Analysis of asymmetry by a slide-vector

The slide-vector scaling model attempts to account for the asymmetry of a proximity matrix by a uniform shift in a fixed direction imposed on a symmetric Euclidean representation of the scaled objects. Although no method for fitting the slide-vector model seems available in the literature, the model can be viewed as a constrained version of the unfolding model, which does suggest one possible algorithm. The slide-vector model is generalized to handle three-way data, and two examples from market structure analysis are presented.

[1]  J. Edward Jackson,et al.  The User's Guide to Multidimensional Scaling , 1985 .

[2]  Willem J. Heiser,et al.  Constrained Multidimensional Scaling, Including Confirmation , 1983 .

[3]  W. Heiser.  Joint Ordination of Species and Sites: The Unfolding Technique , 1987 .

[4]  E. Holman.  Monotonic models for asymmetric proximities , 1979 .

[5]  J. Chang,et al.  Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .

[6]  J. Leeuw.  Convergence of the majorization method for multidimensional scaling , 1988 .

[7]  J. Kruskal.  Nonmetric multidimensional scaling: A numerical method , 1964 .

[8]  A. Tversky.  Features of Similarity , 1977 .

[9]  J. Carroll,et al.  Chapter 12 – MULTIDIMENSIONAL PERCEPTUAL MODELS AND MEASUREMENT METHODS , 1974 .

[10]  Willem J. Heiser,et al.  Constrained Multidimensional Scaling: more directions than Dimensions , 1984 .

[11]  R. Harshman,et al.  A Model for the Analysis of Asymmetric Data in Marketing Research , 1982 .

[12]  A. Okada.  Asymmetric multidimensional scaling of car switching data , 1988 .

[13]  R. Nosofsky.  Stimulus bias, asymmetric similarity, and classification , 1991, Cognitive Psychology.

[14]  John C. Gower,et al.  Graphical Representation of Asymmetric Matrices , 1978 .

[15]  Willem J. Heiser,et al.  13 Theory of multidimensional scaling , 1982, Classification, Pattern Recognition and Reduction of Dimensionality.

[16]  G. W. Milligan,et al.  An examination of the effect of six types of error perturbation on fifteen clustering algorithms , 1980 .

[17]  J. Kruskal.  Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis , 1964 .

[18]  C. Krumhansl.  Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. , 1978 .

[19]  W. Tobler,et al.  A Cappadocian Speculation , 1971, Nature.

[20]  Henri Caussinus,et al.  Contribution à l'analyse statistique des tableaux de corrélation , 1965 .

[21]  Willem J. Heiser,et al.  Analyzing rectangular tables by joint and constrained multidimensional scaling , 1983 .

[22]  G. Keren,et al.  Recognition models of alphanumeric characters. , 1981, Perception & psychophysics.

[23]  M. P. Friedman,et al.  HANDBOOK OF PERCEPTION , 1977 .

[24]  Peter M. Bentler,et al.  Restricted multidimensional scaling models for asymmetric proximities , 1982 .