Computational Statistics

, Volume 28, Issue 2, pp 565–580 | Cite as

Goodness-of-fit indices for partial least squares path modeling

Open Access
Original Paper

Abstract

This paper discusses a recent development in partial least squares (PLS) path modeling, namely goodness-of-fit indices. In order to illustrate the behavior of the goodness-of-fit index (GoF) and the relative goodness-of-fit index (GoFrel), we estimate PLS path models with simulated data, and contrast their values with fit indices commonly used in covariance-based structural equation modeling. The simulation shows that the GoF and the GoFrel are not suitable for model validation. However, the GoF can be useful to assess how well a PLS path model can explain different sets of data.

Keywords

Partial least squares path modeling (PLS) Goodness-of-fit index (GoF) 

JEL Classification

C39 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

References

  1. Addinsoft SARL (2007–2008) XLSTAT-PLSPM. Paris, France. http://www.xlstat.com/en/products/xlstat-plspm/
  2. Akaike H (1987) Factor analysis and AIC. Psychometrika 52(3): 317–332MathSciNetMATHCrossRefGoogle Scholar
  3. Arbuckle JL (2003) Amos 5 User’s Guide. SPSSGoogle Scholar
  4. Bagozzi RP, Yi Y (1994) Advanced topics in structural equation models. In: Bagozzi RP (eds) Advanced methods of marketing research. Blackwell, Oxford, p 151Google Scholar
  5. Bass B, Avolio B, Jung D, Berson Y (2003) Predicting unit performance by assessing transformational and transactional leadership. J Appl Psychol 88(2): 207–218CrossRefGoogle Scholar
  6. Bentler PM (1990) Comparative fit indexes in structural models. Psychol Bull 107(2): 238–246CrossRefGoogle Scholar
  7. Bollen KA (1989a) A new incremental fit index for general structural equation models. Sociol Methods Res 17(3): 303MathSciNetCrossRefGoogle Scholar
  8. Bollen KA (1989b) Structural equations with latent variables. Wiley, New York, NYMATHGoogle Scholar
  9. Chin W (2010) How to write up and report PLS analyses. In: EspositoVinzi V, Chin WW, Henseler J, Wang H (eds) Handbook of partial least squares: concepts, methods and applications. Springer, Heidelberg, pp 655–690CrossRefGoogle Scholar
  10. Chin WW, Newsted PR (1999) Structural equation modeling analysis with small samples using partial least squares. In: Hoyle RH (eds) Statistical strategies for small sample research. Sage, Thousand Oaks, CA, pp 334–342Google Scholar
  11. Chin WW, Marcolin BL, Newsted PR (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. Inf Syst Res 14(2): 189–217CrossRefGoogle Scholar
  12. Dijkstra TK (1981) Latent variables in linear stochastic models: reflections on “Maximum Likelihood” and “Partial Least Squares” methods. PhD thesis, Groningen University, Groningen, a second edition was published in 1985 by Sociometric Research FoundationGoogle Scholar
  13. Dijkstra TK (2010) Latent variables and indices: Herman Wold’s basic design and partial least squares. In: Vinzi VE, Chin WW, Henseler J, Wang H (eds) Handbook of partial least squares: concepts, methods, and applications, computational statistics, vol II, Springer, Heidelberg, pp 23–46 (in print)Google Scholar
  14. Duarte P, Raposo M (2010) A PLS model to study brand preference: an application to the mobile phone market. In: EspositoVinzi V, Chin WW, Henseler J, Wang H (eds) Handbook of partial least squares: concepts, methods and applications. Springer, Heidelberg, pp 449–485CrossRefGoogle Scholar
  15. EspositoVinzi V, Trinchera L, Squillacciotti S, Tenenhaus M (2008) REBUS-PLS: A response-based procedure for detecting unit segments in PLS path modelling. Appl Stoch Models Bus Ind 24(5): 439–458MathSciNetCrossRefGoogle Scholar
  16. Esposito Vinzi V, Chin WW, Henseler J, Wang H (eds) (2010a) Handbook of partial least squares: concepts, methods and applications. Springer, HeidelbergGoogle Scholar
  17. Esposito Vinzi V, Trinchera L, Amato S (2010b) PLS path modeling: from foundations to recent developments and open issues for model assessment and improvement. In: EspositoVinzi V, Chin WW, Henseler J, Wang H (eds) Handbook of partial least squares: concepts, methods and applications. Springer, Heidelberg, pp 47–82CrossRefGoogle Scholar
  18. Fornell C (1995) The quality of economic output: empirical generalizations about its distribution and relationship to market share. Market Sci 14(3): G203–G211CrossRefGoogle Scholar
  19. Fornell C, Bookstein FL (1982) Two structural equation models: LISREL and PLS applied to consumer exit-voice theory. J Market Res 19(4): 440–452CrossRefGoogle Scholar
  20. Fornell C, Larcker DF (1981) Evaluating structural equation models with unobservable variables and measurement error. J Market Res 18(1): 39–50CrossRefGoogle Scholar
  21. Hair J, Sarstedt M, Ringle C, Mena J (2012) An assessment of the use of partial least squares structural equation modeling in marketing research. J Acad Market Sci (forthcoming)Google Scholar
  22. Hanafi M (2007) PLS path modelling: computation of latent variables with the estimation mode B. Comput Stat 22(2): 275–292MathSciNetMATHCrossRefGoogle Scholar
  23. Henseler J (2010) On the convergence of the partial least squares path modeling algorithm. Comput Stat 25(1): 107–120MathSciNetMATHCrossRefGoogle Scholar
  24. Henseler J, Ringle C, Sinkovics R (2009) The use of partial least squares path modeling in international marketing. Adv Int Market 20(2009): 277–319Google Scholar
  25. Hu LT, Bentler PM (1999) Cutoff criteria for fit indexes in covariance structure analysis: conventional criteria versus new alternatives. Struct Equ Model 6(1): 1–55CrossRefGoogle Scholar
  26. Hulland J (1999) Use of partial least squares (PLS) in strategic management research: a review of four recent studies. Strateg Manag J 20(2): 195–204CrossRefGoogle Scholar
  27. Jöreskog KG, Sörbom D (1986) LISREL VI: Analysis of linear structural relationships by maximum likelihood and least squares methods. Scientific Software, Mooresville, INGoogle Scholar
  28. Krijnen W, Dijkstra T, Gill R (1998) Conditions for factor (in) determinacy in factor analysis. Psychometrika 63(4): 359–367MathSciNetCrossRefGoogle Scholar
  29. Lohmöller JB (1989) Latent variable path modeling with partial least squares. Physica, HeidelbergGoogle Scholar
  30. Monecke A, Leisch F (2012) semPLS: Structural equation modeling using partial least squares. J Stat Softw (forthcoming)Google Scholar
  31. Mulaik SA, James LR, van Alstine J, Bennett N, Lind S, Stilwell CD (1989) Evaluation of goodness-of-fit indices for structural equation models. Psychol Bull 105: 430–445CrossRefGoogle Scholar
  32. Paxton P, Curran P, Bollen K, Kirby J, Chen F (2001) Monte carlo experiments: design and implementation. Struct Equ Model 8(2): 287–312CrossRefGoogle Scholar
  33. Reinartz WJ, Haenlein M, Henseler J (2009) An empirical comparison of the efficacy of covariance-based and variance-based SEM. Int J Res Market 26(4): 332–344CrossRefGoogle Scholar
  34. Rigdon EE (1998) Structural equation modeling. In: Marcoulides GA (ed) Modern methods for business research, Lawrence Erlbaum Associates. Mahwah, pp 251–294Google Scholar
  35. Rigdon EE, Ringle CM, Sarstedt M (2010) Structural modeling of heterogeneous data with partial least squares. In: Malhotra NK (ed) Review of marketing research, vol 7. Sharpe, pp 255–296Google Scholar
  36. Ringle C, Sarstedt M, Straub D (2012) A critical look at the use of pls-sem in mis quarterly. MIS Q 36(1): iii–xivGoogle Scholar
  37. Ringle CM, Wende S, Will A (2005) SmartPLS 2.0 M3. University of Hamburg, Hamburg, Germany. http://www.smartpls.de
  38. Sarstedt M, Ringle CM (2010) Treating unobserved heterogeneity in PLS path modelling: a comparison of FIMIX-PLS with different data analysis strategies. J Appl Stat 37(8): 1299–1318MathSciNetCrossRefGoogle Scholar
  39. Sarstedt M, Henseler J, Ringle CM (2011) Multigroup analysis in partial least squares (PLS) path modeling: Alternative methods and empirical results. Adv Int Market 22: 195–218CrossRefGoogle Scholar
  40. Soft Modeling, Inc (1992–2002) PLS-Graph Version 3.0. Houston, TX. http://www.plsgraph.com
  41. Sosik J, Kahai S, Piovoso M (2009) Silver bullet or voodoo statistics. Group Organ Manag 34(1): 5CrossRefGoogle Scholar
  42. Steiger JH (1990) Structural model evaluation and modification: an interval estimation approach. Multivar Behav Res 25(2): 173–180MathSciNetCrossRefGoogle Scholar
  43. Tenenhaus A, Tenenhaus M (2011) Regularized generalized caconical correlation analysis. Psychometrika 76(2): 257–284MathSciNetMATHCrossRefGoogle Scholar
  44. Tenenhaus M, Amato S, Esposito Vinzi V (2004) A global goodness-of-fit index for PLS structural equation modelling. In: Proceedings of the XLII SIS scientific meeting. pp 739–742Google Scholar
  45. Tenenhaus M, Vinzi VE, Chatelin YM, Lauro C (2005) PLS path modeling. Comput Stat Data Anal 48(1): 159–205MATHCrossRefGoogle Scholar
  46. Wheaton B, Muthén B, Alwin DF, Summers GF (1977) Assessing reliability and stability in panel models. In: Heise D (eds) Sociological methodology. Jossey-Bass, Washington, DC, pp 84–136Google Scholar
  47. Wold HOA (1966) Non-linear estimation by iterative least squares procedures. In: David FN (eds) Research papers in statistics. Wiley, London, pp 411–444Google Scholar
  48. Wold HOA (1973) Nonlinear iterative partial least squares (NIPALS) modelling. Some current developments. In: Krishnaiah PR (ed) Proceedings of the 3rd international symposium on multivariate analysis, Dayton, OH. pp 383–407Google Scholar
  49. Wold HOA (1974) Causal flows with latent variables: partings of the ways in the light of NIPALS modelling. Eur Econ Rev 5(1): 67–86CrossRefGoogle Scholar
  50. Wold HOA (1982) Soft modelling: the basic design and some extensions. In: Jöreskog KG, Wold HOA (eds) Systems under indirect observation. Causality, structure, prediction, vol II. North-Holland, Amsterdam, New York, Oxford, pp 1–54Google Scholar
  51. Wold HOA (1985a) Partial least squares. In: Kotz S, Johnson NL (eds) Encyclopaedia of statistical sciences, vol 6. Wiley, New York, NY, pp 581–591Google Scholar
  52. Wold HOA (1985b) Partial least squares and LISREL models. In: Nijkamp P, Leitner H, Wrigley N (eds) Measuring the unmeasurable. Nijhoff, Dordrecht, Boston, Lancaster, pp 220–251Google Scholar
  53. Wold HOA (1989) Introduction to the second generation of multivariate analysis. In: Wold HOA (ed) Theoretical empiricism. A general rationale for scientific model-building. Paragon House, New York, pp VIII–XLGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute for Management ResearchRadboud University NijmegenNijmegenThe Netherlands
  2. 2.Institute for Market-based Management, Munich School of ManagementLudwig-Maximilians-Universität MünchenMunichGermany

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