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Genetic algorithm segmentation in partial least squares structural equation modeling

Abstract

When applying the partial least squares structural equation modeling (PLS-SEM) method, the assumption that the data stem from a single homogeneous population is often unrealistic. For the full set of data, unobserved heterogeneity in the PLS path model estimates may result in misleading interpretations. This research presents the PLS genetic algorithm segmentation (PLS-GAS) method to account for unobserved heterogeneity in the path model estimates. The results of a simulation study guide an assessment of this novel approach. PLS-GAS allows for uncovering unobserved heterogeneity and identifying different groups within a data set. In an application on customer satisfaction data and the American customer satisfaction index model, the method identifies distinctive group-specific PLS path model estimates which allow for a further differentiated interpretation of the results.

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Notes

  1. 1.

    Wold (1982) differentiates between Mode A and Mode B measurement models. In Mode A, the weight relations are from the latent variable to the associated manifest variables; in Mode B, the weight relations are from the manifest variables to the associated latent variable. In line with Wold (1982), we refer to Mode C path model constellations if each of Modes A and B was chosen at least once in the model.

  2. 2.

    Note that Becker et al. (2013) recently presented another segmentation approach for PLS-SEM: PLS prediction-oriented segmentation (PLS-POS). The comparison of PLS-GAS and PLS-POS remains an issue for future research.

  3. 3.

    To determine the number of individuals and generations, we examined these parameters’ effects on the fitness. The results revealed only marginal effects of the population size for higher numbers of generations.

  4. 4.

    In this study, we generate highly non-normal data with a skewness of 6.183 and an excess (resulting from the difference between two log-normal distributions) of 33.067. See the Online Appendix II (http://www.pls-sem.com/orsp/oa.pdf) for further information on the data generation procedure.

  5. 5.

    Although such changes in Mode B measurement models do not change the error variances, the pre-specified weights of these measurement models are changed similarly—as in Mode A measurement models—in the computational experiments. When the weights are low (high), they have a pre-specified value of 0.20 (0.40). The mixed factor level assigns the high pre-specified weight of 0.40 to the first manifest variable and the low weight of 0.20 to the last manifest variable per Mode B measurement model; in the mixed factor level constellation, weights linearly increase from 0.20 to 0.40.

  6. 6.

    See Equation 16 in Online Appendix II (http://www.pls-sem.com/orsp/oa.pdf).

  7. 7.

    For two segments, relative segment sizes are 50 %/50 % (balanced) and 75 %/25 % (unbalanced); for three segments, relative segment sizes are 33 %/33 %/33 % (balanced) and 60 %/20 %/20 % (unbalanced).

  8. 8.

    The data sets that have been used as input for the analyses are available at http://www.pls-sem.com/orsp/data.zip.

  9. 9.

    The GAUSS program to run PLS-GAS is available at http://www.pls-sem.com/orsp/program.zip.

  10. 10.

    Note that PLS-GAS always meets the global optimum solution when no error is present.

  11. 11.

    See Equation 16 in Online Appendix II (http://www.pls-sem.com/orsp/oa.pdf).

  12. 12.

    See the Online Appendix IV (http://www.pls-sem.com/orsp/oa.pdf) for the results of these additional analyses.

  13. 13.

    The data were provided by Fornell, Claes. American Customer Satisfaction Index, 1999 [Computer file]. ICPSR04436-v1. Ann Arbor, MI: University of Michigan. Ross School of Business, National Quality Research Center/Reston, VA: Wirthlin Worldwide [producers], 1999. Ann Arbor, MI: Inter-University Consortium for Political and Social Research [distributor], 2006-06-09. We would like to thank Claes Fornell and the ICPSR for making the data available.

  14. 14.

    In addition to these recommendations, one finds various recommendations on the use of the PLS-SEM method and the evaluation of results in prior literature; examples include: Chin (1998); Chin (2010), Falk and Miller (1992), Götz et al. (2010), Haenlein and Kaplan (2004), Henseler et al. (2009); Henseler et al. (2012), Lohmöller (1989), Roldán and Sánchez-Franco (2012), Sosik et al. (2009), Tenenhaus et al. (2005).

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Acknowledgments

The authors thank the area editor and four anonymous reviewers for their helpful comments as well as the time and care devoted to our research.

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Correspondence to Marko Sarstedt.

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The authors presented the PLS-GAS method at the following conferences: 5th International Symposium of PLS and Related Methods, Ås, Norway, 2007; the 32th Annual Conference of the German Classification Society—Gesellschaft für Klassifikation (GfKl), Hamburg, Germany, 2008; the Australian & New Zealand Marketing Academy (ANZMAC) Annual Conference, Melbourne, Australia, 2009; and the Korean Academy of Marketing Science (KAMS) Global Marketing Conference, Tokyo, Japan, 2010.

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Ringle, C.M., Sarstedt, M. & Schlittgen, R. Genetic algorithm segmentation in partial least squares structural equation modeling. OR Spectrum 36, 251–276 (2014). https://doi.org/10.1007/s00291-013-0320-0

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Keywords

  • Genetic algorithm
  • Partial least squares
  • Path modeling
  • PLS-SEM
  • Segmentation
  • Structural equation modeling