Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-08T00:52:40.959Z Has data issue: false hasContentIssue false
  • English
  • Français

Sequential Estimation in Multidimensional Scaling

Published online by Cambridge University Press:  01 January 2025

Hisao Miyano  and
Yukio Inukai
Hisao Miyano*
Affiliation:
Industrial Products Research Institute
Yukio Inukai
Affiliation:
Industrial Products Research Institute
*
Requests for reprints should be sent to Hisao Miyano, Human Factors Engineering Division, Industrial Products Research Institute, 1-1-4 Yatabe-higashi, Tsukuba, Ibaragi, Japan 305.
Get access Rights & Permissions [Opens in a new window]

Abstract

The concept of sequential estimation is introduced in multidimensional scaling (MDS). The sequential estimation method developed in this paper refers to continually updating estimates of a configuration as new observations are added. This method has a number of advantages, such as a locally optimal design of the experiment can be easily constructed, and dynamic experimentation is made possible. Using artificial data, the performance of our sequential method is illustrated.

Keywords

sequential estimationGauss-Newton methodlocally optimal designInteractive Scaling with Individual Subjects (ISIS)metric multidimensional scaling
Type
Original Paper
Information
Psychometrika , Volume 47 , Issue 3 , September 1982 , pp. 321 - 336
Copyright
Copyright © 1982 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

We are indebted to anonymous reviewers for their suggestions. In addition, we thank Dr. Frank Critchley for his helpful comments on our Q/S algorithm.

References

Beck, J. V. & Arnold, K. J. Parameter estimation in engineering and science, 1977, New York: Wiley.Google Scholar
deLeeuw, J. & Heiser, W. Convergence of correlation-matrix algorithms for multidimensional scaling. In Lingoes, J. C. (Eds.), Geometric representations of relational data, 1977, Ann Arbor, Michigan: Mathesis Press.Google Scholar
Fedorov, V. V. Theory of optimal experiments, 1972, New York: Academic Press.Google Scholar
Girard, R. A. & Cliff, N. A monte carlo evaluation of interactive multidimensional scaling. Psychometrika, 1976, 41, 43–64.CrossRefGoogle Scholar
Lingoes, J. C. & Roskam, E. E. A mathematical and empirical analysis of two multidimensional scaling algorithms. Psychometrika Monograph Supplement, 1973, 38.Google Scholar
Ramsey, J. O. Confidence regions for multidimensional scaling. Psychometrika, 1978, 43, 145–160.CrossRefGoogle Scholar
Takane, Y., Young, F. & deLeeuw, J. Nonmetric individual differences multidimensional scaling: An alternative least squares method with optimal scaling features. Psychometrika, 1977, 42, 7–67.CrossRefGoogle Scholar
Young, F. & Cliff, N. Interactive scaling with individual subjects. Psychometrika, 1972, 37, 385–415.CrossRefGoogle Scholar