Analysis of covariance structures. Psychometrika, 31, 507–534CrossRefGoogle ScholarPubMed
Böckenholt, U., & Takane, Y. (1994). Linear constraints in correspondence analysis. In Greenacre, M. J., & Blasius, J. (Eds.), Correspondence Analysis in Social Sciences (pp. 112–127). London: Academic PressGoogle Scholar
Bollen, K. A. (1989). Structural Equations with Latent Variables. New York: John Wiley and SonsCrossRefGoogle Scholar
Bookstein, F.L. (1982). Soft modeling: The basic design and some extensions. In Jöreskog, K. G., Wold, H. (Eds.), Systems under Indirect Observations II (pp. 55–74). Amsterdam: North-HollandGoogle Scholar
Browne, M. W., & Cudeck, R. (1993). Alternative ways to assessing model fit. In Bollen, K. A., & Long, J. S. (Eds.), Testing Structural Equation Models (pp. 136–162). Newbury Park, CA: Sage PublicationsGoogle Scholar
Chin, W. W. (2001). PLS-Graph User's Guide Version 3.0. Soft Modeling Inc.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. Versailles, France.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, 471–503CrossRefGoogle Scholar
Efron, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans. Philadelphia: SIAMCrossRefGoogle Scholar
Efron, B. (1994). Missing data, imputation, and the bootstrap. Journal of the American Statistical Association, 89, 463–475CrossRefGoogle Scholar
Fornell, C., & Bookstein, F. L. (1982). Two structural equation models: LISREL and PLS applied to consumer exit-voice theory. Journal of Marketing Research, 19, 440–452CrossRefGoogle Scholar
Fornell, C., & Cha, J. (1994). Partial least squares. In Bagozzi, R. P. (Eds.), Advanced Methods of Marketing Research (pp. 52–78). Oxford: BlackwellGoogle Scholar
Gabriel, K. R., & Zamir, S. (1979). Low rank approximation of matrices by least squares with any choice of weights. Technometrics, 21, 489–498CrossRefGoogle Scholar
Griep, M. I., Wakeling, I. N., Vankeerberghen, P., & Massart, D. L. (1995). Comparison of semirobust and robust partial least squares procedures. Chemometrics and Intelligent Laboratory Systems, 29, 37–50CrossRefGoogle Scholar
Hanafi, M., & Qannari, E. M. (2002). An alternative algorithm to the PLS B problem. Paper submitted for publication.Google Scholar
Hwang, H., & Takane, Y. (2002). Structural equation modeling by extended redundancy analysis. In Nishisato, S., Baba, Y., Bozdogan, H., & Kanefuji, K. (Eds.), Measurement and Multivariate Analysis (pp. 115–124). Tokyo: Springer VerlagCrossRefGoogle Scholar
Jöreskog, K. G. (1970). A general method for analysis of covariance structures. Biometrika, 57, 409–426CrossRefGoogle Scholar
Kiers, H. A. L., Takane, Y., & ten Berge, J. M. F. (1996). The analysis of multitrait-multimethod matrices via constrained components analysis. Psychometrika, 61, 601–628CrossRefGoogle Scholar
Lyttkens, E. (1968). On the fixed-point property of Wold's iterative estimation method for principal components. In Krishnaiah, P. R. (Eds.), Multivariate Analysis (pp. 335–350). New York: Academic PressGoogle Scholar
Lyttkens, E. (1973). The fixed-point method for estimating interdependent systems with the underlying model specification. Journal of the Royal Statistical Society, A, 136, 353–394CrossRefGoogle Scholar
Mael, F. A. (1988). Organizational Identification: Construct Redefinition and a Field Application with Organizational Alumni. Unpublished doctoral dissertation, Wayne State University.Google Scholar
McDonald, R. P. (1996). Path analysis with composite variables. Multivariate Behavioral Research, 31, 239–270CrossRefGoogle ScholarPubMed
Meredith, W., & Millsap, R. E. (1985). On component analysis. Psychometrika, 50, 495–507CrossRefGoogle Scholar
Micceri, T. (1989). The unicorn, the normal curve, and other improvable creatures. Psychological Bulletin, 105, 156–166CrossRefGoogle Scholar
Mulaik, S. A. (1972). The Foundations of Factor Analysis. New York: McGraw-HillGoogle Scholar
Paxton, P., Curran, P. J., Bollen, K. A., Kirby, J., & Chen, F. (2001). Monte Carlo experiments: Design and implementation. Structural Equation Modeling, 8, 287–312CrossRefGoogle Scholar
Schönemann, P. H., & Steiger, J. H. (1976). Regression component analysis. British Journal of Mathematical and Statistical Psychology, 29, 175–189CrossRefGoogle Scholar
Schafer, J. L. (1997). Analysis of Incomplete Multivariate Data. New York: Chapman & Hall/CRCCrossRefGoogle Scholar
Seber, G. A. F. (1984). Multivariate Observations. New York: John Wiley and SonsCrossRefGoogle Scholar
Takane, Y., Kiers, H., & de Leeuw, J. (1995). Component analysis with different sets of constraints on different dimensions. Psychometrika, 60, 259–280CrossRefGoogle Scholar
Takane, Y., Yanai, H., & Mayekawa, S. (1991). Relationships among several methods of linearly constrained correspondence analysis. Psychometrika, 56, 667–684CrossRefGoogle Scholar
ten Berge, J. M. F. (1993). Least Squares Optimization in Multivariate Analysis. Leiden: DSWO PressGoogle Scholar
Tucker, L. R. (1951). A method for synthesis of factor analysis studies. Washington, DC: U.S. Department of the ArmyCrossRefGoogle Scholar
Wold, H. (1965). A fixed-point theorem with econometric background, I–II. Arkiv for Matematik, 6, 209–240CrossRefGoogle Scholar
Wold, H. (1966). Estimation of principal components and related methods by iterative least squares. In Krishnaiah, P. R. (Eds.), Multivariate Analysis (pp. 391–420). New York: Academic PressGoogle Scholar
Wold, H. (1973). Nonlinear iterative partial least squares (NIPALS) modeling: Some current developments. In Krishnaiah, P. R. (Eds.), Multivariate Analysis (pp. 383–487). New York: Academic PressGoogle Scholar
Wold, H. (1981). The Fixed Point Approach to Interdependent Systems. Amsterdam: North HollandGoogle Scholar
Wold, H. (1982). Soft modeling: The basic design and some extensions. In Jöreskog, K. G., & Wold, H. (Eds.), Systems under Indirect Observations II (pp. 1–54). Amsterdam: North-HollandGoogle Scholar
Young, F. W. (1981). Quantitative analysis of qualitative data. Psychometrika, 46, 357–388CrossRefGoogle Scholar