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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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    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. 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.
    5. 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.
    6. P. Seetharaman & Siddhartha Chib & Andrew Ainslie & Peter Boatwright & Tat Chan & Sachin Gupta & Nitin Mehta & Vithala Rao & Andrei Strijnev, 2005. "Models of Multi-Category Choice Behavior," Marketing Letters, Springer, vol. 16(3), pages 239-254, December.
    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.
    8. 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.
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