A direct approach to individual differences scaling using increasingly complex transformations

A family of models for the representation and assessment of individual differences for multivariate data is embodied in a hierarchically organized and sequentially applied procedure called PINDIS. The two principal models used for directly fitting individual configurations to some common or hypothesized space are the dimensional salience and perspective models. By systematically increasing the complexity of transformations one can better determine the validities of the various models and assess the patterns and commonalities of individual differences. PINDIS sheds some new light on the interpretability and general applicability of the dimension weighting approach implemented by the commonly used INDSCAL procedure.

[1]  C. Horan Multidimensional scaling: Combining observations when individuals have different perceptual structures , 1969 .

[2]  P. Schönemann,et al.  A solution to the weighted procrustes problem in which the transformation is in agreement with the loss function , 1976 .

[3]  J. Gower Generalized procrustes analysis , 1975 .

[4]  J. Douglas Carroll,et al.  Chapter 13 – APPLICATIONS OF INDIVIDUAL DIFFERENCES SCALING TO STUDIES OF HUMAN PERCEPTION AND JUDGMENT , 1974 .

[5]  J. Berge,et al.  Orthogonal procrustes rotation for two or more matrices , 1977 .

[6]  C. Helm MULTIDIMENSIONAL RATIO SCALING ANALYSIS OF PERCEIVED COLOR RELATIONS. , 1964, Journal of the Optical Society of America.

[7]  Louis Guttman,et al.  On the Multivariate Structure of Wellbeing , 1975 .

[8]  Forrest W. Young,et al.  Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features , 1977 .

[9]  Joseph L. Zinnes,et al.  Theory and Methods of Scaling. , 1958 .

[10]  R. MacCallum A Comparison of Two Individual Differences Models for Multidimensional Scaling: Carroll and Chang's Indscal and Tucker's Three-Mode Factor Analysis , 1974 .

[11]  P. Schönemann,et al.  A generalized solution of the orthogonal procrustes problem , 1966 .

[12]  P. Schönemann,et al.  Fitting one matrix to another under choice of a central dilation and a rigid motion , 1970 .

[13]  Bruce Bloxom,et al.  INDIVIDUAL DIFFERENCES IN MULTIDIMENSIONAL SCALING , 1968 .

[14]  E. B. Andersen,et al.  Modern factor analysis , 1961 .

[15]  L. Tucker,et al.  Individual differences in the structure of color-perception. , 1960, The American journal of psychology.

[16]  Shlomit Levy,et al.  Use of the mapping sentence for coordinating theory and research: A cross-cultural example , 1976 .

[17]  P. Schönemann,et al.  An algebraic solution for a class of subjective metrics models , 1972 .

[18]  L. Tucker Relations between multidimensional scaling and three-mode factor analysis , 1972 .

[19]  R. MacCallum,et al.  Effects of conditionality on INDSCAL and ALSCAL weights , 1977 .

[20]  H. Harman Modern factor analysis , 1961 .

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

[22]  Peter H. Schönemann,et al.  Alternative measures of fit for the Schönemann-carroll matrix fitting algorithm , 1974 .

[23]  Louis Guttman,et al.  The Guttman-Lingoes nonmetric program series , 1973 .