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Generalized Structured Component Analysis with Latent Interactions

Published online by Cambridge University Press:  01 January 2025

Heungsun Hwang ,
Moon-Ho Ringo Ho  and
Jonathan Lee
Heungsun Hwang*
Affiliation:
McGill University
Moon-Ho Ringo Ho
Affiliation:
Nanyang Technological University
Jonathan Lee
Affiliation:
California State University
*
heungsun.hwang@mcgill.ca
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Abstract

Generalized structured component analysis (GSCA) is a component-based approach to structural equation modeling. In practice, researchers may often be interested in examining the interaction effects of latent variables. However, GSCA has been geared only for the specification and testing of the main effects of variables. Thus, an extension of GSCA is proposed to effectively deal with various types of interactions among latent variables. In the proposed method, a latent interaction is defined as a product of interacting latent variables. As a result, this method does not require the construction of additional indicators for latent interactions. Moreover, it can easily accommodate both exogenous and endogenous latent interactions. An alternating least-squares algorithm is developed to minimize a single optimization criterion for parameter estimation. A Monte Carlo simulation study is conducted to investigate the parameter recovery capability of the proposed method. An application is also presented to demonstrate the empirical usefulness of the proposed method.

Keywords

generalized structured component analysislatent interactionsalternating least squares

Information

Type
Original Paper
Information
Psychometrika , Volume 75 , Issue 2 , June 2010 , pp. 228 - 242
Copyright
Copyright © 2010 The Psychometric Society

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References

Abela, J.R.Z., Ho, M.R., Webb, C.A., & McWhinnie, C.M. (2008). Materialistic values and well-being: a multi-wave longitudinal analysis. Paper submitted for publication.Google Scholar
Algina, J., & Moulder, B.C. (2001). A note on estimating the Jöreskog–Yang model for latent variable interaction using LSIRESL 8.3. Structural Equation Modeling: A Multidisciplinary Journal, 8, 40–52.CrossRefGoogle Scholar
Bagozzi, R.P., Baumgartner, H., & Yi, Y. (1992). State versus action orientation and the theory of reasoned action: an application to coupon usage. Journal of Consumer Research, 18, 505–518.CrossRefGoogle Scholar
Blankstein, K.R., & Flett, G.L. (1993). Development of the general Hassles scale for students. Unpublished manuscript, University of Toronto at Mississauga.Google Scholar
Bollen, K.A., Kirby, J.B., Curran, P.J., Paxton, P.M., & Chen, F. (2007). Latent variable models under misspecification: two-stage least squares (2SLS) and maximum likelihood (ML) estimators. Sociological Methods and Research, 36, 46–86.CrossRefGoogle Scholar
Busemeyer, J.R., & Jones, L.E. (1983). Analysis of multiplicative combination rules when the causal variables are measured with error. Psychological Bulletin, 93, 549–562.CrossRefGoogle Scholar
Chin, W.W., Marcolin, B.L., & Newsted, P.R. (1996). A partial least squares latent variable approach for measuring interaction effects: results from a Monte Carlo simulation study and voice mail emotion/adoption study. In DeGross, J.I., Jarvenpaa, S., & Srinivasan, A. (Eds.), Proceedings of the seventeenth international conference on information systems, Cleveland: Association for Information Systems.Google Scholar
Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analyses for the behavioural sciences, Hillsdale: Lawrence Erlbaum Associates.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, 471–503.CrossRefGoogle Scholar
Efron, B. (1982). The jackknife, the bootstrap and other resampling plans, Philadelphia: SIAM.CrossRefGoogle Scholar
Egri, K., & Ralston, D.A. (2004). Generation cohorts and personal values: a comparison of China and the United States. Organization Science, 15, 210–220.CrossRefGoogle Scholar
Fornell, C., & Cha, J. (1994). Partial least squares. In Bagozzi, R. (Eds.), Advanced methods of marketing research (pp. 52–78). Oxford: Blackwell.Google Scholar
Glang, M. (1988). Maximierung der Summe erklärter Varianzen in linearrekursiven Strukturgleichungsmodellen mit multiple Indikatoren: eine Alternative zum Schätzmodus B des Partial-Least-Squares-Verfahren. Dissertation zur Erlangung der Würde des Doktors der Philosophie de Universität Hamburg, Hamburg.Google Scholar
Hwang, H., & Takane, Y. (2004). Generalized structured component analysis. Psychometrika, 69, 81–99.CrossRefGoogle Scholar
Hwang, H., DeSarbo, S.W., & Takane, Y. (2007). Fuzzy clusterwise generalized structured component analysis. Psychometrika, 72, 181–198.CrossRefGoogle Scholar
Hwang, H., Malhotra, N.K., Kim, Y., Tomiuk, M.A., & Hong, S. (in press). A comparative study on parameter recovery of three approaches to structural equation modeling. Journal of Marketing Research.Google Scholar
Jaccard, J., & Wan, C.H. (1995). LISREL approaches to interaction effects in multiple regression, Thousand Oaks: Sage.Google 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, 631–639.Google Scholar
Jöreskog, K.G., & Yang, F. (1996). Non-linear structural equation models: the Kenny–Judd model with interaction effects. In Marcoulides, G.A., & Shumacker, R.P. (Eds.), Advanced structural equation modeling: issues and techniques (pp. 57–88). Mahwah: Lawrence Erlbaum Associates.Google Scholar
Kasser, T., & Ryan, R.M. (1993). A dark side of the American dream: correlates of financial success as a central life aspiration. Journal of Personality and Social Psychology, 65, 410–422.CrossRefGoogle ScholarPubMed
Kasser, T., & Ryan, R.M. (1996). Further examining the American dream: differential correlates of intrinsic and extrinsic goals. Personality and Social Psychology Bulletin, 22, 280–287.CrossRefGoogle Scholar
Kenny, D.A., & Judd, C.M. (1984). Estimating the non-linear and interactive effects of latent variables. Psychological Bulletin, 96, 201–210.CrossRefGoogle Scholar
Lei, P.-W. (2009). Evaluating estimation methods for ordinal data in structural equation modeling. Quality and Quantity, 43, 495–507.CrossRefGoogle Scholar
Marsh, H.W., Wen, Z., & Hau, K.-T. (2004). Structural equation models of latent interactions: evaluation of alternative estimation strategies and indicator construction. Psychological Methods, 9, 275–300.CrossRefGoogle ScholarPubMed
McArdle, J.J., & McDonald, R.P. (1984). Some algebraic properties of the reticular action model for moment structures. British Journal of Mathematical and Statistical Psychology, 37, 234–251.CrossRefGoogle ScholarPubMed
Mood, A.M., Graybill, F.A., & Boes, D.C. (1974). Introduction to the theory of statistics, New York: McGraw-Hill.Google Scholar
Radloff, L.S. (1977). The CES-D scale: a self-report depression scale for research in the general population. Applied Psychological Measurement, 1, 385–401.CrossRefGoogle Scholar
Richins, M.L., & Dawson, S. (1992). A consumer values orientation for materialism and its measurement: scale development and validation. Journal of Consumer Research, 19, 303–316.CrossRefGoogle Scholar
Ridgon, E.E., Schumacker, R.E., & Worthe, W. (1998). A comparative review of interaction and nonlinear modeling. In Schumaker, R.E., & Marcoulides, G.A. (Eds.), Interaction and nonlinear effects in structural equation modeling (pp. 1–16). Mahwah: Lawrence Erlbaum Associates.Google Scholar
Schumacker, R.E., & Marcoulides, G.A. (1998). Interaction and nonlinear effects in structural equation modeling, Mahwah: Lawrence Erlbaum Associates.Google Scholar
Sheldon, K.M., & Elliot, A.J. (1999). Goal striving, need satisfaction, and longitudinal well-being: the self-concordance model. Journal of Personality and Social Psychology, 76, 482–497.CrossRefGoogle ScholarPubMed
Sheldon, K.M., & Kasser, T. (1998). Pursuing personal goals: skills enable progress but not all progress is beneficial. Personality and Social Psychology Bulletin, 24, 1319–1331.CrossRefGoogle Scholar
ten Berge, J.M.F. (1993). Least squares optimization in multivariate analysis, Leiden: DSWO.Google Scholar
Tenenhaus, M. (2008). Component-based structural equation modelling. Total Quality Management and Business Excellence, 19, 871–886.CrossRefGoogle Scholar
Watson, D., & Clark, L.A. (1991). The mood and anxiety symptom questionnaire. Unpublished manuscript, University of Iowa, Iowa City, IA.Google Scholar
Widaman, K.F. (1990). Bias in pattern loadings represented by common factor analysis and component analysis. Multivariate Behavioral Research, 25, 89–95.CrossRefGoogle ScholarPubMed
Yang Jonsson, F. (1998). Modeling interaction and nonlinear effects: a step-by-step LISREL example. In Schumaker, R.E., & Marcoulides, G.A. (Eds.), Interaction and nonlinear effects in structural equation modeling (pp. 17–42). Mahwah: Lawrence Erlbaum Associates.Google Scholar