# Discussant's Comments

##### Citation:

*
Robert C. Blattberg (1979) ,"Discussant's Comments", in NA - Advances in Consumer Research Volume 06, eds. William L. Wilkie, Ann Abor, MI : Association for Consumer Research, Pages: 587-588.
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COVARIANCE BIAS OF THURSTONE CASE V SCALING AS APPLIED TO CONSUMER PREFERENCES AND PURCHASE INTENTIONS

Joel Huber, Duke University

Murphy A. Sewall, University of Connecticut

This article raises a number of important questions about the use of Thurstone scales based upon paired comparisons. The paper demonstrates that certain biases exist in the scale when the assumption of equal covariances is violated. This problem is definitely relevant to marketing and consumer researchers. My comments relate to the following: (1) the need for a theory of choice to demonstrate the key problems that they have found; (2) specific attempts to overcome this problem in the econometric literature.

A choice model is needed because the problem the authors are describing may have one of two causes: (1) correlation between products or implicitly between attributes of products or (2) a two-stage choice process. The second problem is irrelevance of independent attributes and is different from correlation. For example, suppose there are three soft drinks available, Pepsi, Coke, and Seven-up. If one were to use paired comparisons, they might find out that Pepsi and Seven-up were equally chosen by consumers or equally be preferred, Coke and Seven-up were equally preferred, and Pepsi and Coke were equally preferred. In terms of Thurstone's model, one would find out that these could be scaled at exactly the same point. If the consumer used a two-stage process in selecting brands, they may first select on the attribute cola-ness, in which case they may be equally likely to select Seven-up or a cola product. If they select a cola product, then they are equally likely to select Pepsi and Coke. If they select an "un-cola", i.e. Seven-up, there is 100% chance that they will buy Seven-up. Thus, the choice probabilities become .25, .25, .50 for Pepsi, Coke, and Seven-up respectively.

This is really the example that Bock and Jones are describing in the passage given in the article. Thurstone's underlying model does not consider a two-stage choice process. Therefore, the reason Thurstone's Case V does not model the data well may be because the consumer uses a different choice model than Thurstone assumed. Therefore, the problem discussed is really model misspecification bias rather than correlation bias.

Another key question that the authors have not spent much time on but allude to is the implications for designing new products. Again a mathematical formulation of the problem would greatly help the authors and the readers understand the implications for product policy. Without a formal analysis it is difficult to understand the implications of correlation bias or misspecification bias on product design.

Some attempts exist to overcome the correlation bias described. In the econometric literature, Hausman and Wise [1978] try to introduce correlations into a probit model, making it a multivariate probit model. They are trying to overcome the same problem this article considers. Hausman and Wise's solution requires very lengthy computer runs to do numerically integration of multivariate normal distributions. Therefore, it is not clear how easy it is to introduce different correlations into Thurstone's Case V. The cost of solving the problem may be far greater than the biases associated with product selection or product design.

In summary, the authors have raised an important issue. The cause of the problem is ambiguous and the solution may be very costly. However, it offers a direction for some future research.

MARKET SHARES ESTIMATES BASED ON CONJOINT ANALYSIS OF CONCEPTS

James B. Wiley, University of Florida

Robert Bushnell, Wayne State University

The question the authors study is: How does one convert the utilities from conjoint analysis into consumer choices? By making certain statistical assumptions about randomness of utilities, a Thurstone or Luce choice model is recommended for converting utilities into choice probabilities. There are a number of difficulties with this approach. First, the authors do not state the cause of the randomness in the model. Is the randomness in utilities due to heterogeneity in the population or variation across time in individuals' choices? This question is not carefully answered in the article but could result in a very different interpretation of the choice model.

Second, why does one need a complex choice model at all? Why not make the probability of choice simply equal to the fraction of first choices divided by the total number of observations drawn? This may be an accurate estimate of the probability of choosing the k^{th} configuration. This method is obviously very simple. The authors should state why this is inappropriate.

Third, a theory of choice is needed. Suppose the trade-off matrix is the one given in figure 1. The trade-off is between miles per gallon and size of the car. Suppose the consumer is willing to make the first choice, 40 miles per gallon in a large car; second choice, 30 miles in a large car; and third choice, 20 miles in a large car. According to the type of choice model or probabilities that are generated from Luce's model, one would find that it is possible to select a large car that gets 30 miles per gallon X percent of the time when a large car that gets 40 miles per gallon is available. In other words, because the utilities generate probabilistic choices, it is now possible to generate situations in which an individual is willing to choose a car that is less preferred to a car that is more preferred. Obviously, this decision makes very little sense since the consumer clearly prefers a car that gets 40 miles per gallon over 30 miles per gallon, holding everything equal. Yet applying the choice models recommended, this case can occur.

Thus, unless one is very careful about the choice model used, and the measurement of that choice model, cases which violate key choice axioms can be generated. My suspicion is that Luce's model or Thurstone's model is not consistent with the underlying concepts of trade-off analysis. The link between the underlying choice model and the measurement is not very carefully done in this paper or in other papers on conjoint analysis. Therefore, more work has to be done on the issue of linking choice models and the measurement models. I think this is a research direction the authors should seriously consider.

The authors have worried about a key question which has not been worried about very much in the conjoint analysis literature in marketing. They have obviously moved this a step forward by considering some of the issues and raising a number of important questions. Further research in this area is strongly needed.

CHANGES IN CONSUMER PERCEPTIONS: THE IMPACT OF TESTING CONDITIONS ON PERCEPTIONS OF BRANDED PRODUCTS

James McCullough, University of Arizona

Charlene S. Martinsen, University of Washington

Linda Sceurman (Student), University of Washington

The conclusions reached by the authors are important to researchers using Multidimensional Scaling (MDS). For MDS to be a reliable research tool, it is important that the spatial location of stimuli are added to the stimulus set. In order for this result to be widely accepted, two additional research steps need to be taken: (1) sample of "real" people used from the population at large, and (2) many more product categories analyzed. These two steps will insure that the results appearing in this paper are not merely a random occurrence due to a special product or a biased sample. The need to replicate the results across product categories is particularly important to avoid idiosyncratic results. If the result found in this paper is affirmed in these replications, it improves the validity of MDS.

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##### Authors

Robert C. Blattberg, Graduate School of Business University of Chicago

##### Volume

NA - Advances in Consumer Research Volume 06 | 1979

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