# The Decomposition of Aggregate Market Beravior Into Its Consumer Behavior Components: Preference and Preference-Component Estimation Using Upc Data

ABSTRACT - A paramorphic model of consumer behavior is used to construct an aggregate-level method for obtaining estimates of brand preferences (utilities). A conjoint-like approach is presented to predict the estimated brand preferences from the underlying physical brand characteristics. The implications for managerial decision-making, as well as the limitations on applying the approaches, are discussed.

##### Citation:

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Kenneth J. Wisniewski (1984) ,"The Decomposition of Aggregate Market Beravior Into Its Consumer Behavior Components: Preference and Preference-Component Estimation Using Upc Data", in NA - Advances in Consumer Research Volume 11, eds. Thomas C. Kinnear, Provo, UT : Association for Consumer Research, Pages: 662-667.
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A paramorphic model of consumer behavior is used to construct an aggregate-level method for obtaining estimates of brand preferences (utilities). A conjoint-like approach is presented to predict the estimated brand preferences from the underlying physical brand characteristics. The implications for managerial decision-making, as well as the limitations on applying the approaches, are discussed.

ON THEORETICAL AND MANAGERIAL ISSUES

The marketing concept states that the key to long-run corporate success is to offer products consumers "want" more than competitive products (Kotler, 1980)--or in other words, products that have a high degree of utility to the individual. Accepting this premise, it is then not surprising to find the concept of the utility of a product to a consumer is central to a large part of the economics and marketing literature. Demand curves which reflect aggregated preferences may be estimable for a category as a whole (e.g., sugar, margarine, etc.), and less frequently for individual brands within a category if the researcher can show or is willing to assume a variety of conditions hold concerning homogeneity, additivity, transitivity, etc. of the individual-level utility functions (Phlips, 1974). The overall utility of a brand can also be transformed into demand for the various characteristics that are physically designed into the product (Lancaster, 1966; Hauser and Simmie, 1981, extend the theory to demand for consumer perceptual positions derived from the underlying characteristics). If individuals are assumed to be homogeneous with respect to the relative value they place upon these characteristics, estimation techniques such as logit (McFadden, 1973) or preference regression (see, e.g., Urban and Hauser, 1980) can be used. If the homogeneity assumption is not tenable, individual-level estimation approaches can be used, including conjoint-type analyses, e.g. (Johnson, 1974; Green and Wind, 1975) and variants of von Neumann-Morgenstern utility theoretic methods (Keeney and Raiffa, 1976; Hauser, 1978).

While the ability to estimate utility functions at the individual level seems theoretically most-appealing, practical considerations offset some of this theoretical advantage. Individual-level assessments are quite intensive, requiring a substantial number of paired comparisons to be made for any reasonable number of product characteristics. This intensity often precludes very large samples, ind hence may not allow a precise mapping to the population as a whole. Aggregate approaches, being easier to estimate, are also more-indicative of population-level response. However, they may not be tied as closely with the underlying behavior of specific individual consumers. Aggregation biases may creep in. There is evidence to suggest, though, that these biases may not be severe for most cases. Phlips (1974, p. 100) cites Houthakker and Taylor (1970), based on their empirical evidence, as saying, ". . .of all the errors likely to be made in demand analysis, the aggregation error is least troublesome." One reason for this finding is that aggregate models can be directly formulated based upon the expected underlying individual-level theories of consumer behavior. Market response is then treated as if it were a "representative" individual (Hicks. 1956), or is assumed to be paramorphic in its representation (i.e., the market reacts as if each and every consumer were using the aggregate model to make his decisions).

This research presents and evaluates a new and experimental approach for generating brand-level preferences (utilities) from aggregate UPC scanning sales data. This approach is aggregate in nature, but relies on a paramorphic model of consumer behavior in reinterpreting components of the demand curve. Five categories of a large Midwestern grocery chain's sales are analyzed. Having derived estimates of brand-preference, a conjoint-type approach at the market level is proposed to assess the importance of various brand characteristics in determining preference levels. The approach is applied to the margarine category. Finally, the implications, criticisms, area of application, and future extensions are discussed.

CONSUMER BEHAVIOR AND DEMAND CURVE ESTIMATION

Developed in psychology, the Brunswik Lens Model has been modified and variants used to predict consumer behavior in brand - choice scenarios (see, e.g., Tybout and Hauser, 1981; Holbrook, 1981). Figure l presents such a modified Lens model. All product offerings can be distinguished on the basis of their underlying physical characteristics (such as sweetness, size, brand name, etc.). However, consumers tend not to compare all products on all characteristics when making a purchase decision. Rather, characteristics can be abstracted into more-macro overall perceptions (e.g., "taste", "safety", "freedom from chemical additives", etc.). The brand's preference is thus a function of the component worths of the physical characteristics, as mapped through the product perceptions. Economic (retail price), availability (distribution), effort (distance to a store stocking the brand, physical effort to locate the brand in-store, i.e., facings, etc.), and other constraints may cause a consumer to choose something other than his most-preferred brand. Hence, overall utility for a brand is a function of its preference component and the magnitude of the constraints.

The above model is operationalized at the individual level. However, it can be used to provide a paramorphic explanation of sales behavior at the aggregate demand curve level. The demand curve for a specific brand results from a multitude of individual-level decisions. Let Ui(n) be consumer i's overall utility for Brand n, after taking into account all constaints (analogous to "C" in Figure 1). Then, sale for brand" reflect the number of times

Ui(n) > Ui(m) v m = n

when summed across all consumers i. This necessarily assumes each consumer purchases one and only one brand on each shopping occasion. However, in theory we can also assume that the Ui(n) reflects interPersonal as well as interbrand utilities; thus, the values would reflect not just brand choice but also frequency of use for the individual consumer. Under this latter interpretation, sales are proportional to the summation of individual overall utilities. Since these overall utilities are a function of brand preferences and constraints, assuming appropriate combinatorial properties of the underlying utility functions.demand is a function of preference and constraints.

The above discussion gives an interesting interpretation to the standard economic demand curve of the form Q=f(constant, p), where Q=unit sales and p=retail price. In particular, assuming that the only operative constraint is the economic constraint of retail price and that conditio are "normal"--i.e., no special advertising is occurring -- the constant term takes on the character of brand preference or brand utility. In fact, if other constraints such as display, advertising, etc. are operative, suitable additional constants/coefficients can be estimated to remove their residual effect, still leaving demand as a function of brand preference and price.

Economic theory provides us with a variety of functional forms for the demand curve. In particular, linear and constant (price) elasticity variants are common base models. However, marketing theory provides insight into other desirable characteristics of the demand curve. As price+0, demand should not increase without bound. In fact, this upper bound on demand need not even equal total market potential. Let's consider a two-brand example. Let the overall utility function U(n)=B(n)-P(n), where B(n) is the consumer's brand preference (utility) for Brand n, and P(n) is the retail price of Brand n. Let Brand l have a preference utility value of 3.00, and Brand 2 a value of 2.00 for a given consumer. Further, let Brand l be priced at 994 versus 794 for Brand 2. Thus, Brand l's overall utility U(n)=2.01. Even if Brand 2 were to cut its price to 0 (i.e., give it away for free), its overall utility would be a maximum of 2.00 for this consumer. Hence, this consumer would never switch to Brand 9, unless his preferences changed or Brand l substantially raised its price. Brand loyalty to existing brand explained here as an exceptionally-strong preference utility component and a "low-enough" retail price, will prevent a given brand's obtaining a 100% market share even if it price is cut to zero. Thus, the demand curve should be bounded at zero price.

A second useful property is based upon competitive market structure. As a brand reduces its price and its overall utility rises it competes more and more extensively with all other existing brands--i.e., as retail price moves downward, a brand becomes price-competitive with an increasing set of competitors. This should accelerate the rate of increase in demand in the lower price regions as the brand draws share from a larger and larger pool of competitive customers. The rate at which consumers switch is a function of the distribution of brand preferences for the competitive brands.

A third useful property to incorporate in the demand curve is to allow for differential elasticities based not only on price, but also on preference utilities (i.e., to allow an interaction between preference and price in the elasticity). This allows a test of the managerial hypothesis that for a fixed price the more-highly-preferred brands enjoy a higher elasticity (i.e., national brands' elasticities > private labels > generics) for a fixed price).

One functional form which generally meets these requirements is the exponential model. Thus under the assumption that price is the only operative constraint on behavior, three functional forms--linear, constant elasticity, and exponential--are specified in Table l as equations (1)-(3). Although the linear model does not allow for increasing rates of sales growth at lower prices, its elasticities are dependent on both preference and price terms. The elasticity for the constant elasticity model is by definition not dependent on price or preference. It also is unbounded both in terms of sales and price. The exponential model's elasticities are a function of both preference utility and price, and at zero price sales are finite. However, whereas the linear model intercepts the price access at some finite price, the exponential model does not. Thus, if the properties stated above are true of the real world, the exponential and linear models are superior to the constant elasticity model. However, there is no way of determining a priori which of the violations of the above properties--non-linear, accelerating growth versus bounded prices--are more-important for the linear and exponential models, respectively.

A NOTE ON THE DATA AND ESTIMATION PROCEDURES

The difficulty with estimating demand curves has historically been a lack of price variation during a "reasonable" period of time, where "reasonable" is defined as a period short-enough so that the competitive structure of the marketplace has not changed (e.g., via introduction/ withdrawal of new products, general shifts in the entire price structure of the market, etc.). With the advent of UPC scanning systems, brand sales data has become abundant, not just for one brand but for all brands in a category. However, there still is the problem of insufficient variation in the price variable to allow individual brand demand curve estimation over "reasonable" periods of time. Thus, in an earlier paper (Wisniewski, 1983), the author proposed a cross-brand/cross-time-series approach wherein each brand's time-series history was pooled with all other brands' in the category. An analysis of the statistical properties of such estimation techniques indicate that, while they are prone to violation of the non-independence of observations assumptions in most estimation techniques, and while some autocorrelation may exist for individual brands, overall such a cross-sectional/cross-time-series approach is viable and produces relatively unbiased estimates of the preference utility component discussed above. This is true even under situations where there are weekly "shocks" to the system--i.e., store volume is up/down for an unexplained/unmeasured reason.

The data used in the subsequent estimation is collected from a large Midwestern retail grocery store chain. Scanning systems provide price and unit volume information for 42 stores. Advertising data and sale price data is collected separately and appended to the UPC scanning data. This allows identification of "normal" demand periods. Five categories are chosen for analysis. These represent commodities (flour and sugar), branded products (analgesics and liquid dish detergents), and an "in-between" category (margarine, which has elements of both commodities and branded products--e.g., diet, unsalted, etc. ) . Twenty-three weeks of data are available.

Since a cross-sectional/cross-time approach is being used, the actual models estimated are not the ideal specifications shown in Table (l) but are the cross-sectional variants of these models as shown in Equations (4), (5), and (6).

DEMAND CURVE FUNCTIONAL FORMS AND THEIR IMPLICATIONS

where Bi = indicator variable (Bi = 1 Y brand i observations, 0 otherwise) and all other symbols are as defined in Table 1. (n is the number of brands in the category.)

Note that the equations have a slightly different specification. The a'S are still the measure of brand preferences (i.e., a transformation of sales at price=0). The D is now interpreted as a "common" price effect, and has the same impact on all brands. The interactive preference/price term has changed in specification. Instead of YaP it is YbP. This is necessitated because the brand preference term a is unknown and must be estimated; the specifications in equations (4) and (6) basically treat the g's as a brand-specific price effect, that incorporates any effect of preference as well the importance of the interaction relative to the common price term and the constant. In general, however, the marginal equations for each brand-level demand curve are analogous to those in Table 1.

BRAND PREFERENCE ESTIMATION RESULTS

Table 2 presents adjusted R2 estimation results. In general, the recoveries are quite good. However, this is partly to be expected, since a large portion of the variance is accounted for by the mean sales level effects as captured in the brand preference terms (a). Overall, the exponential model outperforms the linear and constant elasticity base models. The only exception is the dish detergent category, where a linear model provides the best fit. In every case, the constant elasticity model is inferior to the linear model, as suggested by the preceding discussion of necessary properties for the demand curve.

DEMAND CURVE ESTIMATION RESULTS--ADJUSTED R2

On average across all categories, brand preference correlates .10 with price, .37 with unit sales, and .51 with dollar volume market share. This is an intuitively-appealing result, and gives some face validity to the brand preference estimates. A marketing manager of a brand with a strong brand utility may choose between two polar strategies--lower price/higher volume versus higher price/lower volume. Thus, there need not be large correlations between preference and price or unit sales. However, if the preference estimates are in fact reliable, then these estimates should correlate significantly with dollar volume market share since stronger-preference brands should be able to command higher total revenues than weaker-preference brands, subject to a rational pricing strategy (perhaps one that keeps the elasticities near -1.00,. Note, though, that at an elasticity--1.00 only revenue-maximization, not profit maximization, is guaranteed. Thus, the correlation between preference and dollar market share should be highly significant, but need not approach 1.00.

An empirical issue arises with regard to the regions of price data on which the demand equations (4)-(6) are calibrated. One of the problems with individual brand demand curve estimation is that there is often insufficient price variation at this level. The pooling of data is what introduces this variance and allows some estimate of the common price effects, and it is these price effects in combination with the average sales levels that drives preference estimation. However, for each individual brand, only a limited amount (for man brands only l) of price points exists. Often these price points are a substantial distance from zero. This means that the brand preference constant, which is equivalent (or a transformation of which is equivalent) to sales at price=0, is being estimated based primarily on the functional form and the characteristics of the slope of that functional form. Figure 2 provides an example. While there are three price points in the time series, the minimum price is $1.60; yet, the brand preference estimator is based upon a price point of zero. The fact that the actual price range of margarine ranges from a minimum of 354 (generic l lb. sticks) to a maximum of $2.09 (Fleischmann's 2 lb. Tub Margarine) provides some confidence in the common price estimator and hence in the demand curve zero-price intercepts. However, it is not known what sensitivity exists in the brand preference estimator with respect to minor variations in the sales levels at the various price points.

EXPONENTIAL DEMAND CURVE--FlEISCHMANN'S 2 LB. TUBS

What is known is that for at least 80-85% of the brands, there is no evidence of autocorrelation. (See Wisniewski. 1983 for details of this sensitivity analysis.) In those few cases where autocorrelation exists, it is invariable a small-share brand that is involved, and the autocorrelation is a result of consistent over/under prediction at a single (or rarely multiple) price point's. The association of the autocorrelation with only the smaller-share brands is a statistical artifact of the cross-sectional approach, which minimizes overall deviations; hence larger-share brands with larger potential deviations are weighted more heavily and thus tend to be predicted more-accurately than small-share brands.

Given the recovery statistics and the generally-good statistical properties of the estimations, we can turn our attention to the face validity of the specific preference estimates. Table 3 presents the results, again for the margarine category for continuity. The average preferences for l lb. stick margarines are in close accord with the expected results: national brands/regular (10.7); national brands/blended (14.4); national brands/unsalted (7.1); private labels ('0.5); house brand (9.3); generic (8.8); and regional brands (4.3). The strong showing of the private labels is due in large part to an exceptionally-strong private label brand that may in fact be perceived as a national brand by some customers of the retail chain.

EXPONENTIAL MODEL PREFERENCE RESULTS--MARGARINES

The seeming closeness of the generics' brand preference of 8.8 compared to the national brands 10.7 is deceiving. Recall that what is being predicted by such brand preferences is unit sales at price=0, assuming all competitors retain their current price structure. The sales equation is exp(a). Hence, the projected average sales levels for these various categories are:

National Brands 44,356

Private Labels 36,315

House Brands 10,938

Generics 6,634

Regional Brands 74

Thus, even small differences (10.1 for the national brands versus 10.5 for private labels) have a dramatic impact on the overall average sales prediction. (Note that currently the regional brands are only selling some 5-10 units per week across all 42 stores; thus the seemingly low sales projection is not unrealistic.)

The preference results for tub margarines also agree with the necessary utility theory conditions. Since brand preferences or utilities are calculated for a given UPC-coded item, item utility should increase with size. In fact, in the tub margarines, a 2 lb. size of a brand always has a higher utility than a l lb. size with the same brand name; and the only 3 lb. brand in the category (Shedd's) has a higher utility than the 2 lb. brand. Under the squeeze margarine category. the l lb. size has nearly twice the utility of the 8 oz. size, although this comparison also includes brand name differences

The average elasticity for the margarine brands at their last regular price in the time series is -3.81. Only four brands report estimated elasticities less than 1.00 in absolute value. (Three of these are Fleischmann's products--l lb. regular and unsalted sticks, and the l lb. tub and the fourth is the private label l lb. tub margarine. The implication is that the retailer is underpricing these brands relative to their demand.) The results are in accord with the expected results, since a profit-maximizing position should generate greater than 1.00 in absolute value. (If the elasticity were between 0. 00 and -1.00, an increase in price would decrease sales by a less than proportionate amount; hence, overall profitability would rise, given a non-negative profit margin.)

Thus, from the multi-category estimation recoveries, statistical properties, and face validity standpoint, exponential demand curve estimations and the brand preferences seem reasonable. The next section tests whether these brand preferences have any systematic, real meaning or whether they are artifactual. The test will examine the margarine category only, since only data on this category was available at the time. Future work will include extensions of the approach in this next section to additional categories.

THE DECOMPOSITION OF PREFERENCES: AN AGGREGATE APPROACH

A sort of predictive "test" of the validity of the above approach to estimating brand utilities is possible. If the Lens Model is an accurate representation of consumer choice, then preferences are "caused" or "created" by the part-worth utilities of the underlying physical characteristics of the brand (as possibly mediated through perceptions). Avoiding the issue of advertising and the image or goodwill of a brand name for a moment, the Lens Model predicts that there is a real and systematic component to preferences. If the above demand curve approach has identified the underlying preferences, the systematic component should be predicted by the underlying physical characteristics. This would mean, though, that 2 brands having identical physical characteristics should have equal brand preference utilities; market share differences would be solely attributable to differences in price. However, advertising weight has been argued to be an important factor in increasing sales volume, partly through the mechanism of increasing the probability of evoking the brand and through the related mechanism of possibly increasing brand preference. Thus, advertising is one factor explaining market share differences for virtually-identically-formulated products with comparable prices. A second differentiating factor, and one that is partly correlated with national (although not local) advertising is the brand type. National brands have a distribution advantage over private labels and generics. This greater presence (i.e., appears in all stores, is advertised more at the national level, etc.) can also influence evoking and thus the probabilities of choice. At the extreme, there may even be brand-name-specific effects, perhaps due to other phenomena such as the order the brand entered the market relative to its competitors, the length of its history in the marketplace, etc. Such brand specific-effects are really brand-name-specific effects and may incorporate aspects of brand image and brand goodwill. (These effects are similar to those postulated by Srinivasan (1979) to account for all other components of overall preference not explained by the attributes. In this paper, however, brand-specific-effects refer to brand-name-specific effects --i.e., there is a "Fleischmann's"effect that applies equally to the regular and unsalted sticks, and 1 and 2 lb. tubs, as well as to the diet Fleischmann's.)

There are five major physical product differences in the margarine category. These are: size (8 oz., 1, 2, and 3 lb.); form (squeeze, sticks/quarters, and tub/soft); diet/non-diet; regular/unsalted; and regular/blended. These physical characteristics, along with the advertising, distributional, and brand-name-specific effects comprise the predictor variables in equation (7).

The data for this estimation consist of 39 observations, each appropriately coded as to its physical characteristics and each associated with the brand preference estimated in equation (6). The approach is analogous to a conjoint-type analysis, where the "individual" is really the entire market. The results of the two estimations are shown in Table 4.

DECOMPOSITION OF PREFERENCE: ESTIMATION RESULTS

The overall recovries are quite respectable for empirical data especially when one considers that the dependent variable is actually the output of the earlier demand estimation and is itself subject to some error. The results indicate that the previous approach does seem to be uncovering a systematic component of sales behavior, and that this component is well-predicted by the underlying physical characteristics of the brand, combined with advertising and other brand-specific information.

The coefficients all tend to be "reasonable" in that they are in the predicted directions--e.g., as size increases, so does utility (the only exception is for the 8 oz. size in the brand-type model equation (6)); diet margarines and unsalted margarines are generally less-preferred than regular formulations, etc. Advertising weight is highly significant, correlating .54 with brand preference. The most-frequent advertiser during the period advertised the brand-name (in a variety of sizes) nearly 30 times in a six-month period; thus, the addition to utility for that brand is (.05)(30)=1.5, a significant increase. National brands and private labels have generally a positive relation to brand preference--people like them "more" than the less-distributed house brands and generics. The brandname-specific effects are all negative. This does not indicate they have a negative effect, but is merely an artifact of the brand name chosen for the base.

The fact that the approach is non-experimental, however, leads to some multicollinearity in the data. In particular advertising tends to correlate with some brand names, making a precise discourse on the exact meaning of the brand-specific effects a slightly risky proposition. Other specifications can potentially reduce this correlational difficulty, dependent on the objectives of the analyst.

DECOMPOSITION REVISITED: A SUMMARY AND CONCLUSIONS

The research reported is a positive step toward being able to use aggregate UPC sales data, supplemented with additional marketing variables of strategic interest, to analyze consumer response to marketing actions. UPC scanning systems offer voluminous data (e.g., the University of Chicago Scanning Project is currently receiving upwards of 1.5 million scanning sales records per week, for a single-retailer). Thus, a primary advantage of scanning data is the ability to examine not just a single brand in isolation, but all brands in a given category. This is essential when considering the lack of significant independent variable variation at the individual brand level or the need to use such long time series that the assumption of constant structural market conditions becomes tenuous.

A cross-brand/cross-time approach was developed that began with a basic modes of consumer behavior. Assuming the only constraint is price, the behavioral model allows us to reinterpret the demand curve as composed of a brand utility component, and a price constraint. The exponential function is found to be a theoretically-appealing and superior-performing operationalization of the demand curve. Predictive fits across 5 categories average . 96. The statistical properties of the cross-sectional/cross-time estimation approach are also generally quite good. (See Wisniewski, 1983 for a fuller discussion of these properties.) Finally, there is strong face validity for the brand preference estimates and elasticity results. On average, national brands > private labels > house brands > generics. The elasticity results are also intuitively-appealing.

The second stage of this research presented a method for decomposing preferences. This section also served to strengthen the face validity of the prior approach's brand preference estimates, since a systematic component of the preferences is well predicted by the brand's physical characteristics. In addition, a strong effect of advertising on preference is evident, although these effects are correlated with brand-name-specific effects. Future work is planned to extend this second conjoint-like approach to other categories. As it currently stands, the approach recovers preferences well. However, due to possible aggregation biases, the predictive validity of the model has yet to be tested. The approach recovers existing combinations but cannot yet be used to predict utility for combinations not currently represented. In addition the issue of cannibalization deserves future attention.

REFERENCES

Green, P. E. and Y. Wind (1975), "New Ways to Measure Consumers' Judgements", Harvard Business Review, 53, 4, 107-117.

Houthakker, H. and L. D. Taylor (1970), Consumer Demand in the United States 1929-1970, 2nd. Ed., Cambridge: Harvard University Press.

Hicks, J. R. (1956), A Revision of Demand Theory, Oxford: Oxford University Press.

Hauser, J. R. (1978), "Consumer Preference Axioms: Behavioral Postulates for Describing and Predicting Stochastic Choice," Management Science, 24, 13, 1331-1341.

Hauser, J. R. and P. Simmie (1981), "Profit Maximizing Perceptual Positions", Management Science, 27, 1, 33-56.

Johnson, R. M. (1974), "Trade-Off Analysis of Consumer Values", Journal of Marketing Research, 11, 2, 121-127.

Keeney, R. L. and H. Raiffa (1976), Decision Analysis with Multiple Objectives, New York: John Wiley and Sons, Inc.

Kotler, P. (1980), Marketing Management, 4th ed., Englewood Cliffs: Prentice-Hall, Inc.

Lancaster, K. (1966), "A New Approach to Consumer Theory", Journal of Political Economy, 74, 132-157.

McFadden, D. (1973), "Conditional Logit Analysis of Qualitative Choice Behavior", in Frontiers in Econometrics, P. Zarembka, ed., New York: Academic Press, pp. 105-142.

Phlips, L. (1974), Applied Consumption Analysis, New York: American Elsevier Pub. Co., Inc.

Srinivasan, V. (1979), "Network Models for Estimating Brand Specific Effects in Multi-Attribute Marketing Models", Management Science, 25, 1, 11-21.

Tybout, A. M. and J. R. Hauser (1981), "A Marketing Audit Using a Conceptual Model of Consumer Behavior: Application and Evaluation", Journal of Marketing, 45, 3, 82-101.

Urban, G. L. and J. R. Hauser (1980), Design and Marketing of New Products, Prentice-Hall.

Wisniewski, K. J. (1983), "Analytical Approaches to Demand Estimation: Statistical Issues", American Statistical Association proceedings, August.

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##### Authors

Kenneth J. Wisniewski, University of Chicago [GSB, 1101 E. 58th St., Chicago, IL 60637]

##### Volume

NA - Advances in Consumer Research Volume 11 | 1984

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