Pattern goodness and redundancy revisited: Multidimensional scaling and hierarchical clustering analyses

Glushko, Robert J.

doi:10.3758/bf03203880

Cited by 19 publications

(14 citation statements)

References 8 publications

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“…if it turns out to be justified, this will give the configuration the form of a chain of rectangular regions. In fact, Glushko's (1975) unconstrained MDS results already satisfy such multiple constraints nearly perfectly, which is of Figure 2 Circumplex as a Circular Graph with Path-Length Metric course strong support for the primacy of his redundancy measure. Finally, an example of more complex inequality constraints is worth mentioning.…”

Section: Constraints On the Coordinatesmentioning

confidence: 78%

“…For now, consider the following example of the in-betweenness notion. Glushko (1975) used the concept that the redundancy of visual patterns should be characterized by the number of distinct alternatives obtained under rigid rotations in 90-degree steps or reflections of the original patterns. According to this definition, a circle or a cross is highly redundant because both remain perceptually equivalent under the indicated set of transformations.…”

Section: Constraints On the Coordinatesmentioning

confidence: 99%

See 1 more Smart Citation

Constrained Multidimensional Scaling, Including Confirmation

Heiser

Meulman

1983

Applied Psychological Measurement

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Constrained and confirmatory multidimensional scaling (MDS) are not equivalent. Constraints refer to the translation of either theoretical or data analytical objectives into computational specifications. Confirmation refers to a study of the balance between systematic and random variation in the data for modeling of the systematic part. Among the topics discussed from this perspective are the role of substantive theory in MDS studies, the type of constraints currently envisaged, and the relationships with other data analysis methods. This paper points out the possibility of using either sampling models or resampling schemes to study the stability of MDS solutions. Parallel to Akaike's (1974) information criterion for choosing one out of many models for the same data, a general stability criterion is proposed and illustrated, based on the ratio of within to total spread of configurations issued from resampling. Scaling Analysis and OptimizationThe coupling of constraints and scaling, although not new, is still extremely vital. The first modem scaling model, developed by Thurstone (e.g., 1927), immediately entailed the necessity of a judicious choice of constraints, as classified in the five famous 6bc~sese&dquo; These were internal constraints in the sense that the modified model would still accommodate the same set of observations, possibly less accurately, but with more predictive value. Guttman (1946) took a number of important additional steps. He showed that Thurstone's s method, relying on an underlying multivariate normal distribution, could be replaced by an approach in which the optimization of a goodness-of-fit function is the central concept. This was an extension of similar developments occurring at that time in test theory and in contingency table analysis (for current reviews, s~e l~lishisato, 1980, and Gin, 1981) to the scaling of paired comparison and rank order data. Moreover, Guttman showed that introducing an additional type of constraint was not a problem. The proper objective would be to find scale values for the stimulus objects that are &dquo;best able to reproduce the judgment of each person in the population on each comparison&dquo; (Guttman, 1946, p. 14~) and that are also perfectly linearly predictable from a predeterrrgined set of (design) variables.Although through hindsight it seems clear that it would have been possible to formulate a constrained multidimensional scaling (MDS) method within Guttman's framework, the early paradigm for MDS was to split the problem into two distinct steps. From the very first published psychometric application by Klingberg (1941)-based on earlier work by Richardson (1938)-to the authoritative presentation in Torgerson's (1958) book, it is evident that the main burden and first step of the analysis was to find a one-dimensional scale of psychological distances between pairs of stimulus objects. This was usually done by any of the varat UNIVERSITE DE MONTREAL on June 23, 2015 apm.sagepub.com Downloaded from

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Section: Constraints On the Coordinatesmentioning

confidence: 78%

Section: Constraints On the Coordinatesmentioning

confidence: 99%

Constrained Multidimensional Scaling, Including Confirmation

Heiser

Meulman

1983

Applied Psychological Measurement

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“…The data sets are all available online courtesy of Michael Lee (www.socsci.uci.edu/~mdlee/sda.html) and cover a range of collection methodologies and domains. Specifically the data relate to colors (Ekman, 1954), countries (Navarro & Lee, 2002), congressional voting patterns (Romesburg, 1984), dot patterns (Glushko, 1975), patterns of drug use (Huba et al, 1981), photographs of faces (unpublished data, Michael Lee), drawings of flower pots (Gati & Tversky, 1982), fruits (Tversky & Hutchinson, 1986), kinship terms (Rosenberg & Kim, 1975), the numbers 0-9 (Shepard et al, 1975), morse code patterns (Rothkopf, 1957) and rectangles with interior line segments (Kruschke, 1993).…”

Section: On the Goodness Of Categoriesmentioning

confidence: 99%

Hypothesis generation, sparse categories, and the positive test strategy.

Navarro

Perfors

2011

Psychological Review

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If a paper is unpublished, the author may distribute it on the Internet or post it on a website but should label the paper with the date and with a statement that the paper has not (yet) been published. (Example: Draft version 1.3, 1/5/08. This paper has not been peer reviewed. Please do not copy or cite without author's permission.) Authors of articles published in APA journals may post a copy of the final manuscript, as accepted for publication, as a word processing file, on their personal website, their employer's server, or in their institution's repository after it is accepted for publication. The following conditions would prevail: The posted article must carry an APA copyright notice and include a link to the APA journal home page or to the final published version using the article's DOI, or digital object identifier, that may be found on the first page of the published article, in the upper right-hand corner. AbstractWe consider the situation in which a reasoner must induce the rule that explains an observed set of data but the hypothesis space of possible rules is not explicitly enumerated or identified. The first part of the paper demonstrates that as long as hypotheses are sparse (i.e., index less than half of the possible entities in the domain) then a positive test strategy is near-optimal. The second part of this paper then demonstrates that a preference for sparse hypotheses (a sparsity bias) emerges as a natural consequence of the family resemblance principle; that is, it arises from the requirement that good rules index entities that are more similar to one another than they are to entities that do not satisfy the rule.

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“…MDS representations have their origins in, and some considerable status as, plausible models of human conceptual structure, particularly in relation to lowlevel, continuous sensory stimulus domains (Shepard, 1957(Shepard, , 1987(Shepard, , 1994. For this reason, MDS representations have been used as a tool for analyzing the psychological similarity structure of a variety of stimulus domains (e.g., Glushko, 1975;Jones, Roberts, & Holman, 1978;Heaps & Handel, 1999). In addition, they are used as the representational basis of a number of successful cognitive models, including the Generalized Context Model (Nosofsky, 1984(Nosofsky, , 1986, and ALCOVE (Kruschke, 1992).…”

Section: Introductionmentioning

confidence: 99%

Avoiding the dangers of averaging across subjects when using multidimensional scaling

Lee

Pope

2003

Journal of Mathematical Psychology

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Ashby, Maddox and Lee (Psychological Science, 5 (3) 144) argue that it can be inappropriate to fit multidimensional scaling (MDS) models to similarity or dissimilarity data that have been averaged across subjects. They demonstrate that the averaging process tends to make dissimilarity data more amenable to metric representations, and conduct a simulation study showing that noisy data generated using one distance metric, when averaged, may be better fit using a different distance metric. This paper argues that a Bayesian measure of MDS models has the potential to address these difficulties, because it takes into account data-fit, the number of dimensions used by an MDS representation, and the precision of the data. A method of analysis based on the Bayesian measure is demonstrated through two simulation studies with accompanying theoretical analysis. In the first study, it is shown that the Bayesian analysis rejects those MDS models showing better fit to averaged data using the incorrect distance metric, while accepting those that use the correct metric. In the second study, different groups of simulated 'subjects' are assumed to use different underlying configurations. In this case, the Bayesian analysis rejects MDS representations where a significant proportion of subjects use different configurations, or when their dissimilarity judgments contain significant amounts of noise. It is concluded that the Bayesian analysis provides a simple and principled means for systematically accepting and rejecting MDS models derived from averaged data. r

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Pattern goodness and redundancy revisited: Multidimensional scaling and hierarchical clustering analyses

Cited by 19 publications

References 8 publications

Constrained Multidimensional Scaling, Including Confirmation

Constrained Multidimensional Scaling, Including Confirmation

Hypothesis generation, sparse categories, and the positive test strategy.

Avoiding the dangers of averaging across subjects when using multidimensional scaling

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