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The Proportional Hazard Model for Purchase Timing: A Comparison of Alternative Specifications

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  • Seetharaman, P B
  • Chintagunta, Pradeep K

Abstract

We use the proportional hazard model (PHM) to study purchase-timing behavior of households in two product categories: laundry detergents and paper towels. The PHM decomposes a household's instantaneous probability of buying the product at a point of time into two components: the baseline hazard that captures the household's intrinsic purchase pattern over time and the covariate function that captures the effects of marketing variables on the household's purchase timing decision. We compare the continuous-time and discrete-time PHMs, where the latter explicitly accounts for households' shopping trips that do not involve purchase of the product. We find that the discrete-time PHM empirically outperforms the continuous-time PHM in terms of explaining the observed purchase outcomes. We compare five different parametric specifications of the baseline hazard, and find that the three-parameter expo-power specification outperforms the exponential, Erlang-2, Weibull, and log-logistic specifications. We use a cause specific, competing-risks PHM to distinguish between two types of purchase events that differ in terms of whether or not they were preceded by a shopping trip that involved purchase of the product. Such a cause-specific, competing-risks PHM is shown to outperform the traditional discrete-time PHM. We then estimate a nonparametric version of the PHM and find that it does not offer any additional insights compared to the parsimonious parametric PHM. Finally, we accommodate unobserved heterogeneity across households by allowing all of the parameters of the PHM to follow a discrete distribution across households whose locations and supports are nonparametrically estimated from the data. We find evidence for substantial unobserved heterogeneity in the data, both in the parameters of marketing variables and in the baseline hazards. This study will be a useful reference to researchers hoping to use the PHM to study event times.

Suggested Citation

  • Seetharaman, P B & Chintagunta, Pradeep K, 2003. "The Proportional Hazard Model for Purchase Timing: A Comparison of Alternative Specifications," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 368-382, July.
  • Handle: RePEc:bes:jnlbes:v:21:y:2003:i:3:p:368-82
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    6. P. B. Seetharaman, 2004. "The Additive Risk Model for Purchase Timing," Marketing Science, INFORMS, vol. 23(2), pages 234-242, March.
    7. Marko Sarstedt & Sebastian Scharf & Alexander Thamm & Michael Wolff, 2010. "Die Prognose von Serviceintervallen mit der Hazard-Raten-Analyse – Ergebnisse einer empirischen Studie im Automobilmarkt," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 20(3), pages 269-283, April.
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    10. Vishal P. Singh & Karsten T. Hansen & Robert C. Blattberg, 2006. "Market Entry and Consumer Behavior: An Investigation of a Wal-Mart Supercenter," Marketing Science, INFORMS, vol. 25(5), pages 457-476, September.
    11. Olearius, Gotz & Roosen, Jutta & Drescher, Larissa S., 2011. "A Hazard Analysis Of Consumers’ Switching Behaviour In German Food Retailing For Dairy Products," 51st Annual Conference, Halle, Germany, September 28-30, 2011 114516, German Association of Agricultural Economists (GEWISOLA).
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    13. A. Prinzie & D. Van Den Poel, 2007. "Predicting home-appliance acquisition sequences: Markov/Markov for Discrimination and survival analysis for modeling sequential information in NPTB models," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 07/442, Ghent University, Faculty of Economics and Business Administration.
    14. Wendy W. Moe & Peter S. Fader, 2004. "Dynamic Conversion Behavior at E-Commerce Sites," Management Science, INFORMS, vol. 50(3), pages 326-335, March.
    15. 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.
    16. Andreeva, Galina & Ansell, Jake & Crook, Jonathan, 2007. "Modelling profitability using survival combination scores," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1537-1549, December.
    17. Ryosuke Igari & Takahiro Hoshino, 2017. "Bayesian Data Combination Approach for Repeated Durations under Unobserved Missing Indicators: Application to Interpurchase-Timing in Marketing," Keio-IES Discussion Paper Series 2017-015, Institute for Economics Studies, Keio University.
    18. Young-Hoon Park & Peter S. Fader, 2004. "Modeling Browsing Behavior at Multiple Websites," Marketing Science, INFORMS, vol. 23(3), pages 280-303, May.
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    22. repec:eee:ijrema:v:29:y:2012:i:3:p:292-305 is not listed on IDEAS
    23. Yi Qian & Hui Xie, 2011. "No Customer Left Behind: A Distribution-Free Bayesian Approach to Accounting for Missing Xs in Marketing Models," Marketing Science, INFORMS, vol. 30(4), pages 717-736, July.
    24. Surendra Rajiv & Junhong Chu & Zhiying Jiang, 2015. "Publication, Citation, Career Development, and Recent Trends: Empirical Evidence for Quantitative Marketing Researchers," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 2(1), pages 71-90, March.
    25. Theoharakis, Vasilis & Vakratsas, Demetrios & Wong, Veronica, 2007. "Market-level information and the diffusion of competing technologies: An exploratory analysis of the LAN industry," Research Policy, Elsevier, vol. 36(5), pages 742-757, June.

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