European Journal of Information Systems

, Volume 21, Issue 1, pp 99–112 | Cite as

Analysing quadratic effects of formative constructs by means of variance-based structural equation modelling

  • Jörg Henseler
  • Georg Fassott
  • Theo K Dijkstra
  • Bradley Wilson
Research Article

Abstract

Together with the development of information systems research, there has also been increased interest in non-linear relationships between focal constructs. This article presents six Partial Least Squares-based approaches for estimating formative constructs’ quadratic effects. In addition, these approaches’ performance is tested by means of a complex Monte Carlo experiment. The experiment reveals significant and substantial differences between the approaches. In general, the performance of the hybrid approach as suggested by Wold (1982) is most convincing in terms of point estimate accuracy, statistical power, and prediction accuracy. The two-stage approach suggested by Chin et al (1996) showed almost the same performance; differences between it and the hybrid approach – although statistically significant – were unsubstantial. Based on these results, the article provides guidelines for the analysis of non-linear effects by means of variance-based structural equation modelling.

Keywords

partial least squares path modelling PLS non-linear effect quadratic effect 

References

  1. Addinsoft (2007) XLSTAT-PLS. Addinsoft, Paris, France.Google Scholar
  2. Albers S (2010) PLS and success factor studies in marketing. In Handbook of Partial Least Squares: Concepts, Methods, and Applications. Vol. II of Computational Statistics (ESPOSITO VINZI V, CHIN WW, HENSELER J and WANG H, Eds), pp 409–425, Springer, Heidelberg.CrossRefGoogle Scholar
  3. Bollen KA and Lennox R (1991) Conventional wisdom on measurement: a structural equation perspective. Psychological Bulletin 110 (2), 305–314.CrossRefGoogle Scholar
  4. Busemeyer JB and Jones LE (1983) Analysis of multiplicative combination rules when causal variables are measured with error. Psychological Bulletin 93 (3), 549–562.CrossRefGoogle Scholar
  5. Carte TA and Russell CJ (2003) In pursuit of moderation: nine common errors and their solution. MIS Quarterly 27 (3), 479–501.Google Scholar
  6. Cassel C, Hackl P and Westlund A (1999) Robustness of partial least-squares method of estimating latent variable quality structures. Journal of Applied Statistics 26 (4), 435–446.CrossRefGoogle Scholar
  7. Chin WW (1998) The partial least squares approach to structural equation modeling. In Modern Methods for Business Research (MARCOULIDES GA, Ed), pp 295–336, Lawrence Erlbaum Associates, Inc., Mahwah, NJ.Google Scholar
  8. Chin WW, Marcolin BL and Newsted PR (1996) A partial least squares latent variable modeling approach for measuring interaction effects. Results from a Monte Carlo simulation study and voice mail emotion/adoption study. In Proceedings of the Seventeenth International Conference on Information Systems (DeGROSS JI, JARVENPAA S and SRINIVASAN A, Eds), pp 21–41, Cleveland, OH.Google Scholar
  9. Chin WW, Marcolin BL and Newsted PR (June 2003) A partial least squares latent variable modeling approach for measuring interaction effects. Results from a Monte Carlo simulation study and an electronic-mail emotion/adopion study. Information Systems Research 14 (2), 189–217.CrossRefGoogle Scholar
  10. Cohen J (1978) Partialed products are interactions; partialed powers are curve components. Psychological Bulletin 85 (4), 858–866.CrossRefGoogle Scholar
  11. Cohen J (1988) Statistical Power Analysis for the Behavioral Sciences, 2nd edn, Lawrence Erlbaum Associates, Hillsdale.Google Scholar
  12. Cortina JM (1993) Interaction, nonlinearity, and multicollinearity: implications for multiple regression. Journal of Management 19 (4), 915–922.CrossRefGoogle Scholar
  13. Cronbach LJ (1987) Statistical tests for moderator variables: flaws in analyses recently proposed. Psychological Bulletin 102 (3), 414–417.CrossRefGoogle Scholar
  14. Diamantopoulos A (2006) The error term in formative measurement models: interpretation and modeling implications. Journal of Modelling in Management 1 (1), 7–17.CrossRefGoogle Scholar
  15. Diamantopoulos A and Siguaw JA (2006) Formative versus reflective indicators in organizational measure development: a comparison and empirical illustration. British Journal of Management 17 (4), 263–282.CrossRefGoogle Scholar
  16. Diamantopoulos A and Winklhofer HM (2001) Index construction with formative indicators: an alternative to scale development. Journal of Marketing Research 38 (2), 269–277.CrossRefGoogle Scholar
  17. Dijkstra TK (2010) Latent variables and indices: Herman Wold's basic design and partial least squares. In Handbook of Partial Least Squares: Concepts, Methods, and Applications. Vol. II of Computational Statistics (VINZI VE, CHIN WW, HENSELER J and WANG H, Eds), pp 23–46, Springer, Heidelberg.CrossRefGoogle Scholar
  18. Dijkstra TK and Henseler J (forthcoming) Prescriptions for dimension reduction, with interacting factors. Quality & Quantity 26 (3), 438–445.Google Scholar
  19. Echambadi R and Hess J (2007) Mean-centering does not alleviate collinearity problems in moderated multiple regression. Marketing Science 26 (3), 438–445.CrossRefGoogle Scholar
  20. Fornell C (1982) A second generation of multivariate analysis: an overview. In A Second Generation of Multivariate Analysis (FORNELL C, Ed), Vol. 1, pp 1–21, Greenwood, Westport.Google Scholar
  21. Fornell C and Larcker DF (1981) Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research 18 (1), 39–50.CrossRefGoogle Scholar
  22. Gefen D and Straub D (1997) Gender differences in the perception and use of e-mail: an extension to the technology acceptance model. MIS Quarterly 21 (4), 389–400.CrossRefGoogle Scholar
  23. Gibson C and Birkinshaw J (2004) The antecedents, consequences, and mediating role of organizational ambidexterity. Academy of Management Journal 47 (2), 209–226.CrossRefGoogle Scholar
  24. Goodhue D, Lewis W and Thompson R (2007) Statistical power in analyzing interaction effects: questioning the advantage of PLS with product indicators. Information Systems Research 18 (2), 211–227.CrossRefGoogle Scholar
  25. Henseler J (2010) On the convergence of the partial least squares path modeling algorithm. Computational Statistics 25 (1), 107–120.CrossRefGoogle Scholar
  26. Henseler J and Chin WW (2010) A comparison of approaches for the analysis of interaction effects between latent variables using partial least squares path modeling. Structural Equation Modeling: A Multidisciplinary Journal 17 (1), 82–109.CrossRefGoogle Scholar
  27. Henseler J and Fassott G (2010) Testing moderating effects in PLS path models: an illustration of available procedures. In Handbook of Partial Least Squares: Concepts, Methods, and Applications. Vol. II of Computational Statistics (ESPOSITO VINZI V, CHIN WW, HENSELER J and WANG H, Eds), pp 713–735, Springer, Heidelberg.CrossRefGoogle Scholar
  28. Henseler J, Ringle CM and Sinkovics RR (2009) The use of partial least squares path modeling in international marketing. Advances in International Marketing 20, 277–319.Google Scholar
  29. Jarvis CB, MacKenzie SB and Podsakoff P (2003) A critical review of construct indicators and measurement model misspecification in marketing and consumer research. Journal of Consumer Research 30 (2), 199–218.CrossRefGoogle Scholar
  30. Jonsson FY (1998) Nonlinear structural equation models: the kenny-judd model with interaction effects. In Interaction and Nonlinear Effects in Structural Equation Modeling (SCHUMACKER RE and MACOULIDES GA, Eds), pp 17–42, Lawrence Erlbaum Associates, Mahwah, NJ.Google Scholar
  31. Jöreskog KG and Yang F (1996) Nonlinear structural equation models: the Kenny-Judd model with interaction effects. In Advanced Structural Equation Modeling: Issues and Techniques (MACOULIDES GA and SCHUMACKER RE, Eds), pp 57–88, Lawrence Erlbaum Associates, Hillsdale, NJ.Google Scholar
  32. Kenny DA and Judd CM (1984) Estimating the nonlinear and interactive effects of latent variables. Psychological Bulletin 96 (1), 201–210.CrossRefGoogle Scholar
  33. Lance CE (1988) Residual centering, exploratory and confirmatory moderator analysis, and decomposition of effects in path models containing interactions. Applied Psychological Measurement 12 (2), 163–175.CrossRefGoogle Scholar
  34. Little TD, Bovaird JA and Widaman KF (2006) On the merits of orthogonalizing powered and product terms: implications for modeling interactions among latent variables. Structural Equation Modeling 13 (4), 497–519.CrossRefGoogle Scholar
  35. Lohmöller J-B (1987) LVPLS 1.8 Program Manual: Latent Variable Path Analysis with Partial Least Squares Estimation. Zentralarchiv für Empirische Sozialforschung, Universität zu Köln, Cologne, Germany.Google Scholar
  36. Lohmöller J-B (1989) Latent Variable Path Modeling with Partial Least Squares. Physica, Heidelberg.CrossRefGoogle Scholar
  37. Marsh H, Wen Z and Hau K (2006) Structural equation models of latent interaction and quadratic effects. In Structural Equation Modeling: A Second Course (HANCOCK GR and MUELLER RO, Eds), pp 225–265, IAS, Charlotte, NC.Google Scholar
  38. Marsh HW, Wen Z and Hau KT (2004) Structural equation models of latent interactions: evaluation of alternative estimation strategies and indicator construction. Psychological Methods 9 (3), 275–300.CrossRefGoogle Scholar
  39. Mathieson K, Peacock E and Chin W (2001) Extending the technology acceptance model: the influence of perceived user resources. ACM SIGMIS Database 32 (3), 86–112.CrossRefGoogle Scholar
  40. Moulder B and Algina J (2002) Comparison of methods for estimating and testing latent variable interactions. Structural Equation Modeling: A Multidisciplinary Journal 9 (1), 1–19.CrossRefGoogle Scholar
  41. Petter S, Straub D and Rai A (2007) Specifying formative constructs in information systems research. MIS Quarterly 31 (4), 623–656.Google Scholar
  42. Podsakoff N, Shen W and Podsakoff P (2006) The role of formative measurement models in strategic management research: review, critique, and implications for future research. Research Methodology in Strategy and Management 3 (1), 197–252.CrossRefGoogle Scholar
  43. R Development Core Team (2007) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria. [WWW document] http://www.R-project.org.
  44. Reinartz WJ, Echambadi R and Chin WW (2002) Generating nonnormal data for simulation of structural equation models using Mattson's method. Multivariate Behavioral Research 37 (2), 227–244.CrossRefGoogle Scholar
  45. Reinartz WJ, Haenlein M and Henseler J (2009) An empirical comparison of the efficacy of covariance-based and variance-based SEM. International Journal of Research in Marketing 26 (4), 332–344.CrossRefGoogle Scholar
  46. Ringle CM, Wende S and Will A (2007) SmartPLS 2.0 M3. University of Hamburg, Hamburg, Germany. [WWW document] http://www.smartpls.de.Google Scholar
  47. Sánchez G and Trinchera L (2010) plspm – Partial Least Squares Data Analysis Methods. Universitat Politecnica de Catalunya. [WWW document] http://cran.r-project.org/web/packages/plspm/.Google Scholar
  48. Schumacker RE and Marcoulides GA (Eds) (1998) Interaction and Nonlinear Effects in Structural Equation Modeling. Lawrence Erlbaum Associates, Mahwah, NJ.Google Scholar
  49. Soft Modeling, Inc (1992–2002) PLS-Graph Version 3.0. Houston, TX. [WWW document] http://www.plsgraph.com.
  50. Tenenhaus M, Vinzi VE, Chatelin YM and Lauro C (2005) PLS path modeling. Computational Statistics and Data Analysis 48 (1), 159–205.CrossRefGoogle Scholar
  51. Test & Go (2006) SPAD Version 6.0.0. Test & Go, Paris, France.Google Scholar
  52. Wilson B (2010) Using PLS to investigate interaction effects between higher order brand constructs. In Handbook of Partial Least Squares: Concepts, Methods, and Applications. (ESPOSITO VINZI V, CHIN WW, HENSELER J and WANG H, Eds), Vol. II of Computational Statistics pp 621–654, Springer, Heidelberg.CrossRefGoogle Scholar
  53. Wixom B and Watson H (2001) An empirical investigation of the factors affecting data warehousing success. MIS Quarterly 25 (1), 17–41.CrossRefGoogle Scholar
  54. Wold HOA (1966) Non-linear estimation by iterative least squares procedures. In Research Papers in Statistics (DAVID FN, Ed), pp 411–444, Wiley, London, New York, Sydney.Google Scholar
  55. Wold HOA (1982) Soft modelling: the basic design and some extensions. In Systems Under Indirect Observation. Causality, Structure, Prediction Vol. II. (JÖRESKOG KG and WOLD HOA, Eds), pp 1–54, North-Holland, Amsterdam, New York, Oxford.Google Scholar
  56. Wold S, Kettaneh-Wold N and Skagerberg B (1989) Nonlinear PLS modeling. Chemometrics and Intelligent Laboratory Systems 7 (1), 53–65.CrossRefGoogle Scholar
  57. Yi M and Davis F (2003) Developing and validating an observational learning model of computer software training and skill acquisition. Information Systems Research 14 (2), 146–169.CrossRefGoogle Scholar

Copyright information

© Operational Research Society 2011

Authors and Affiliations

  • Jörg Henseler
    • 1
    • 2
  • Georg Fassott
    • 3
  • Theo K Dijkstra
    • 4
  • Bradley Wilson
    • 5
  1. 1.Institute for Management Research, Radboud University NijmegenThe Netherlands
  2. 2.Higher Institute of Statistics and Knowledge Management (ISEGI), Universidade Nova de LisboaPortugal
  3. 3.Faculty of Business Studies and Economics, University of KaiserslauternGermany
  4. 4.Faculty of Economic and Business, University of GroningenThe Netherlands
  5. 5.School of Media and Communication, RMIT UniversityMelbourneAustralia

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