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The “Shopping Basket”: A Model for Multicategory Purchase Incidence Decisions


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  • Puneet Manchanda

    (Graduate School of Business, University of Chicago, Chicago, Illinois 60637)

  • Asim Ansari

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • Sunil Gupta

    (Graduate School of Business, Columbia University, New York, New York 10027)

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    Consumers make multicategory decisions in a variety of contexts such as choice of multiple categories during a shopping trip or mail-order purchasing. The choice of one category may affect the selection of another category due to the complementary nature (e.g., cake mix and cake frosting) of the two categories. Alternatively, two categories may co-occur in a shopping basket not because they are complementary but because of similar purchase cycles (e.g., beer and diapers) or because of a host of other unobserved factors. While complementarity gives managers some control over consumers' buying behavior (e.g., a change in the price of cake mix could change the purchase probability of cake frosting), co-occurrence or co-incidence is less controllable. Other factors that may affect multi-category choice may be (unobserved) household preferences or (observed) household demographics. We also argue that not accounting for these three factors simultaneously could lead to erroneous inferences. We then develop a conceptual framework that incorporates complementarity, co-incidence and heterogeneity (both observed and unobserved) as the factors that could lead to multi-category choice. We then translate this framework into a model of multi-category choice. Our model is based on random utility theory and allows for simultaneous, interdependent choice of many items. This model, the multi probit model, is implemented in a Hierarchical Bayes framework. The hierarchy consists of three levels. The first level captures the choice of items for the shopping basket during a shopping trip. The second level captures differences across households and the third level specifies the priors for the unknown parameters. We generalize some recent advances in Markov chain Monte Carlo methods in order to estimate the model. Specifically, we use a substitution sampler which incorporates techniques such as the Metropolis Hit-and-Run algorithm and the Gibbs Sampler. The model is estimated on four categories (cake mix, cake frosting, fabric detergent and fabric softener) using multicategory panel data. The results disentangle the complementarity and co-incidence effects. The complementarity results show that pricing and promotional changes in one category affect purchase incidence in related product categories. In general, the cross-price and cross-promotion effects are smaller than the own-price and own-promotions effects. The cross-effects are also asymmetric across pairs of categories, i.e., related category pairs may be characterized as having a “primary” and a “secondary” category. Thus these results provide a more complete description of the effects of promotional changes by examining them both within and across categories. The co-incidence results show the extent of the relationship between categories that arises from uncontrollable and unobserved factors. These results are useful since they provide insights into a general structure of dependence relationships across categories. The heterogeneity results show that observed demographic factors such as family size influence the intrinsic category preference of households. Larger family sizes also tend to make households more price sensitive for both the primary and secondary categories. We find that price sensitivities across categories are not highly correlated at the household level. We also find some evidence that intrinsic preferences for cake mix and cake frosting are more closely related than preferences for fabric detergent and fabric softener. We compare our model with a series of null models using both estimation and holdout samples. We show that both complementarity and co-incidence play a significant role in predicting multicategory choice. We also show how many single-category models used in conjunction may not be good predictors of joint choice. Our results are likely to be of interest to retailers and manufacturers trying to optimize pricing and promotion strategies across many categories as well as in designing micromarketing strategies. We illustrate some of these benefits by carrying out an analysis which shows that the “true” impact of complementarity and co-incidence on profitability is significant in a retail setting. Our model can also be applied to other domains. The combination of item interdependence and individual household level estimates may be of particular interest to database marketers in building customized “cross-selling” strategies in the direct mail and financial service industries.

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    Bibliographic Info

    Article provided by INFORMS in its journal Marketing Science.

    Volume (Year): 18 (1999)
    Issue (Month): 2 ()
    Pages: 95-114

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    Handle: RePEc:inm:ormksc:v:18:y:1999:i:2:p:95-114

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    Keywords: Multicategory Models; Shopping Baskets; Retailing; Micromarketing; Multivariate Probit Model; Hierarchical Bayes Models;


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    Cited by:
    1. Yasemin Boztug & Lutz Hildebrandt, 2005. "A Market Basket Analysis Conducted with a Multivariate Logit Model," SFB 649 Discussion Papers SFB649DP2005-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Yasemin Boztug & Thomas Reutterer, 2006. "A Combined Approach for Segment-Specific Analysis of Market Basket Data," SFB 649 Discussion Papers SFB649DP2006-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Bhat, Chandra R. & Srinivasan, Sivaramakrishnan & Sen, Sudeshna, 2006. "A joint model for the perfect and imperfect substitute goods case: Application to activity time-use decisions," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 827-850, December.
    4. Ahn, Dae-Yong, 2012. "A multivariate discrete choice method based on inequality restrictions," Economics Letters, Elsevier, vol. 115(3), pages 516-518.
    5. Xiaojing Dong & Pradeep Chintagunta & Puneet Manchanda, 2011. "A new multivariate count data model to study multi-category physician prescription behavior," Quantitative Marketing and Economics, Springer, vol. 9(3), pages 301-337, September.
    6. Castro, Marisol & Bhat, Chandra R. & Pendyala, Ram M. & Jara-Díaz, Sergio R., 2012. "Accommodating multiple constraints in the multiple discrete–continuous extreme value (MDCEV) choice model," Transportation Research Part B: Methodological, Elsevier, vol. 46(6), pages 729-743.
    7. Sobhani, Anae & Eluru, Naveen & Faghih-Imani, Ahmadreza, 2013. "A latent segmentation based multiple discrete continuous extreme value model," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 154-169.
    8. Paap, R. & van Dijk, A., 2006. "Explaining individual response using aggregated data," Econometric Institute Research Papers EI 2006-05, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Baranchuk, Nina & Kieschnick, Robert & Moussawi, Rabih, 2014. "Motivating innovation in newly public firms," Journal of Financial Economics, Elsevier, vol. 111(3), pages 578-588.
    10. Bhat, Chandra R., 2005. "A multiple discrete-continuous extreme value model: formulation and application to discretionary time-use decisions," Transportation Research Part B: Methodological, Elsevier, vol. 39(8), pages 679-707, September.
    11. Tripathi Sanjeev & Sinha, Piyush Kumar & Sinha, Piyush Kumar, . "Family and Store Choice - A Conceptual Framework," IIMA Working Papers WP2006-11-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    12. MartI´n-Herrán, Guiomar & Sigué, Simon P., 2011. "Prices, promotions, and channel profitability: Was the conventional wisdom mistaken?," European Journal of Operational Research, Elsevier, vol. 211(2), pages 415-425, June.
    13. Katrin Dippold & Harald Hruschka, 2013. "Variable selection for market basket analysis," Computational Statistics, Springer, vol. 28(2), pages 519-539, April.
    14. Eyal Carmi & Gal OEstreicher-Singer & Arun Sundararajan, 2010. "Is Oprah Contagious? Identifying Demand Spillovers in Product Networks," Working Papers 10-18, NET Institute.
    15. van Nierop, J.E.M. & Paap, R. & Bronnenberg, B. & Franses, Ph.H.B.F. & Wedel, M., 2005. "Retrieving unobserved consideration sets from household panel data," Econometric Institute Research Papers EI 2005-49, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    16. Bhat, Chandra R., 2008. "The multiple discrete-continuous extreme value (MDCEV) model: Role of utility function parameters, identification considerations, and model extensions," Transportation Research Part B: Methodological, Elsevier, vol. 42(3), pages 274-303, March.


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