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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.

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 21 (2003)
Issue (Month): 3 (July)
Pages: 368-82

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Handle: RePEc:bes:jnlbes:v:21:y:2003:i:3:p:368-82

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Cited by:
  1. 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).
  2. Vardit Landsman & Moshe Givon, 2010. "The diffusion of a new service: Combining service consideration and brand choice," Quantitative Marketing and Economics, Springer, vol. 8(1), pages 91-121, March.
  3. 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.
  4. 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.
  5. Bhat, Chandra R. & Srinivasan, Sivaramakrishnan & Axhausen, Kay W., 2005. "An analysis of multiple interepisode durations using a unifying multivariate hazard model," Transportation Research Part B: Methodological, Elsevier, vol. 39(9), pages 797-823, November.
  6. Lee, Backjin & Timmermans, Harry J.P., 2007. "A latent class accelerated hazard model of activity episode durations," Transportation Research Part B: Methodological, Elsevier, vol. 41(4), pages 426-447, May.
  7. David Bell & Sangyoung Song, 2007. "Neighborhood effects and trial on the internet: Evidence from online grocery retailing," Quantitative Marketing and Economics, Springer, vol. 5(4), pages 361-400, December.

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