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Modeling Multivariate Distributions Using Copulas: Applications in Marketing

Author

Listed:
  • Peter J. Danaher

    () (Melbourne Business School, University of Melbourne, Carlton, Victoria 3053, Australia)

  • Michael S. Smith

    () (Melbourne Business School, University of Melbourne, Carlton, Victoria 3053, Australia)

Abstract

In this research we introduce a new class of multivariate probability models to the marketing literature. Known as "copula models," they have a number of attractive features. First, they permit the combination of any univariate marginal distributions that need not come from the same distributional family. Second, a particular class of copula models, called "elliptical copula," has the property that they increase in complexity at a much slower rate than existing multivariate probability models as the number of dimensions increase. Third, they are very general, encompassing a number of existing multivariate models and providing a framework for generating many more. These advantages give copula models a greater potential for use in empirical analysis than existing probability models used in marketing. We exploit and extend recent developments in Bayesian estimation to propose an approach that allows reliable estimation of elliptical copula models in high dimensions. Rather than focusing on a single marketing problem, we demonstrate the versatility and accuracy of copula models with four examples to show the flexibility of the method. In every case, the copula model either handles a situation that could not be modeled previously or gives improved accuracy compared with prior models.

Suggested Citation

  • Peter J. Danaher & Michael S. Smith, 2011. "Modeling Multivariate Distributions Using Copulas: Applications in Marketing," Marketing Science, INFORMS, vol. 30(1), pages 4-21, 01-02.
  • Handle: RePEc:inm:ormksc:v:30:y:2011:i:1:p:4-21
    as

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    File URL: http://dx.doi.org/10.1287/mksc.1090.0491
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    References listed on IDEAS

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    1. Rossi P. E & Gilula Z. & Allenby G. M, 2001. "Overcoming Scale Usage Heterogeneity: A Bayesian Hierarchical Approach," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 20-31, March.
    2. Dipak C. Jain & Naufel J. Vilcassim, 1991. "Investigating Household Purchase Timing Decisions: A Conditional Hazard Function Approach," Marketing Science, INFORMS, vol. 10(1), pages 1-23.
    3. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models," Journal of Econometrics, Elsevier, vol. 143(2), pages 291-316, April.
    4. Peter Xue‐Kun Song, 2000. "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 305-320, June.
    5. Smith, Michael & Kohn, Robert & Mathur, Sharat K., 2000. "Bayesian Semiparametric Regression: An Exposition and Application to Print Advertising Data," Journal of Business Research, Elsevier, vol. 49(3), pages 229-244, September.
    6. Michael Pitt & David Chan & Robert Kohn, 2006. "Efficient Bayesian inference for Gaussian copula regression models," Biometrika, Biometrika Trust, vol. 93(3), pages 537-554, September.
    7. David R. Bell & James M. Lattin, 1998. "Shopping Behavior and Consumer Preference for Store Price Format: Why “Large Basket” Shoppers Prefer EDLP," Marketing Science, INFORMS, vol. 17(1), pages 66-88.
    8. Smith M. & Kohn R., 2002. "Parsimonious Covariance Matrix Estimation for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1141-1153, December.
    9. Wendy W. Moe & Peter S. Fader, 2004. "Dynamic Conversion Behavior at E-Commerce Sites," Management Science, INFORMS, vol. 50(3), pages 326-335, March.
    10. Peter M. Guadagni & John D. C. Little, 1983. "A Logit Model of Brand Choice Calibrated on Scanner Data," Marketing Science, INFORMS, vol. 2(3), pages 203-238.
    11. David A. Schweidel & Peter S. Fader & Eric T. Bradlow, 2008. "A Bivariate Timing Model of Customer Acquisition and Retention," Marketing Science, INFORMS, vol. 27(5), pages 829-843, 09-10.
    12. Young-Hoon Park & Peter S. Fader, 2004. "Modeling Browsing Behavior at Multiple Websites," Marketing Science, INFORMS, vol. 23(3), pages 280-303, May.
    13. Danaher, Peter J. & Hardie, Bruce G.S., 2005. "Bacon With Your Eggs? Applications of a New Bivariate Beta-Binomial Distribution," The American Statistician, American Statistical Association, vol. 59, pages 282-286, November.
    14. Peter J. Danaher, 2002. "Optimal Pricing of New Subscription Services: Analysis of a Market Experiment," Marketing Science, INFORMS, vol. 21(2), pages 119-138, February.
    15. Morrison, Donald G & Schmittlein, David C, 1988. "Generalizing the NBD Model for Customer Purchases: What Are the Implications and Is It Worth the Effort?," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(2), pages 145-159, April.
    16. Morrison, Donald G & Schmittlein, David C, 1988. "Generalizing the NBD Model for Customer Purchases: What Are the Implications and Is It Worth the Effort? Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(2), pages 165-166, April.
    17. David C. Schmittlein & Donald G. Morrison & Richard Colombo, 1987. "Counting Your Customers: Who-Are They and What Will They Do Next?," Management Science, INFORMS, vol. 33(1), pages 1-24, January.
    18. Peter J. Danaher, 2007. "Modeling Page Views Across Multiple Websites with an Application to Internet Reach and Frequency Prediction," Marketing Science, INFORMS, vol. 26(3), pages 422-437, 05-06.
    19. Ser-Huang Poon, 2004. "Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 581-610.
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