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Individual Demand Models

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Modeling Markets

Part of the book series: International Series in Quantitative Marketing ((ISQM))

Abstract

Big Data obtained through web search, digital media, e-commerce, mobile and social media have become important for understanding consumers’ behavior. Studying and modeling individual behavior has become more and more the focus in marketing research. Individual demand constitutes an important part of individual behavior, but we are now also able to study word-of-mouth (WOM-behavior), online-browsing

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Notes

  1. 1.

    See, for example, the Special Issues on Choice Models of Marketings Letters, vol 8(3), 1997; vol 10(3),1999; and Chandukala et al. (2007) .

  2. 2.

    The authors like to thank Hans Risselada who provided important information for this chapter.

  3. 3.

    Du and Kamakura (2008) .

  4. 4.

    The text of this subsection is based, a.o., on Franses and Paap (2001, Chapter 4) and Wooldridge (2012, Chapter 17) .

  5. 5.

    Economists, however, tend to favor the normality assumption for \(\varepsilon _{i}\) which is why the probit model is more popular than logit in econometrics (Wooldridge 2012, p. 562) .

  6. 6.

    We closely follow Franses and Paap (2001, p. 57) .

  7. 7.

    We closely follow Wieringa and Verhoef (2007) .

  8. 8.

    For marketing applications see, for example, Punj and Staelin (1978) ; Guadagni and Little (1983) ; Louvière and Hensher (1983) ; Carpenter and Lehmann (1985) ; Kamakura and Russell (1989) ; Chintagunta et al. (1991) ; Erdem (1996) ; Ainslie and Rossi (1998) ; Seetharaman (2004) ; Gilbride and Allenby (2006) ; Chandukala et al. (2007) . An overview of issues arising in logit model applications in marketing is provided by Malhotra (1984) ; McFadden (1986) ; Franses and Paap (2001, Chapter 5) ; Hruschka et al. (2004) .

  9. 9.

    See also Roberts and Lilien (1993) .

  10. 10.

    We assume that the hierarchical structure is consumer specific. See also Vanden Abeele and Gijsbrechts (1991) and Siddarth et al. (1995) .

  11. 11.

    We only consider so-called discrete-time Markov chains.

  12. 12.

    Massy et al. (1970, Chapter 3) .

  13. 13.

    We closely follow Gensler et al. (2007) .

  14. 14.

    Other examples of HMM’s in marketing are Liechty et al. (2003) ; Montgomery et al. (2004) ; Moon et al. (2007) ; Paas et al. (2007) ; Ebbes et al. (2010) ; Kumar et al. (2011) ; Schwartz et al. (2014) ; Zhang et al. (2014) .

  15. 15.

    Purchase quantity models at the product category level have often been used to explain the composition of shopping baskets. See, for example, Manchanda et al. (1999) ; Seetharaman et al. (2005) ; Blattberg et al. (2008, Chapter 13) ; Chen and Steckel (2012) .

  16. 16.

    See Sichel (1982) who has proposed the family of generalized inverse Gaussian distributions; Sikkel and Hoogendoorn (1995) who consider the inverse Gaussian, the lognormal and the Weibull distributions. Abe (2009) extends the Poisson purchase incidence model in several ways to account for drop outs of customers of a customer-base. See also: Fader et al. (2005) .

  17. 17.

    See, for example, Gupta (1991) ; Jain and Vilcassim (1991) ; Gönül and Srinivasan (1993) ; Helsen and Schmittlein (1993) ; Wedel et al. (1995) ; Dekimpe et al. (2000) ; Prins and Verhoef (2007) ; Schweidel et al. (2008) ; Risselada et al. (2014) .

  18. 18.

    An extension of the formulation to multiple purchases is straightforward.

  19. 19.

    See, for example, Jain and Vilcassim (1991) ; Bayus and Mehta (1995) ; Wedel et al. (1995) ; Chang et al. (1999) ; Schweidel et al. (2008) .

  20. 20.

    An alternative model is the so-called accelerated lifetime (hazard) model. In this model one may scale (or accelerate) t by a function of explanatory variables (Franses and Paap 2001, pp. 165–166) .

  21. 21.

    We do not show the results that have been obtained through the inclusion of interaction effects: see Table 3 in Prins and Verhoef (2007) .

  22. 22.

    Some examples of integrated models are Böckenholt (1993a,b) ; Bucklin et al. (1998) ; Song and Chintagunta (2007) ; Andrews and Currim (2009) ; Vroegrijk et al. (2013) . An aggregate level version of the integrated model by Gupta (1988) was proposed by Pauwels et al. (2002) , who show that the long-term brand sales effects of price promotions are mostly due to lifts in category incidence, not brand choice.

  23. 23.

    One way to deal with these truncations is to estimate a model using Truncated Regression. See, for example, Wooldridge (2012, pp. 589–591) .

  24. 24.

    This bias can be measured by the so-called inverse Mills ratio; see, for example, Franses and Paap (2001, p. 138) .

  25. 25.

    They correspond with the Probit part.

  26. 26.

    This is the standard regression model for the positive values of y i ∗.

  27. 27.

    First the parameters of the first equation (the probit part) are estimated using ML. Correcting for the bias using the inverse Mills ratio , the parameters of the second equation can be estimated using a regression model.

  28. 28.

    Other examples of the application of Type-2 Tobit models in marketing are found in, for example, Bucklin and Sismeiro (2003) ; Fox et al. (2004) ; Prins et al. (2009) ; Danaher and Dagger (2013) .

  29. 29.

    The following text is taken from Van Nierop et al. (2011) .

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Authors and Affiliations

  1. Department of Marketing, University of Groningen, Groningen, The Netherlands

    Peter S. H. Leeflang, Jaap E. Wieringa & Tammo H. A. Bijmolt

  2. Aston Business School, Birmingham, UK

    Peter S. H. Leeflang

  3. University of St. Gallen, St. Gallen, Switzerland

    Peter S. H. Leeflang

  4. Department of Marketing, Özyeğin University, Istanbul, Turkey

    Koen H. Pauwels

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  1. Peter S. H. Leeflang
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Leeflang, P.S.H., Wieringa, J.E., Bijmolt, T.H.A., Pauwels, K.H. (2015). Individual Demand Models. In: Modeling Markets. International Series in Quantitative Marketing. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2086-0_8

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