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The Additive Risk Model for Purchase Timing

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  • P. B. Seetharaman

    (John M. Olin School of Business, Washington University, Campus Box 1133, One Brookings Drive, St. Louis, Missouri 63130-4899)

Abstract

This paper proposes the (ARM), first used by Aalen (1980), to explain households' interpurchase times. Unlike the Proportional Hazard Model (PHM), first proposed by Cox (1972), the ARM incorporates the effects of covariates on the individual hazard function in an (as opposed to ) manner. While a large number of previous studies on interpurchase timing have dealt with the question of correctly specifying the parametric distribution for interpurchase times, no study has explicitly investigated the question of correctly specifying the effects of covariates in the model. This study looks at this issue. We propose an ARM that is suitable for purchase-timing data, and compare its empirical performance to that of the PHM and the Accelerated Failure Time Model (AFTM) using scanner panel data on laundry detergents, paper towels, and toilet tissue. We find that the ARM not only estimates and validates the observed interpurchase times better than existing models, but also recovers a time-varying price elasticity and shows a high degree of robustness in the estimated covariate effects to alternative parametric specifications of the baseline hazard. The estimates of covariate parameters under the PHM, on the other hand, are highly sensitive to alternative parametric specifications of the baseline hazard.

Suggested Citation

  • P. B. Seetharaman, 2004. "The Additive Risk Model for Purchase Timing," Marketing Science, INFORMS, vol. 23(2), pages 234-242, March.
    • Handle: RePEc:inm:ormksc:v:23:y:2004:i:2:p:234-242
    DOI: 10.1287/mksc.1030.0021
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    References listed on IDEAS

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    Cited by:

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    2. Koray Cosguner & P. B. (Seethu) Seetharaman, 2022. "Dynamic Pricing for New Products Using a Utility-Based Generalization of the Bass Diffusion Model," Management Science, INFORMS, vol. 68(3), pages 1904-1922, March.
    3. Fok, Dennis & Paap, Richard & Franses, Philip Hans, 2012. "Modeling dynamic effects of promotion on interpurchase times," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3055-3069.
    4. Zhang, Qin & Seetharaman, P.B. & Narasimhan, Chakravarthi, 2012. "The Indirect Impact of Price Deals on Households’ Purchase Decisions Through the Formation of Expected Future Prices," Journal of Retailing, Elsevier, vol. 88(1), pages 88-101.
    5. Xinxue (Shawn) Qu & Aslan Lotfi & Dipak C. Jain & Zhengrui Jiang, 2022. "Predicting upgrade timing for successive product generations: An exponential‐decay proportional hazard model," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2067-2083, May.
    6. Nitin Mehta, 2007. "Investigating Consumers' Purchase Incidence and Brand Choice Decisions Across Multiple Product Categories: A Theoretical and Empirical Analysis," Marketing Science, INFORMS, vol. 26(2), pages 196-217, 03-04.
    7. George, Morris & Kumar, V. & Grewal, Dhruv, 2013. "Maximizing Profits for a Multi-Category Catalog Retailer," Journal of Retailing, Elsevier, vol. 89(4), pages 374-396.
    8. Vardit Landsman & Moshe Givon, 2010. "The diffusion of a new service: Combining service consideration and brand choice," Quantitative Marketing and Economics (QME), Springer, vol. 8(1), pages 91-121, March.
    9. 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.
    10. Qiu, Guiyou & Papatla, Purushottam, 2008. "An empirical analysis of inter-acquisition time of free online content," Journal of Interactive Marketing, Elsevier, vol. 22(2), pages 19-27.

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