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This revised edition presents the relevant aspects of transformational geometry, matrix algebra, and calculus to those who may be lacking the necessary mathematical foundations of applied multivariate analysis. It brings up-to-date many definitions of mathematical concepts and their operations. It also clearly defines the relevance of the exercises to concerns within the business community and the social and behavioral sciences. Readers gain a technical background for tackling applications-oriented multivariate texts and receive a geometric perspective for understanding multivariate methods. Mathematical Tools for Applied Multivariate Analysis, Revised Edition illustrates major concepts in matrix algebra, linear structures, and eigenstructures geometrically, numerically, and algebraically. The authors emphasize the applications of these techniques by discussing potential solutions to problems outlined early in the book. They also present small numerical examples of the various concepts. Key Features * Provides a technical base for tackling most applications-oriented multivariate texts * Presents a geometric perspective for aiding ones intuitive grasp of multivariate methods * Emphasizes technical terms current in the social and behavioral sciences, statistics, and mathematics * Can be used either as a stand-alone text or a supplement to a multivariate statistics textbook * Employs many pictures and diagrams to convey an intuitive perception of matrix algebra concepts * Toy problems provide a step-by-step approach to each model and matrix algebra concept * Provides solutions for all exercises

ABSTRACTProduct‐concept testing is a popular activity in marketing research. Often the number of new product/service concepts under study far exceeds the time available for any single respondent. Respondents therefore may receive only a subset of the concepts comprising the total design. Researchers are interested in making plausible imputations for the missing evaluations of any given respondent.This paper proposes a model and an iterative estimation procedure to impute missing entries for each evaluator. The model and the procedure incorporate (1) the internal structure of the response matrix and (2) an ancillary matrix of (nonmissing) respondent background data; they also (3) allow for individual differences in respondents' uses of the numerical rating scale. The model is applied to both real and synthetic data. Suggestions also are given on how the data imputations may be used in market segmentation and product‐line decisions.

Two recently developed probabilistic multidimensional models for analyzing pairwise choice data are introduced, discussed in terms of their differential properties, and extended in several ways. The first one, the wandering vector model, was originally suggested by Carroll [12] and extended by De Soete and Carroll [30]. The second model, called the wandering ideal point model, is a more recently proposed [32] unfolding analog of the wandering vector model. A general maximum likelihood estimation method for fitting the various models described is mentioned, as well as a statistical test for assessing the goodness of fit. Finally, an application of the models is provided concerning consumer choice for some 14 brands of over‐the‐counter analgesics to illustrate how such models can be gainfully utilized for marketing decision making concerning product positioning.