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Purchase timing models in marketing: a review

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Abstract

In this work we review various approaches to modeling the purchase behavior of consumers in marketing. Special emphasis is given to the timing of purchases. We also discuss in detail a new approach which models the hazard function in a flexible dynamic way thus yielding self-exciting phenomena. In particular our approach is able to incorporate seasonal and advertising effects and past purchase decisions. The method is applied to panel data for fast moving consumer goods.

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References

  • Aalen, O.O., Gjessing, H.K.: Understanding the shape of the hazard rate: A process point of view. Stat. Sci. 16(1), 1–22 (2001)

    MathSciNet  MATH  Google Scholar 

  • Ailawadi, K.L., Neslin, S.A.: The effect of promotion on consumption: Buying more and consuming it faster. J. Mark. Res. 35(3), 390–398 (1998)

    Article  Google Scholar 

  • Akaike, H.: A new look at statistical model identification. IEEE Trans. Autom. Control 19(6), 716–723 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  • Allenby, G.M., Lenk, P.J.: Modeling household purchase behavior with logistic normal regression. J. Am. Stat. Assoc. 89(428), 1218–1231 (1994)

    Article  Google Scholar 

  • Altmann, T., Schmidt, T., Stute, W.: A shot noise model for financial assets. Int. J. Theor. Appl. Finance 11(1), 87–106 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Ben-Akiva, M., Lerman, S.R.: Discrete Choice Analysis. MIT Press, Cambridge (1985)

    Google Scholar 

  • Bucklin, R.E., Lattin, J.M.: A two-state model of purchase incidence and brand choice. Mark. Sci. 10(1), 24–39 (1991)

    Article  Google Scholar 

  • Chatfield, C., Goodhardt, G.J.: A consumer purchasing model with Erlang interpurchase times. J. Am. Stat. Assoc. 68(344), 828–835 (1973)

    Article  Google Scholar 

  • Chatfield, C., Ehrenberg, A.S.C., Goodhardt, G.J.: Progress on a simplified model of stationary purchasing behavior. J. R. Stat. Soc. A 29(3), 317–367 (1966)

    Google Scholar 

  • Chintagunta, P.K.: Investigating purchase incidence, brand choice and purchase quantity decisions of households. Mark. Sci. 12(2), 184–208 (1993)

    Article  Google Scholar 

  • Chintagunta, P.K.: Inertia and variety seeking in a model of brand-purchase timing. Mark. Sci. 17(3), 253–270 (1998)

    Article  Google Scholar 

  • Chintagunta, P.K., Haldar, S.: Investigating purchase timing behavior in two related product categories. J. Mark. Res. 35(1), 43–53 (1998)

    Article  Google Scholar 

  • Chintagunta, P.K., Prasad, A.R.: An empirical investigation of the dynamic McFadden model of purchase timing and brand choice: Implications for market structure. J. Bus. Econ. Stat. 16(1), 2–12 (1998)

    Article  Google Scholar 

  • Chintagunta, P.K., Jain, D.C., Vilcassim, N.J.: Investigating heterogeneity in brand preferences in logit models for panel data. J. Mark. Res. 28(4), 417–428 (1991)

    Article  Google Scholar 

  • Deighton, J., Henderson, C.M., Neslin, S.A.: The effects of advertising on brand switching and repeat purchasing. J. Mark. Res. 31(1), 28–43 (1994)

    Article  Google Scholar 

  • East, R., Hammond, K.: The erosion of repeat-purchase loyalty. Mark. Lett. 7(2), 163–171 (1996)

    Article  Google Scholar 

  • Ehrenberg, A.S.C.: The pattern of consumer purchases. Appl. Stat. 8(1), 26–41 (1959)

    Article  Google Scholar 

  • Ehrenberg, A.S.C.: Repeat-Buying: Facts, Theory And Applications. Charles Griffin/Oxford University Press, New York/London (1988)

    Google Scholar 

  • Ehrenberg, A.S.C.: Comments on how advertising works. Mark. Res. Today 20(3), 167–169 (1992)

    Google Scholar 

  • Ehrenberg, A.S.C.: Repetitive advertising and the consumer. J. Advert. Res. 40(6), 39–49 (2000)

    Google Scholar 

  • Fader, P.S., Hardie, B.G.S.: Modeling the evolution of repeat buying (1999). Available at http://www-marketing.wharton.upenn.edu/ideas/pdf/98-031.pdf

  • Franses, P.H., Paap, R.: Quantitative Models in Marketing Research. University Press, Cambridge (2001)

    Google Scholar 

  • Gönül, F., Srinivasan, K.: Consumer purchase behavior in a frequently bought product category: Estimation issues and managerial insights from a hazard function model with heterogeneity. J. Am. Stat. Assoc. 88(424), 1219–1227 (1993a)

    Article  Google Scholar 

  • Gönül, F., Srinivasan, K.: Modeling multiple sources of heterogeneity in multinomial logit models: Methodological and managerial issues. Mark. Sci. 12(3), 213–229 (1993b)

    Article  Google Scholar 

  • Gould, B.W.: Consumer promotion and purchase timing: the case of cheese. Appl. Econ. 29(4), 445–457 (1997)

    Article  Google Scholar 

  • Günther, M., Vossebein, U., Wildner, R.: Marktforschung mit Panels. Gabler, Wiesbaden (1998)

    Google Scholar 

  • Gupta, S.: Stochastic models of interpurchase time with time-dependent covariates. J. Mark. Res. 28(1), 1–15 (1991)

    Article  Google Scholar 

  • Heckman, J., Singer, B.: A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica 52(2), 271–320 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  • Hruschka, H.: Marketing-Entscheidungen. Vahlen, München (1996)

    Google Scholar 

  • Jain, D.C., Vilcassim, N.J.: Estimating household purchase rates for consumer non-durable goods. Appl. Stoch. Models Data Anal. 10, 15–26 (1994)

    Article  Google Scholar 

  • Jain, D.C., Vilcassim, N.J., Chintagunta, P.K.: A random-coefficients logit brand-choice model applied to panel data. J. Bus. Econ. Stat. 12(3), 317–328 (1994)

    Article  Google Scholar 

  • Jones, J.M.: A composite heterogeneous model for brand choice behavior. Manag. Sci. 19(5), 499–509 (1973)

    Article  MATH  Google Scholar 

  • Jones, J.P.: Over-promise and under-delivery. Mark. Res. Today 19(4), 195–203 (1991)

    Google Scholar 

  • Kopperschmidt, K.: Statistische Analyse von Kaufverhaltensmodellen. Doctoral Thesis, Gießen (2005)

  • Lancaster, T.: The Econometric Analysis of Transition Data. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  • Leeflang, P.S.H.: Mathematical Models in Marketing, a Survey, the Stage of Development, Some Extensions and Applications. H.E. Stenfert Kroese, Leiden (1974)

    Google Scholar 

  • Leeflang, P.S.H., Wittink, D.R., Wedel, M., Naert, P.A.: Building Models for Marketing Decisions. Kluwer Academic, Dordrecht (2000)

    Google Scholar 

  • Maier, G., Weiss, P.: Modelle diskreter Entscheidungen—Theorie und Anwendung in den Sozial- und Wirtschaftswissenschaften. Springer, New York (1989)

    Google Scholar 

  • Massy, W.F., Montgomery, D.B., Morrison, D.G.: Stochastic Models of Buying Behavior. MIT Press, Cambridge (1970)

    Google Scholar 

  • Mino, H.: Parameter estimation of the intensity process of self-exciting point processes using the EM algorithm. IEEE Trans. Instrum. Meas. 50(3), 658–664 (2001)

    Article  Google Scholar 

  • Morrison, D.G., Schmittlein, D.C.: Generalizing the NBD model for customer purchases: What are the implications and is it worth the effort? J. Bus. Econ. Stat. 6(2), 145–159 (1988)

    Article  Google Scholar 

  • Narendranathan, W., Stewart, M.B.: How does the benefit vary as unemployment spells lenghten? J. Appl. Econom. 8(4), 361–381 (1993)

    Article  Google Scholar 

  • Neslin, S.A., Schneider Stone, L.G.: Consumer inventory sensitivity and the postpromotion dip. Mark. Lett. 7(1), 77–94 (1996)

    Article  Google Scholar 

  • Poulsen, C.S.: Mixed Markov and latent Markov modeling applied to brand choice behavior. Int. J. Res. Mark. 7, 5–19 (1990)

    Article  Google Scholar 

  • Ramsay, J.O., Silverman, B.W.: Functional Data Analysis. Springer, New York (1997)

    MATH  Google Scholar 

  • Rosenbach, M.: Werbung: ‘Weil isch es mir wert bin’. Der Spiegel 49, Hamburg (2001)

    Google Scholar 

  • Schmidt, T., Stute, W.: Shot-noise processes and the minimal martingale measure. Stat. Probab. Lett. 77, 1332–1338 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Sichel, H.S.: Repeat buying and the generalized inverse Gaussian–Poisson distribution. Appl. Stat. 31(3), 193–204 (1982)

    Article  Google Scholar 

  • Sikkel, D., Hoogendoorn, A.W.: Models for monthly penetrations with incomplete panel data. Stat. Neerl. 49, 378–391 (1995)

    Article  Google Scholar 

  • Snyder, D.L., Miller, M.I.: Random Point Processes in Time and Space. Springer, New York (1991)

    MATH  Google Scholar 

  • Sueyoshi, G.T.: A class of binary response models for grouped duration data. J. Appl. Econom. 10(4), 411–431 (1995)

    Article  Google Scholar 

  • Tapiero, C.S.: The NBD repeat purchase process and M/G/∞ queues. Int. J. Prod. Econ. 63(2), 141–145 (2000)

    Article  MathSciNet  Google Scholar 

  • Vakratsas, D.: Household cost effects on purchase timing decisions: do demographics matter? J. Consum. Mark. 15(1), 6–22 (1998)

    Article  Google Scholar 

  • Vilcassim, N.J., Jain, D.C.: Modeling purchase-timing and brand-switching behavior incorporating explanatory variables and unobserved heterogeneity. J. Mark. Res. 28(1), 29–41 (1991)

    Article  Google Scholar 

  • Wangler, A.: Heterogenitätsprobleme in der Verlaufsdatenanalyse. Peter Lang GmbH, Europäischer Verlag der Wissenschaften, Frankfurt am Main (1997)

    Google Scholar 

  • Wedel, M., DeSarbo, W.S., Bult, J.R., Ramaswamy, V.: A latent class Poisson regression model for heterogeneous count data. J. Appl. Econom. 8(4), 397–411 (1993)

    Article  Google Scholar 

  • Wedel, M., Kamakura, W.A., DeSarbo, W.S., Ter Hofstede, F.: Implications for asymmetry, nonproportionality and heterogeneity in brand switching from piece-wise exponential mixture hazard models. J. Mark. Res. 32(4), 457–462 (1995)

    Article  Google Scholar 

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Kopperschmidt, K., Stute, W. Purchase timing models in marketing: a review. AStA Adv Stat Anal 93, 123–149 (2009). https://doi.org/10.1007/s10182-008-0096-8

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