Generalized Structured Component Analysis | Psychometrika | Cambridge Core (original) (raw)

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.

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

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

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

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