Skip to main content

Uncovering and Treating Unobserved Heterogeneity with FIMIX-PLS: Which Model Selection Criterion Provides an Appropriate Number of Segments?

Abstract

Since its first introduction in the Schmalenbach Business Review, Hahn et al.’s (2002) finite mixture partial least squares (FIMIX-PLS) approach to response-based segmentation in variance-based structural equation modeling has received much attention from the marketing and management disciplines. When applying FIMIX-PLS to uncover unobserved heterogeneity, the actual number of segments is usually unknown. As in any clustering procedure, retaining a suitable number of segments is crucial, since many managerial decisions are based on this result. In empirical research, applications of FIMIX-PLS rely on information and classification criteria to select an appropriate number of segments to retain from the data. However, the performance and robustness of these criteria in determining an adequate number of segments has not yet been investigated scientifically in the context of FIMIX-PLS. By conducting computational experiments, this study provides an evaluation of several model selection criteria’s performance and of different data characteristics’ influence on the robustness of the criteria. The results engender key recommendations and identify appropriate model selection criteria for FIMIX-PLS. The study’s findings enhance the applicability of FIMIX-PLS in both theory and practice.

This is a preview of subscription content, access via your institution.

References

  1. Akaike, Hirotsugu (1973), Information Theory and an Extension of the Maximum Likelihood Principle, in Boris N. Petrov and Frigyes Csáki (eds.), Second International Symposium on Information Theory, Budapest: Académiai Kiadó, 267–281.

    Google Scholar 

  2. Aitkin, Murray and Donald B. Rubin (1985), Estimation and Hypothesis Testing in Finite Mixture Models, Journal of the Royal Statistical Society, Series B, Methodological 47, 67–75.

    Google Scholar 

  3. Albers, Sönke (2010), PLS and Success Factors Studies in Marketing, in Vincenzo Esposito Vinzi, Wynne W. Chin, Jörg Henseler and Huiwen Wang (eds.), Handbook of Partial Least Squares: Concepts, Methods and Applications in Marketing and Related Fields, Berlin et al.: Springer, 409–425.

    Chapter  Google Scholar 

  4. Andrews, Rick L. and Imran S. Currim (2003a), A Comparison of Segment Retention Criteria for Finite Mixture Logit Models, Journal of Marketing Research 40, 235–243.

    Article  Google Scholar 

  5. Andrews, Rick L. and Imran S. Currim (2003b), Recovering and Profiling the True Segmentation Structure in Markets: An Empirical Investigation, International Journal of Research in Marketing 20, 177–192.

    Article  Google Scholar 

  6. Andrews, Rick L. and Imran S. Currim (2003c), Retention of Latent Segments in Regression-based Marketing Models, International Journal of Research in Marketing 20, 315–321.

    Article  Google Scholar 

  7. Ansari, Asim, Kamel Jedidi, and Sharan Jagpal (2000), A Hierarchical Bayesian Methodology for Treating Heterogeneity in Structural Equation Models, Marketing Science 19, 328–347.

    Article  Google Scholar 

  8. Arminger, Gerhard and Petra Stein (1997), Finite Mixtures of Covariance Structure Models with Regressors, Sociological Methods & Research 16, 148–182

    Article  Google Scholar 

  9. Arminger, Gerhard, Petra Stein, and Jörg Wittenberg (1999), Mixtures of Conditional Mean- and Covariance-Structure Models, Psychometrika 64, 475–494.

    Article  Google Scholar 

  10. Banfield, Jeffrey D. and Adrian E. Raftery (1993), Model-Based Gaussian and Non-Gaussian Clustering, Biometrics 49, 803–821.

    Article  Google Scholar 

  11. Becker, Jan U. (2004), File Sharing in Peer-to-Peer-Netzwerken. Ökonomische Analyse des Nutzerverhaltens, Wiesbaden: Deutscher Universitäts-Verlag.

    Book  Google Scholar 

  12. Becker, Jan-Michael, Christian M. Ringle, and Franziska Völckner (2009), Prediction-Oriented Segmentation: A New Methodology to Uncover Unobserved Heterogeneity in PLS Path Models, in Proceedings of the 38th Annual Conference of the European Marketing Academy, Nantes, France, CD-Rom Proceedings.

    Google Scholar 

  13. Becker, Jan-Michael, Marko Sarstedt, Christian M. Ringle, and Franziska Völckner (2010), Segment Retention and Collinearity in Mixture Regression Analysis, in Proceedings of the 39th Annual Conference of the European Marketing Academy, Copenhagen, Denmark, CD-Rom Proceedings.

    Google Scholar 

  14. Bezdek, James C. (1981), Pattern Recognition with Fuzzy Objective Function Algorithms, Berlin et al.: Springer.

    Book  Google Scholar 

  15. Biernacki, Christophe and Gérard Govaert (1997), Using the Classification Likelihood to Choose the Number of Clusters, Computing Science and Statistics 29, 451–457.

    Google Scholar 

  16. Biernacki, Christophe, Gilles Celeux, and Gérard Govaert (2000), Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood, IEEE Transactions on Pattern Analysis and Machine Intelligence 22, 719–725.

    Article  Google Scholar 

  17. Boone, Derrick S. and Michelle Roehm (2002), Evaluating the Appropriateness of Market Segmentation Solutions Using Artificial Neural Networks and the Membership Clustering Criterion, Marketing Letters 13, 317–333.

    Article  Google Scholar 

  18. Bozdogan, Hamparsum (1987), Model Selection and Akaike’s Information Criterion (AIC): The General Theory and its Analytical Extensions, Psychometrika 52, 345–370.

    Article  Google Scholar 

  19. Bozodogan, Hamparsum (1994), Mixture-Model Cluster Analysis Using Model Selection Criteria and a New Information Measure of Complexity, in Hamparsum Bozdogan (ed.), Proceedings of the First US/Japan Conference on Frontiers of Statistical Modelling: An Informational Approach, Vol. 2, Boston: Kluwer Academic Publishers, 69–113.

    Google Scholar 

  20. Celeux, Gilles and Gilda Soromenho (1996), An Entropy Criterion for Assessing the Number of Clusters in a Mixture Model, Journal of Classification 13, 195–212.

    Article  Google Scholar 

  21. Chin, Wynne W. (1998), The Partial Least Squares Approach for Structural Equation Modeling, in George A. Marcoulides (ed.), Modern Methods for Business Research, London: Lawrence Erlbaum Associates, 295–336.

    Google Scholar 

  22. Chin, Wynne W., Barbara L. Marcolin, and Peter R. Newsted (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/Adoption Study, Information Systems Research 14, 189–217.

    Article  Google Scholar 

  23. Conze, Oliver (2007), Kundenloyalität durch Kundenvorteile. Segmentspezifische Analyse und Implikationen für das Kundenbeziehungsmanagement, Wiesbaden: DUV.

    Google Scholar 

  24. Dempster, Arthur P., Arthur M. Laird, and Donald B. Rubin (1977), Maximum Likelihood from Incomplete Data via the EM Algorithm, Journal of the Royal Statistical Society, Series B, 39, 1–38.

    Google Scholar 

  25. DeSarbo, Wayne S. and William L. Cron (1988), A Maximum Likelihood Methodology for Clusterwise Linear Regression, Journal of Classification 5, 249–282.

    Article  Google Scholar 

  26. Dolan, Conor V. and Han L. J. van der Maas (1998), Fitting Multivariate Normal Finite Mixtures Subject to Structural Equation Modeling, Psychometrika 63, 227–253.

    Article  Google Scholar 

  27. Esposito Vinzi, Vincenzo, Christian M. Ringle, Silvia Squillacciotti, and Laura Trinchera (2007), Capturing and Treating Heterogeneity by Response Based Segmentation in PLS Path Modeling, A Comparison of Alternative Methods by Computational Experiments, Essec Research Center, DR-07019 July 07, retrieved from http://www45.essec.edu/pwr/servlet/showRef?bibID=7153.

    Google Scholar 

  28. Esposito Vinzi, Vincenzo, Laura Trinchera, Silvia Squillacciotti, and Michel Tenenhaus (2008), REBUS-PLS: A Response-Based Procedure for Detecting Unit Segments in PLS Path Modelling, Applied Stochastic Models in Business and Industry 24, 439–458.

    Article  Google Scholar 

  29. Everitt, Brian S. and Diavid J. Hand (1981), Finite Mixture Distributions, London and New York, NY: Chapman & Hall.

    Book  Google Scholar 

  30. Hahn, Carsten H. (2002), Segmentspezifische Kundenzufriedenheitsanalyse, Wiesbaden: DUV.

    Book  Google Scholar 

  31. Hahn, Carsten H., Michael D. Johnson, Andreas Herrmann, and Frank Huber (2002), Capturing Customer Heterogeneity Using a Finite Mixture PLS Approach, sbr 54, 243–269.

    Google Scholar 

  32. Hair, Joseph F., Christian M. Ringle, and Marko Sarstedt (2011), PLS-SEM–Indeed a Silver Bullet, Journal of Marketing Theory & Practice, forthcoming.

    Google Scholar 

  33. Hannan, E. J. and B. G. Quinn (1979), The Determination of the Order of an Autoregression, Journal of the Royal Statistical Society, Series B, 41, 190–195.

    Google Scholar 

  34. Hawkins, Dollena S., David M. Allen, and Arnold J. Stromberg (2001), Determining the Number of Components in Mixtures of Linear Models, Computational Statistics and Data Analysis 38, 15–48.

    Article  Google Scholar 

  35. Henseler, Jörg and Wynne W. Chin (2010), A Comparison of Approaches for the Analysis of Interaction Effects Between Latent Variables Using Partial Least Squares Path Modeling, Structural Equation Modeling 17, 82–109.

    Article  Google Scholar 

  36. Henseler, Jörg, Christian M. Ringle, and Rudolf R. Sinkovics (2009), The Use of Partial Last Squares Path Modeling in International Marketing, in Rudolf R. Sinkovics and Pervez N. Ghauri (eds.), Advances in International Marketing, Vol. 19, Bingley: Emerald, 277–320.

    Google Scholar 

  37. Henson, James M., Steven P. Reise, and Kevin H. Kim (2007), Detecting Mixtures from Structural Model Differences Using Latent Variable Mixture Modeling: A Comparison of Relative Fit Statistics, Structural Equation Modeling 14, 202–226.

    Article  Google Scholar 

  38. Hui, Baldwin S. and Herman Wold (1982), Consistency and Consistency at Large of Partial Least Squares Estimates, in Herman Wold and Karl G. Jöreskog (eds.), Systems Under Indirect Observation, Part II, Amsterdam: North-Holland, 119–130.

    Google Scholar 

  39. Hurvich, Clifford M. and Chih-Ling Tsai (1989), Regression and Time Series Model Selection in Small Samples, Biometrika 76, 297–307.

    Article  Google Scholar 

  40. Jedidi, Kamel, Harsharanjeet S. Jagpal, and Wayne S. DeSarbo (1997a), Finite-Mixture Structural Equation Models for Response-Based Segmentation and Unobserved Heterogeneity, Marketing Science 16, 39–59.

    Article  Google Scholar 

  41. Jedidi, Kamel, Harsharanjeet S. Jagpal, and Wayne S. DeSarbo (1997b), STEMM: A General Finite Mixture Structural Equation Model, Journal of Classification 14, 23–50.

    Article  Google Scholar 

  42. Jöreskog, Karl G. and Herman Wold (1982), The ML and PLS Techniques For Modeling with Latent Variables: Historical and Comparative Aspects, in Herman Wold and Karl G. Jöreskog (eds.), Systems Under Indirect Observation, Part I, Amsterdam: North-Holland, 263–270.

    Google Scholar 

  43. Liang, Zhengrong, Ronald J. Jaszczak, and R. Edward Coleman (1992), Parameter Estimation of Finite Mixtures Using the EM Algorithm and Information Criteria with Applications to Medical Image Processing, IEEE Transactions on Nuclear Science 39, 1126–1133.

    Article  Google Scholar 

  44. Lin, Ting H. and C. Mitchell Dayton (1997), Model Selection Information Criteria for Non-Nested Latent Class Models, Journal of Educational and Behavioral Statistics 22, 249–264.

    Article  Google Scholar 

  45. Lohmöller, Jan-Bernd (1989), Latent Variable Path Modelling with Partial Least Squares, Heidelberg: Physica.

    Book  Google Scholar 

  46. Mattson, Stefan (1997), How to Generate Non-Normal Data for Simulation of Structural Equation Models, Multivariate Behavioral Research 32, 355–373.

    Article  Google Scholar 

  47. McLachlan, Geoffrey J. and Kaye E. Basford (1988), Mixture Models: Inference and Applications to Clustering, New York, NY: Marcel Dekker.

    Google Scholar 

  48. McLachlan, Geoffrey J. and David Peel (2000), Finite Mixture Models, New York, NY: Wiley and Sons.

    Book  Google Scholar 

  49. Mooi, Erik A. and Marko Sarstedt (2011), A Concise Guide to Market Research. The Process, Data and Methods using IBM SPSS Statistics, Berlin: Springer.

    Book  Google Scholar 

  50. Muthén, Bent O. (2008), Latent Variable Hybrids. Overview of Old and New Methods, in Gregory R. Hancock and Karen M. Samuelsen (eds.), Advances in Latent Variable Mixture Models, Charlotte, CN: Information Age Publishing, 1–24.

    Google Scholar 

  51. Oliveira-Brochado, Ana and Francisco V. Martins (2006), Examining the Segment Retention Problem for the “Group Satellite” Case, FEP Working Papers, retrieved from http://www.fep.up.pt/investigacao/workingpapers/06.07.04_WP220_brochadomartins.pdf

    Google Scholar 

  52. Paxton, Pamela, Patrick J. Curran, Kenneth A. Bollen, Jim Kirby, and Feinian Chen (2001), Monte Carlo Experiments: Design and Implementation, Structural Equation Modeling 8, 287–312.

    Article  Google Scholar 

  53. Ramaswamy, Venkatram, Wayne S. Desarbo, and David J. Reibstein (1993), An Empirical Pooling Approach for Estimating Marketing Mix Elasticities with PIMS Data, Marketing Science 12, 103–124.

    Article  Google Scholar 

  54. Reinartz, Werner J., Michael Haenlein, and Jörg Henseler (2009), An Empirical Comparison of the Efficacy of Covariance-Based and Variance-Based SEM, International Journal of Market Research 26, 332–344.

    Article  Google Scholar 

  55. Rigdon, Edward E., Christian M. Ringle, and Marko Sarstedt (2010), Structural Modeling of Heterogeneous Data with Partial Least Squares, in Naresh K. Malhotra (ed.), Review of Marketing Research, Vol. 7, Bingley: Emerald, 255–296.

    Article  Google Scholar 

  56. Ringle, Christian M. (2006), Segmentation for Path Models and Unobserved Heterogeneity: The Finite Mixture Partial Least Squares Approach, Research Papers on Marketing and Retailing, retrieved from http://www.ibl-unihh.de/RP035.pdf.

    Google Scholar 

  57. Ringle, Christian M. and Rainer Schlittgen (2007), A Genetic Segmentation Approach for Uncovering and Separating groups of Data in PLS Path Modeling, in Harald Martens, Tormod Næs, and Magni Martens (eds.), PLS and Related Methods–Proceedings of the PLS’07 International Symposium, Ås; Matforsk, 75–78.

    Google Scholar 

  58. Ringle, Christian M., Sven Wende, and Alexander Will (2005a), Customer Segmentation with FIMIX-PLS, in Thomàs Aluja, Josep Casanovas, Vincenzo Esposito Vinzi, Alain Morrineau, and Michel Tenenhaus (eds.), PLS and Related Methods–Proceedings of the PLS’05 International Symposium, Paris: Decisia, 507–514.

    Google Scholar 

  59. Ringle, Christian M., Sven Wende, and Alexander Will (2005b), SmartPLS 2.0 (M3) beta, http://www.smartpls.de.

    Google Scholar 

  60. Ringle, Christian M., Oliver Götz, Martin Wetzels, and Bradley Wilson (2009), On the Use of Formative Measurement Specifications in Structural Equation Modeling: A Monte Carlo Simulation Study to Compare Covariance-based and Partial Least Squares Model Estimation Methodologies, in METEOR Research Memoranda (RM/09/014): Maastricht University.

    Google Scholar 

  61. Ringle, Christian M., Marko Sarstedt, and Erik A. Mooi (2010), Response-Based Segmentation Using FIMIX-PLS, in Robert Stahlbock, Sven F. Crone, and Stefan Lessmann (eds.), Annals of Information Systems, Vol. 48, Berlin: Springer, 19–49.

    Article  Google Scholar 

  62. Ringle, Christian M., Marko Sarstedt, and Rainer Schlittgen (2010), Finite Mixture and Genetic Algorithm Segmentation in Partial Least Squares Path Modeling: Identification of Multiple Segments in a Complex Path Model, in Andreas Fink, Berthold Lausen, Wilfried Seidel, and Alfred Ultsch (eds.), Advances in Data Analysis, Data Handling and Business Intelligence. Berlin/Heidelberg: Springer, 167–176.

    Google Scholar 

  63. Ringle, Christian M., Sven Wende, and Alexander Will (2010), The Finite Mixture Partial Least Squares Approach: Methodology and Application, in Vincenzo Esposito Vinzi, Wynne W. Chin, Jörg Henseler, and Huiwen Wang (eds.), Handbook of Partial Least Squares: Concepts, Methods and Applications in Marketing and Related Fields, Berlin/Heidelberg: Springer, 195–218.

    Chapter  Google Scholar 

  64. Roubens, Marc (1978), Pattern Classification Problems and Fuzzy Sets, Fuzzy Sets and Systems 1, 239–253.

    Article  Google Scholar 

  65. Sarstedt, Marko (2008a), A Review of Recent Approaches for Capturing Heterogeneity in Partial Least Squares Path Modelling, Journal of Modelling in Management 3, 140–161.

    Article  Google Scholar 

  66. Sarstedt, Marko (2008b), Market Segmentation with Mixture Regression Models: Understanding Measures that Guide Model Selection, Journal of Targeting, Measurement and Analysis for Marketing 16, 228–246.

    Article  Google Scholar 

  67. Sarstedt, Marko and Christian M. Ringle (2010), Treating Unobserved Heterogeneity in PLS Path Modeling. A Comparison of FIMIX-PLS with Different Data Analysis Strategies, Journal of Applied Statistics 37, 1299–1318.

    Article  Google Scholar 

  68. Sarstedt, Marko and Matthias P. Schloderer (2010), Developing a Measurement Approach for Reputation of Non-Profit Organizations, International Journal of Nonprofit and Voluntary Sector Marketing 15, 276–299.

    Google Scholar 

  69. Sarstedt, Marko, Manfred Schwaiger, and Christian M. Ringle (2009), Do We Fully Understand the Critical Success Factors of Customer Satisfaction with Industrial Goods?–Extending Festge and Schwaiger’s Model to Account for Unobserved Heterogeneity, Journal of Business Market Management 3, 185–206.

    Article  Google Scholar 

  70. Scheer, Burkhard (2008), Nutzenbasierte Marktsegmentierung: Eine kaufprozessorientierte empirische Untersuchung zur Wirkungsmessung von Marketing-Aktivitäten, Wiesbaden: DUV.

    Google Scholar 

  71. Schwarz, Gideon (1978), Estimating the Dimension of a Model, The Annals of Statistics 6, 461–464.

    Article  Google Scholar 

  72. Wagner, Tillmann, Thorsten Hennig-Thurau, and Thomas Rudolph (2009), Does Customer Demotion Jeopardize Loyalty?, Journal of Marketing 73, 69–85.

    Article  Google Scholar 

  73. Wedel, Michel and Wagner A. Kamakura (2000), Market Segmentation: Conceptual and Methodological Foundations, 2nd edition, Boston, NE et al.: Kluwer Academic Publishers.

    Book  Google Scholar 

  74. Wold, Herman (1982), Soft Modeling: The Basic Design and Some Extensions, in Karl G. Jöreskog and Herman Wold (eds.), Systems under Indirect Observation. Causality–Structure–Prediction, Part II, Amsterdam: North Holland, 1–54.

    Google Scholar 

  75. Wu, C. F. Jeff (1983), On the Convergence Properties of the EM Algorithm, Annals of Statistics 11, 95–103.

    Article  Google Scholar 

  76. Yang, Chih-Chien and Yang, Chih-Chiang (2007), Separating Latent Classes by Information Criteria, Journal of Classification 24, 183–203.

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Marko Sarstedt.

Additional information

The authors would like to thank the anonymous reviewers and the area editor for their helpful comments on prior versions of the manuscript.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sarstedt, M., Becker, JM., Ringle, C.M. et al. Uncovering and Treating Unobserved Heterogeneity with FIMIX-PLS: Which Model Selection Criterion Provides an Appropriate Number of Segments?. Schmalenbach Bus Rev 63, 34–62 (2011). https://doi.org/10.1007/BF03396886

Download citation

JEL-Classification

  • C39
  • M31

Keywords

  • FIMIX-PLS
  • Finite Mixture Modeling
  • Model Selection
  • Partial Least Squares (PLS)
  • Segmentation
  • Structural Equation Modeling