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Psychometrika

, Volume 75, Issue 2, pp 228–242 | Cite as

Generalized Structured Component Analysis with Latent Interactions

  • Heungsun HwangEmail author
  • Moon-Ho Ringo Ho
  • Jonathan Lee
Article

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 analysis latent interactions alternating least squares 

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References

  1. 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
  2. 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
  3. 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
  4. Blankstein, K.R., & Flett, G.L. (1993). Development of the general Hassles scale for students. Unpublished manuscript, University of Toronto at Mississauga. Google Scholar
  5. 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. Google Scholar
  6. 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
  7. 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 J.I. DeGross, S. Jarvenpaa & A. Srinivasan (Eds.), Proceedings of the seventeenth international conference on information systems, Cleveland: Association for Information Systems. Google Scholar
  8. Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analyses for the behavioural sciences. Hillsdale: Lawrence Erlbaum Associates. Google Scholar
  9. 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
  10. Efron, B. (1982). The jackknife, the bootstrap and other resampling plans. Philadelphia: SIAM. Google Scholar
  11. 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
  12. Fornell, C., & Cha, J. (1994). Partial least squares. In R. Bagozzi (Ed.), Advanced methods of marketing research (pp. 52–78). Oxford: Blackwell. Google Scholar
  13. 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
  14. Hwang, H., & Takane, Y. (2004). Generalized structured component analysis. Psychometrika, 69, 81–99. CrossRefGoogle Scholar
  15. Hwang, H., DeSarbo, S.W., & Takane, Y. (2007). Fuzzy clusterwise generalized structured component analysis. Psychometrika, 72, 181–198. CrossRefGoogle Scholar
  16. 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
  17. Jaccard, J., & Wan, C.H. (1995). LISREL approaches to interaction effects in multiple regression. Thousand Oaks: Sage. Google Scholar
  18. 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. CrossRefGoogle Scholar
  19. Jöreskog, K.G., & Yang, F. (1996). Non-linear structural equation models: the Kenny–Judd model with interaction effects. In G.A. Marcoulides & R.P. Shumacker (Eds.), Advanced structural equation modeling: issues and techniques (pp. 57–88). Mahwah: Lawrence Erlbaum Associates. Google Scholar
  20. 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. CrossRefPubMedGoogle Scholar
  21. 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
  22. Kenny, D.A., & Judd, C.M. (1984). Estimating the non-linear and interactive effects of latent variables. Psychological Bulletin, 96, 201–210. CrossRefGoogle Scholar
  23. Lei, P.-W. (2009). Evaluating estimation methods for ordinal data in structural equation modeling. Quality and Quantity, 43, 495–507. CrossRefGoogle Scholar
  24. 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. CrossRefPubMedGoogle Scholar
  25. 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. PubMedGoogle Scholar
  26. Mood, A.M., Graybill, F.A., & Boes, D.C. (1974). Introduction to the theory of statistics. New York: McGraw-Hill. Google Scholar
  27. 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
  28. 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
  29. Ridgon, E.E., Schumacker, R.E., & Worthe, W. (1998). A comparative review of interaction and nonlinear modeling. In R.E. Schumaker & G.A. Marcoulides (Eds.), Interaction and nonlinear effects in structural equation modeling (pp. 1–16). Mahwah: Lawrence Erlbaum Associates. Google Scholar
  30. Schumacker, R.E., & Marcoulides, G.A. (1998). Interaction and nonlinear effects in structural equation modeling. Mahwah: Lawrence Erlbaum Associates. Google Scholar
  31. 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. CrossRefPubMedGoogle Scholar
  32. 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
  33. ten Berge, J.M.F. (1993). Least squares optimization in multivariate analysis. Leiden: DSWO. Google Scholar
  34. Tenenhaus, M. (2008). Component-based structural equation modelling. Total Quality Management and Business Excellence, 19, 871–886. CrossRefGoogle Scholar
  35. Watson, D., & Clark, L.A. (1991). The mood and anxiety symptom questionnaire. Unpublished manuscript, University of Iowa, Iowa City, IA. Google Scholar
  36. Widaman, K.F. (1990). Bias in pattern loadings represented by common factor analysis and component analysis. Multivariate Behavioral Research, 25, 89–95. CrossRefGoogle Scholar
  37. Yang Jonsson, F. (1998). Modeling interaction and nonlinear effects: a step-by-step LISREL example. In R.E. Schumaker & G.A. Marcoulides (Eds.), Interaction and nonlinear effects in structural equation modeling (pp. 17–42). Mahwah: Lawrence Erlbaum Associates. Google Scholar

Copyright information

© The Psychometric Society 2010

Authors and Affiliations

  • Heungsun Hwang
    • 1
    Email author
  • Moon-Ho Ringo Ho
    • 2
  • Jonathan Lee
    • 3
  1. 1.Department of PsychologyMcGill UniversityMontrealCanada
  2. 2.Nanyang Technological UniversitySingaporeSingapore
  3. 3.California State UniversityLong BeachUSA

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