Goodness of fit for random rankings in Kruskal's nonmetric scaling procedure
Bibliographic Data
| ID | 4421911 |
|---|---|
| Authors | Herbert H Stenson, Ronald L Knoll |
| Year | 1969 |
| Volume | 71 |
| Issue | 2 |
| Pages | 122-126 |
| Publication date | 1969-02-01 |
| Open Access | No |
| Type | ARTICLE |
| Venue | Psychological Bulletin (JOURNAL) |
| Journal identifiers | ISSN: 0033-2909 • E-ISSN: 1939-1455 |
| Publisher | American Psychological Association (APA) (PUBLISHER) |
| DOI | 10.1037/h0026864 |
| OpenAlex | W2119330912 |
| Language | EN |
| Citations received | 19 |
| References cited | 2 |
in order to establish null hypotheses for the goodness-of-fit measure. Various numbers of hypothetical stimuli were analyzed using the Euclidean distance metric in various dimensionalities, and the effects of tied ranks were studied. Kruskal (1964a, 1964b) presented a method of multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. His method is an elaboration and refinement of the analysis of proximities proposed by Shepard (1962). In Kruskal's procedure, N points are positioned in an jw-dimensional space in such a way as to achieve the best possible approximation to a monotonic relationship be/N tween the ( . 1 interpoint distances and an experimentally obtained ranking of the dissimilarities among all pairs of N objects. For a given configuration of points, interpoint distance (d) is expressed as a function of ranked dissimilarity (8). The degree to which d is not a monotonic function of 8 for a given configuration is expressed by a measure called stress (S). Stress can be thought of as an
Combinatorics · Econometrics · Goodness of fit · Kruskal's algorithm · Multidimensional scaling · Scaling · Statistics · Advanced Statistical Methods and Models · Mathematics · Multi-Criteria Decision Making · Psychology
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| Citations per year | 0.36 |
|---|---|
| Citation span | 1973 - 2021 (49) |
| Highly cited | No |