Some statistical considerations in multidimensional scaling
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In this article, a statistical model for perceived difference is derived which avoids these difficulties and employs judgments of ratios of differences as data, and three estimators of squared difference are developed.Abstract:
Some shortcomings of current methods of estimating the magnitude of perceived difference are considered. A statistical model for perceived difference is derived which avoids these difficulties and employs judgments of ratios of differences as data. Three estimators of squared difference are developed.read more
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Review of the Development of Multidimensional Scaling Methods
TL;DR: Multidimensional scaling methods are now a common statistical tool in psychophysics and sensory analysis as discussed by the authors and have been used extensively in the field of computer vision and computer vision, where they are used to construct a configuration of n points, usually in Euclidean space, from information about the pairwise distances among a set of n objects or individuals.
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Maximum likelihood estimation in multidimensional scaling
TL;DR: In this article, a variety of distributional assumptions for dissimilarity judgments are considered, with the lognormal distribution being favored for most situations, and an implicit equation is discussed for the maximum likelihood estimation of the configuration with or without individual weighting of dimensions.
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Nonmetric multidimensional scaling: Recovery of metric information
TL;DR: If the ratio of the degrees of freedom of the data to that of the coordinates is sufficiently large then metric information is recovered even when random error is present; and when the number of points being scaled increases the stress of the solution increases even though the degree of metric determinacy increases.
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On a Metric, Unidimensional Unfolding Model for Attitudinal and Developmental Data.
TL;DR: In this paper, the stimulus responses are linearly related to squared distances between stimulus scale values and person scores along a latent continuum, and the stimulus × stimulus correlation matrix display a simplex-like pattern, the signs of first-order partial correlations can be specified in an empirically testable manner, and variables will have a semicircular, two-factor structure.
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Probabilistic, multidimensional unfolding analysis
TL;DR: In this paper, a probabilistic, multidimensional version of Coombs' unfolding model is obtained by assuming that the projections of each stimulus and each individual on each axis are normally distributed.
References
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Journal ArticleDOI
Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
TL;DR: The fundamental hypothesis is that dissimilarities and distances are monotonically related, and a quantitative, intuitively satisfying measure of goodness of fit is defined to this hypothesis.
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A law of comparative judgment
TL;DR: The law of comparative judgment as mentioned in this paper is applicable not only to the comparison of physical stimulus intensities but also to qualitative comparative judgments such as those of excellence of specimens in an educational scale.
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Nonmetric multidimensional scaling: A numerical method
TL;DR: The numerical methods required in the approach to multi-dimensional scaling are described and the rationale of this approach has appeared previously.
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A Rapidly Convergent Descent Method for Minimization
Roger Fletcher,M. J. D. Powell +1 more
TL;DR: A number of theorems are proved to show that it always converges and that it converges rapidly, and this method has been used to solve a system of one hundred non-linear simultaneous equations.