A new solution to the additive constant problem in metric multidimensional scaling is developed. This solution determines, for a given dimensionality, the additive constant and the resulting stimulus projections on the dimensions of a Euclidean space which minimize the sum of squares of discrepancies between the formal model for metric multidimensional scaling and the original data. A modification of Fletcher-Powell style functional iteration is used to compute solutions. A scale free index of the goodness of fit is developed to aid in selecting solutions of adequate dimensionality from multiple candidates. © 1972 Psychometric Society.

This chapter describes that three basic principles motivate the specification of the market-share models. Market-share models should be competitive, descriptive as well as predictive, and profit-oriented. Being fundamentally competitive implies that one cannot know the effect or effectiveness of a marketing action without accounting for the actions of competitors. Market-share models are models for understanding how the marketing efforts of every brand impact the results in a competitive marketplace. Only by describing the influence of each marketing instrument can one gain a basis for marketing planning. Prediction alone is not enough. Time-series models that forecast the future from the past sales provide no insight into how sales are generated. The emphasis on being descriptive also embraces the need to understand the areas in which consumer choice probabilities are synonymous with market shares as well. Part of the goal of description transcends what can be done by market-share models alone. Managers need to understand that their efforts have (potentially) competitive effects and (potentially) market-expansive effects. In sales-response models these effects are comingled, but by combining descriptive market-share models for the competitive effects with descriptive category-volume models for the market-expansive effects, managers obtain a much richer understanding of the market. The profit-oriented goal of market-share analysis urges us to ask how the firm's allocations of resources to aspects of the marketing mix produce bottom-line results. © 1993, Elsevier Science Publishers B.V. All rights reserved.

The domain of this review includes the develop ment and application of multidimensional scaling (MDS) in product planning; in decisions concerning pricing and branding; in the study of channels of dis tribution, personal selling, and the effects of advertis ing ; and in research related to the fact finding and analysis mission of marketing research. In research on product planning, specific attention is given to market structure analysis, to the development of a master con figuration of product perceptions, to the role of indi vidual differences, to representing consumer prefer ences, to issues in market segmentation, and to the use of asymmetric MDS to study market structure. Regarding fact finding and analysis, this review deals with issues in data collection such as the response rate, time, and accuracy of judgments; the validity, re liability, and stability of judgments; and the robustness of data collection techniques and MDS algorithms. A separate section on new-product models deals with the determination of relevant product markets, the identifi cation of determinant attributes, the creation of prod uct perceptual spaces, and the modeling of individual or market-segment decision making. Three trends are discussed briefly; (1) a trend toward finer grained in spection of individual and group perceptions, (2) a trend toward merging consumer level measurement and market level measurements, and (3) a trend to ward the study of the creation of new markets, rather than new products in existing markets.

The concept of preference is of primary importance in psychology. It has had an implicit role in almost every psychological theory, but no major efforts have been directed toward the explication of preference as a psychological concept. Why is one object preferred to another? is a question which has remained unan- swered, at least to the extent that the psychological nature of pref- erence has remained subservient to the other purposes of investigators.

A special case of three-mode factor analysis is used to portray the systematic structure underlying asymmetric cross elasticities for a broad class of market-share attraction models. Analysis of the variation over retail outlets and weeks reveals competitive patterns corresponding to sales for the major brands in the market as well as patterns reflecting shelf-price competition. Analysis of the brand domain results in a joint space. One set of brand positions portrays how brands exert influence over the competition. The other set of points portrays how brands are influenced by others. The interset distances (angles) provide direct measures of competitive pressures. Maps are formed as spatial representations of each of the competitive patterns discovered.

In this article, the author outlines an approach to marketing planning for radically new products, disruptive or discontinuous innovations that change the dimensionality of the consumer decision. The planning process begins with an extensive situation analysis. The factors identified in the situation analysis are woven into the economic webs surrounding the new product. The webs are mapped into Bayesian networks that can be updated as events unfold and used to simulate the impact that changes in assumptions underlying the web have on the prospects for the new product. The author illustrates this method using a historical case regarding the introduction of videotape recorders by Sony and JVC and a contemporary case of the introduction of electric vehicles. The author provides a complete, numerical example pertaining to a software development project in the Appendix.