Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-08T04:38:34.200Z Has data issue: false hasContentIssue false
  • English
  • Français

Multidimensional Scaling of Nominal Data: The Recovery of Metric Information with Alscal

Published online by Cambridge University Press:  01 January 2025

Forrest W. Young  and
Cynthia H. Null
Forrest W. Young*
Affiliation:
University of North Carolina at Chapel Hill
Cynthia H. Null
Affiliation:
College of William and Mary
*
Requests for reprints should be sent to Forrest Young, Psychometric Laboratory, University of North Carolina, Davie Hall 013-A, Chapel Hill, North Carolina 27514.
Get access Rights & Permissions [Opens in a new window]

Abstract

Multidimensional scaling has recently been enhanced so that data defined at only the nominal level of measurement can be analyzed. The efficacy of ALSCAL, an individual differences multidimensional scaling program which can analyze data defined at the nominal, ordinal, interval and ratio levels of measurement, is the subject of this paper. A Monte Carlo study is presented which indicates that (a) if we know the correct level of measurement then ALSCAL can be used to recover the metric information presumed to underlie the data; and that (b) if we do not know the correct level of measurement then ALSCAL can be used to determine the correct level and to recover the underlying metric structure. This study also indicates, however, that with nominal data ALSCAL is quite likely to obtain solutions which are not globally optimal, and that in these cases the recovery of metric structure is quite poor. A second study is presented which isolates the potential cause of these problems and forms the basis for a suggested modification of the ALSCAL algorithm which should reduce the frequency of locally optimal solutions.

Keywords

data analysisdata quantificationoptimal scalingcatetorical datanonmetricMonte Carloeuclidian
Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 3 , September 1978 , pp. 367 - 379
Copyright
Copyright © 1978 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.)

References

Reference Note

de Leeuw, J. Personal communication, 1976.Google Scholar

References

Ekman, G. Dimensions of color vision. Journal of Psychology, 1954, 38, 467–474.CrossRefGoogle Scholar
Hayashi, C. Minimum dimension analysis. Behaviormetrika, 1974, 1, 1–24.CrossRefGoogle Scholar
Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 1964, 29, 1–27.CrossRefGoogle Scholar
Schonemann, P. H., & Carroll, R. M. Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika, 1970, 35, 245–256.CrossRefGoogle Scholar
Spence, I. A Monte Carlo evaluation of three nonmetric multidimensional scaling algorithms. Psychometrika, 1972, 37, 461–486.CrossRefGoogle Scholar
Spence, I. Multidimensional scaling. In Colgan, P. (Eds.), Quantitative ethology, 1977, New York: Wiley-Interscience.Google Scholar
Takane, Y., Young, F. W., & de Leeuw, J. Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features. Psychometrika, 1977, 42, 7–67.CrossRefGoogle Scholar
Young, F. W. Nonmetric multidimensional scaling: Recovery of metric information. Psychometrika, 1970, 35, 455–474.CrossRefGoogle Scholar