Discrete choice analysis has been a

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1 arketing Research Forum Disaggregate Discrete Choice Assuming consumers are not alike enhances a marketer's decision-making ability. By Tm Renken Tim Renken is Vice Pn;sident, Senior Methodologist, Angus Reid Group, Minneapolis. Discrete choice analysis has been a favorite topic in marketing research journals and conferences in recent years. The popularity of this technique derives from its ability to answer a wide range of marketing questions, providing models of which product a consumer is most likely to choose given the attributes of a set of products he or she can choose form. These attributes typically include such key marketing variables as features, packaging, pricing, and promotions. The marketing manager can thus use the model to assess the impact of given sets of features, types of packaging, pricing and/or promotional strategies on consumer choice behavior. A major enhancement of discrete choice analysis, the hierarchical Bayes disaggregate discrete choice model should make this tool even more valuable for marketing managers. Discrete choice analyses are typically done using aggregate models, i.e., models that assume all consumers have the same preferences. The resulting analysis provides a model of the choice behavior of a representative, or average, consumer. If the category's consumers tend not to differ very much, then the aggregate model will he a good representation of their behavior. In most categories, however, there are no representative consumers they differ from each other in the brands tbey prefer, the features they look for, the packages they prefer, how they respond to price changes and promotions, etc. mdiscrete choice models came from economics and pychology^ and their assumptions reflect those origins. W Some differ greatly from eacb otber, and the marketing manager would benefit from knowing bow these segments behave, how big tbey are, how often they buy, where they shop, their demographics and psychographics, etc. This would help the manager decide which of the segments to target and which marketing strategy is most likely to appeal to the targeted segments. Aggregate models, however, assume away consumer segments, and marketing researchers have long heen aware of this limitation. The stumbling block has been lack of data; in discrete choice experiments, for example, we typically only present respondents with l2-[8 choice sets. There are not enough data from any one respondent to ^^^ ^^^^,^^,^ ^.^^^^ behavior. Researchers have designed various procedures for overcoming this information deficiency. One of the most recent attempts is the hierarchical Bayes model described by Greg Allenby and James Ginter in the November 1995 issue of Journal of Marketing Research. 1 bave applied a variant of this model to discrete cboice studies in a variety of categories and find it to be a reliable and, more important, practical tool for marketing practitioners. MODEL ASSUMPTIONS Discrete cboice models came from economics and psychology, and their assumptions reflect those origins. All discrete choice models, for example, assume that consumers assess each alter- 18 MARKETING RESEARCH

2 native in the set and choose the alternative with the highest expected utility. Expected utility is the total amount of satisfaction a consumer expects to derive from choosing a given altemative. All discrete choice models must also assume a particular form for the utility function goveming consumers' choice behavior. Consider a purely fictitious choice exercise in which a consumer chooses between buying a case of, a case of, or buying nothing. A simple utility function describing the person's behavior might take the form: «Pep.i = where u^.^^^ is the utility of ; P^,,,^ is the price of in dollars; and E^^^ is an error term. The 5 in the equation is a measure of the consumer's expected utility from consuming, and the -0.5 /^^.^^^ is the disutility from having to pay P^.,,^^ dollars for it. The -0.5 thus measures the customer's disutility from parting with dollars, which, in the above model, is independent of his or her expected utility from consuming the product hence, the same number (-0.5) for all three altematives. Note finally that the consumer characterized by the above utility function prefers consuming (5) to consuming (4) to consuming nothing (0). Plugging numbers into the utility function enables us to model which product the consumer will choose. At $8 each for and and zeros for the error terms, for example, we get: «c,*e = 5-0.5($8) + 0=1 "pep. = 4-0.5($8) + 0 = 0 "N,. = 0-0.5($0) + 0 = 0 This indicates that the consumer will choose. However, when 's price drops from $8 to $4, the consumer switches from to as a result of the price change: "rck. = 5-0.5($8) + 0=1 «P.p. = 4-0.5($4) + 0 = 2 "N, = 0-0.5($0) + 0 = 0 Note the key role the utility function's parameters (5, 4, and -0.5) play in modeling the consumer's behavior. If instead of a 5, the utility of consuming had been a 7, then the consumer would enjoy too much to switch to even when 's price drops to $4. The parameters of the utility function are estimated from the discrete choice data. If a respondent picks on every choice occasion regardless of its price, the estimate for the utility of consuming (J) will be driven up, while the pricesensitivity parameter (-0.5) will be driven toward zero. Aggregate and disaggregate models differ in that aggregate models provide one set of parameter estimates characterizing the behavior of the ''average" respondent in the sample, whereas disaggregate models provide parameter estimates for each respondent in the sample. If the 5,4, and -0.5 parameter estimates were derived from an aggregate model, they would mean that, on average, respondents prefer to, and the "average" respondent's price sensitivity is A disaggregate model, however, provides output such as the following: Respondent I Respondent 2 Respondent 1 greatly prefers to and is price sensitive; Respondent 2 prefers to and is price insensitive. The disaggregate model would provide parameter estimates for every respondent in the study, in essence a separate choice model for each respondent. MODEL ESTIMATION Estimating an aggregate discrete choice model is relatively straightforward: We assume a utility function such as the one in the previous example, assume that the error terms in that function have a double exponential distribution, and estimate the model using maximum likelihood estimation techniques. This technique works well when there are enough respondents to get reliable parameter estimates. If, however, we attempt to use this technique to estimate the parameters for one respondent by only using the choice data for that respondent, the parameters will not be reliable. There are typically too few choices per respondent to get stable estimates. Consider, for example, a respondent who chooses in all 12 choice sets of a discrete choice experiment. Estimating her utility MARKEriNG RESEARCH 19

3 Demogmphic variables such as age provide little information about preferences. Z' function parameters using only her 12 choices might yield parameters such as these: HM,,,, = 0 - C ' crete choice experiment, her parameter estimates will look like those of Respondent 2, the lover. The key contribution of the information from similar respondents is in limiting the possibility of irrational parameter estimates. While the utility function clearly shows that the respondent prefers to, the parameter estimates are extreme; the 25 and the imply that at prices as high as $2, a case, the respondent will prefer buying a ease of to buying nothing (none), a situation unlikely to oceur in the real world. The small amount of data per respondent often leads to such irrational parameter estimates. To get around this infomiation deficiency, the hierarchical Bayes model estimates the utility function paiameters for a given respondent by using information from (I) the choice data for that respondent, and (2) the choice data for similar respondents. If, for example, young people tend to prefer to, the hierarchical model will find that age plays a role in vs. preferences and will use that infomiation in estimating utility function parameters for a given person. The person's parameter estimates thus depend on (1) how often he or she chooses in the discrete choice experiment, and (2) how often persons in the same age group choose. In my experience, an individual's choice data play a far larger role in determining his or her parameter estimates than do the choice data of similar respondents. Thus, if a young person, despite her age, always chooses in our dis- In many categories, demographic variables such as age provide little information about preferences. Usage valuables such as brand bought most often, heavy vs. light category usage, or types of usage situations tend to have far more power to predict how a given respondent will behave in a ehoice situation. The hierarchical Bayes model can accommodate usage, demographic, psychographic, or any type of variables characterizing the respondents. The analyst simply chooses a list of the variables he or she feels might influence choice behavior in a given category, and the model identifies which of the variables do, in fact, influence choice behavior. The model then uses these predictive variables to augment each individual respondent's choice data to obtain reliable parameter estimates. Estimating a hierarchical Bayes discrete choice model is not possible with the maximum likelihood estimation technique used to estimate the aggregate model. Instead we must make use of an exciting, and very recent, development in statistics called the Gibbs sampler. The Gibbs sampler is technically a Monte Carlo integration technique, a technique that makes use of random number generators in modern high speed computers instead of relying on standard calculus derivations. The Gibbs sampler allows us to integrate functions we could not integrate before, and, as a result, estimate statistical models we could not estimate before. The hierarchical Bayes discrete choice model is an example of such a model. CLUSTERING CONSUMERS The disaggregate model provides two major practical advantages over the aggregate model. First, the former provides a more accurate representation of consumers. Ailenby and Ginter present evidence that disaggregate models make fewer predictive errors than do aggregate models. Second, disaggregate models allow us to cluster consumers into segments with similar choice behaviors, adding an important new dimension to the discrete choice analysis. A good way to obtain consumer segments is to run a cluster analysis procedure on the respondents' utility function parameter estimates (such as the 5 and 4 in the fn'st / example). We can then examine the impact on choice behavior of changing product attributes at the segment level as well as the market level. Going back to the example, we might have the output shown in Exhibit I. This exhibit shows a hypothetical three-cluster solution in which 50% of respondents are " loyals," 30% are " loyals," and 20% are "price shoppers." The numbers in the table represent choice shares; the 75.3, for example, indicates that loyals have a 75.3% chance of choosing when choosing between,, and none at these prices. Note that while there are more loyals (50% of respondents) than 20 MARKETING RESEARCH

4 loyals (30% of respondents) in this example, loyals are more loyal to their product (85.6% choice share) than are loyals. Exhibit 2 shows what happens when lowers its price from $8 to $7. As one would expect, choice shares increase for ail three segments. The increase, however, is largest among the price shoppers because they can now get for a lower price than. One can thus analyze the behavior of the different segments under different marketplace scenarios and, as with any cluster analysis, run crosstabs to characterize the different segments' demographics, usage, psychographics, etc. Exhibit 1 Scenario 1 Product None $0 and at $8 a case Choice shares (%) loyals Total (50%) loyais (30%) shoppers (20%) Applications The ability to combine segmentation with discrete choice analysis gives the marketing researcher added value in several areas of marketing decision making. New product marketing: By including a new product in a disaggregate discrete choice analysis, we can assess the new product's trial potential and identify which segments are most interested. We can also decide several other issues, including: Product features. By varying the new product's features from choice set to choice set, we can use the disaggregate discrete choice model to assess the value of each feature to each respondent and each segment. In this way, the disaggregate approach helps design a new product that appeals to key target segments. Packaging/labeling. Just as we can vary the new product's features from ehoice set to choice set, we also can vary its packaging and labeling. Pricing. The goal here is to maximize profit in view of key segments' priee sensitivities. Distribution. We know where the respondents live, and we can ask them where they shop. If the new product appeals to segments that live in certain regions or shop for the category predominantly in certain outlet types, then the disaggregate discrete choice analysis provides information on where the new product should be distributed. Promotion. Because we can include such promotional vehicles as shelf talkers, coupons, sweepstakes, etc. in our discrete choice exper- Exhibit 2 Scenario 2 Product None at$8 a case, at $7 a case $8 $7 $0 Choice shares (%) Total loyals (50%) iment, we can assess the impact of each of these vehicles on each respondent and identify clusters of respondents who are sensitive to them. We can thus assess the potential of running a given promotion to Induce trial of the new product. Product line. We can estimate the impact of the new product's introduction on the rest of the line. If, for example, the new product appeals primarily to segments that are loyal to the firm's existing products, introducing the new product may simply cannibalize existing products' sales, leading to little or no increase in overall market share. Competitive analyses: The - example shows how disaggregate discrete choice can be used to analyze the competitive relationships in a category. In that example. and really only compete for the price shopper segment. The disaggregate model thus enables the researcher to identify who competes with whom in a category and for which segments. ioyals (30%) shoppers (20%) MARKETING RESEARCH

5 Such precise knowledge of the market's structure is important, for example, in decisions about phasing out elements of a product line (e.g., SKU dehsting). If the primary buyers that management is thinking of phasing out are in a segment that switches between that product and another of the firm's products, then the phaseout will not significantly damage the firm's overall market share. Pricing studies: In eases where price discrimination is possible, the disaggregate model is particularly valuable because it allows the researcher to identify a profit-maximizing price for each target segment. The model, though, offers benefits in other contexts as well. Consider, for example, the problem of pricing to counter a private label threat. A disaggregate model enables the researcher to identify price levels sufficient to entice each of the private label-buying segments away from their brands. Or consider the problem of identifying the impact on a product line of a change in pricing strategy for one product in that line. The disaggregate model would show, for example, which segments switch to the product in response to a drop in its price and which of the other products in the line and the category suffer as a result. Promotion profitability analyses: Some discrete ehoice studies are designed purely to assess mahh the xtstaxai^ to idmti/f price Imh su^dm to mticemcho/the private f^ g jrom thrir hxan&s. the profitability of a given promotion, and a disaggregate model is particularly valuable in these studies because it allow the researcher to identify which segments are sensitive to the promotion and which are not. If the promotion is not appealing to the targeted segments, then running that promotion is probably not a good idea. Brand equity studies: Some discrete choice studies are designed to assess the value of a given brand name to see if a given brand name on a product increases the likelihood consumers will choose it over an unbranded product. The disaggregate model allows the researcher to identify the value, in incremental choice share or in dollars, of a given brand name for each respondent. In this way, we can identify the key segments together with their demographics, psychographics, etc. ^responsible for a brand's equity in the marketplace.? ACKNOWLEDGMENT This article was written while the author was Director of Statistical Services at Conway/Milliken & Assocs. He would like to thank Fay Conway, John Golanty, Scot Richardson, and Becky Leiviska for comments on earlier drafts. ADDITIONAL READING Greg M. AUenby and James L. Ginter (1995), "Using Extremes to Design Products and Segment Markets," Journal of Marketing Research, 32 (November), Moshe Ben-Akiva and Steven R. Lerman (1985), Discrete Choice Analysis: Theory and Application to Travel Demand, The MIT Press. 22 SPRING 1997 MARKETING RESEARCH

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