IDEAS home Printed from
   My bibliography  Save this article

A Multiplicative Fixed-Effects Model of Consumer Choice


  • Purushottam Papatla

    (University of Wisconsin-Milwaukee)


The issue of consumer heterogeneity in discrete choice analysis has been attracting much attention recently. Research has suggested that heterogeneity can result in biased parameter estimates which, in turn, can lead to incorrect conclusions. Among the many methods proposed in the literature to handle heterogeneity, models seem to be the most attractive from a substantive point of view. However, in order to provide consistent estimates, these models typically require long purchase histories. This difficult constraint has prevented their widespread use. In this paper, we propose a new model which offers the benefits of fixed effects models without requiring long purchase histories. Our approach differs from the classic formulation in two ways. First, we calibrate the common and fixed-effects sequentially rather than simultaneously. This two-stage estimation permits us to obtain unbiased estimates of the common parameters even when the sample has households with very few observations. Second, we incorporate the fixed effects in a multiplicative rather than in an additive form. Our assumptions regarding the error term result in a probit model with heteroskedastic and temporally correlated random utilities. We develop a method of moments based estimator to calibrate parameters of models with this type of error structure. This procedure exploits the property that the method of moments yields estimates which are asymptotically as efficient as the maximum likelihood estimates given an appropriate starting point and a matrix of instruments. This is a very general procedure in that its mechanics are not tied to the proposed model. It can be readily applied to other problems where probit models are used to analyze data with serial correlation. This is a methodological contribution of the paper. The model and estimation procedure are illustrated on the A. C. Nielsen scanner data base for the liquid detergent category. Our results indicate that the proposed model can provide a better fit than random effects and loyalty based models and better predictive performance than random effects models. From a substantive perspective, our analysis provides the following findings. (a) —thus, most households have very similar price sensitivity in this category; (b) —suggesting that there are some households that are highly responsive to promotions while there are quite a few households that are less influenced by promotions; (c) —which is an indication that a reduction in preference for a brand is associated with an increase in price sensitivity and ; (d) —thus, as the preference for a brand increases, response to promotions by the brand also increases; and (e) —implying that, as households become more price sensitive, purchases may be driven more by price than by promotions; in other words, rather than responding to promotions such as displays and features as signals of a reduced price, price sensitive households actively evaluate prices in arriving at a choice. The proposed approach can be used by theoretical as well as applied researchers of brand choice behavior. Specifically, estimates of fixed-effects provided by the model can be used to cluster households into groups with similar parameters. Profiling the resulting groups in terms of demographics would provide interesting insights—from a theoretical perspective—regarding the household characteristics that are associated with different types of response behavior. It would also help managers to better target their brands. Using the proposed approach for cross-category analyses of fixed-effects would be an interesting area of future research. For instance, given a sample of households and their purchase histories in multiple categories, the proposed model can be used to explore the relationship between household behavior and category characteristics. In particular, issues such as the following can be investigated by comparing household-level estimates across categories: (a) are households that are highly price sensitive in one category also price sensitive in other categories? (b) what household characteristics are associated with high (low) price sensitivity or high (low) promotion response across categories? and (c) in what types of categories are households likely to exhibit high (low) price sensitivity or high (low) promotion response?

Suggested Citation

  • Purushottam Papatla, 1996. "A Multiplicative Fixed-Effects Model of Consumer Choice," Marketing Science, INFORMS, vol. 15(3), pages 243-261.
  • Handle: RePEc:inm:ormksc:v:15:y:1996:i:3:p:243-261

    Download full text from publisher

    File URL:
    Download Restriction: no


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Greg M. Allenby & Thomas S. Shively & Sha Yang & Mark J. Garratt, 2004. "A Choice Model for Packaged Goods: Dealing with Discrete Quantities and Quantity Discounts," Marketing Science, INFORMS, vol. 23(1), pages 95-108, June.
    2. Jie Zhang, 2006. "An Integrated Choice Model Incorporating Alternative Mechanisms for Consumers' Reactions to In-Store Display and Feature Advertising," Marketing Science, INFORMS, vol. 25(3), pages 278-290, 05-06.
    3. Arnd Huchzermeier & Ananth Iyer & Julia Freiheit, 2002. "The Supply Chain Impact of Smart Customers in a Promotional Environment," Manufacturing & Service Operations Management, INFORMS, vol. 4(3), pages 228-240, November.
    4. Rinus Haaijer & Michel Wedel & Marco Vriens & Tom Wansbeek, 1998. "Utility Covariances and Context Effects in Conjoint MNP Models," Marketing Science, INFORMS, vol. 17(3), pages 236-252.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormksc:v:15:y:1996:i:3:p:243-261. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.