, Volume 6, Issue 3, pp 257–277

Non-normal simultaneous regression models for customer linkage analysis

  • Jeffrey P. Dotson
  • Joseph Retzer
  • Greg M. Allenby


Simultaneous systems of equations with non-normal errors are developed to study the relationship between customer and employee satisfaction. Customers interact with many employees, and employees serve many customers, such that a one-to-one mapping between customers and employees is not possible. Analysis proceeds by relating, or linking, distribution percentiles among variables. Such analysis is commonly encountered in marketing when data are from independently collected samples. We demonstrate our model in the context of retail banking, where drivers of customer and employee satisfaction are shown to be percentile-dependent.


Bayesian analysis Customer satisfaction 

JEL classification

C11 C31 M31 


  1. Anderson, E. W., & Mittal, V. (2000). Strengthening the satisfaction-profit chain. Journal of Service Research, 3, 107–120 (Nov).CrossRefGoogle Scholar
  2. Anderson, E. W., & Sullivan, M. W. (1993). The antecedents and consequences of customer satisfaction for firms. Marketing Science, 12, 125–143 (Spring).CrossRefGoogle Scholar
  3. Fernandez, C., & Steel, M. F. J. (1998). On Bayesian modeling of fat tails and skewness. Journal of the American Statistical Association, 93, 359–371.CrossRefGoogle Scholar
  4. Greene, W. H. (2003). Econometric analysis. New Jersey: Prentice Hall.Google Scholar
  5. Heskett, J. L., Jones, T. O., Loveman, G. W., Earl Sasser Jr., W., & Schlesinger, L. A. (1994). Putting the service-profit chain to work. Harvard Business Review, 72, 164–170 (Mar/Apr).Google Scholar
  6. Heskett, J. L., Sasser Jr., W. E., & Schlesinger, L. A. (1997). The service profit chain. New York: Free Press.Google Scholar
  7. Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47, 263–291.CrossRefGoogle Scholar
  8. Kamakura, W. A., Mittal, V., de Rosa, F., & Mazzon, J. A. (2002). Assessing the service-profit chain. Marketing Science, 21(3), 294–317.CrossRefGoogle Scholar
  9. Koenker, R. (2005). Quantile regression. Cambridge: Cambridge University Press.Google Scholar
  10. Koenker, R., & Bassett Jr., G. (1978). Regression quantiles. Econometrica, 46, 33–50.CrossRefGoogle Scholar
  11. Kottas, A., & Krnjajic, M. (2007). Bayesian nonparametric modeling in quantile regression. Working paper, Santa Cruz: Department of Applied Mathematics and Statistics, University of California.Google Scholar
  12. Morgan, N. A., Anderson, E. W., & Mittal, V. (2005). Understanding firms’ customer satisfaction information usage. Journal of Marketing, 69, 131–151.CrossRefGoogle Scholar
  13. Mittal, V., Ross Jr., W. T., & Baldasare, P. M. (1998). The asymmetric impact of negative and positive attribute-level performance on overall satisfaction and repurchase intentions. Journal of Marketing, 62, 33–47.CrossRefGoogle Scholar
  14. Newton, M., & Raftery, A. (1994). Approximate Bayesian interference by the weighted likelihood bootstrap. Journal of the Royal Statistical Society Series B, 56, 3–48.Google Scholar
  15. Rossi, P. E., Allenby, G. M., & McCulloch, R. (2005). Bayesian statistics and marketing. New York: Wiley.Google Scholar
  16. Rust, R. T., & Chung, T. S. (2006). Marketing models of service and relationships. Marketing Science, 25, 560–580.CrossRefGoogle Scholar
  17. Streukens, S., & De Ruyter, K. (2004). Reconsidering nonlinearity and asymmetry in customer satisfaction and loyalty models: An empirical study in three retail service settings. Marketing Letters, 15, 99–111.CrossRefGoogle Scholar
  18. Yu, K., & Moyeed, R. A. (2001). Bayesian quantile regression. Statistics and Probability Letters, 54, 437–447.CrossRefGoogle Scholar
  19. Yu, K., & Zhang, J. (2005). A three-parameter asymmetric Laplace distribution and its extension. Communications in Statistics: Theory & Methods, 34, 1867–79.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Jeffrey P. Dotson
    • 1
  • Joseph Retzer
    • 2
  • Greg M. Allenby
    • 1
  1. 1.Fisher College of BusinessOhio State UniversityColumbusUSA
  2. 2.Maritz ResearchGraftonUSA

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