Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-07T18:18:26.944Z Has data issue: false hasContentIssue false
  • English
  • Français

Determining Parameter Values in the Generalized Image System

Published online by Cambridge University Press:  01 January 2025

Raymond F. Koopman
Raymond F. Koopman*
Affiliation:
Simon Fraser University
Get access Rights & Permissions [Opens in a new window]

Abstract

Generalized image analysis is considered as a logical algebraic extension of Guttmanian image analysis. Under the assumption that a reduced-rank description of the images is desired, a procedure is developed which achieves the scale-free property by simultaneously rescaling in the metrics of both the images and anti-images, and which produces images and anti-images that are maximally independent in terms of the dimensions needed to account for them.

Type
Original Paper
Information
Psychometrika , Volume 38 , Issue 4 , December 1973 , pp. 495 - 511
Copyright
Copyright © 1973 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

*

Research leading to this paper was partially supported by a grant from the National Research Council of Canada.

References

Bentler, P. M. Alpha-maximized factor analysis (alphamax): its relation to alpha and canonical factor analysis. Psychometrika, 1968, 33, 335–345CrossRefGoogle ScholarPubMed
Bentler, P. M. Some extensions of image analysis. Psychometrika, 1969, 34, 77–83CrossRefGoogle Scholar
Bentler, P. M. A regression model for factor analysis. Proceedings of the 78th Annual Convention of the American Psychological Association, 1970, 109–110.Google Scholar
Guttman, L. Image theory for the structure of quantitative variates. Psychometrika, 1953, 18, 277–296CrossRefGoogle Scholar
Harman, H. H. Modern Factor Analysis, Second Edition, Chicago: University of Chicago Press, 1967Google Scholar
Harris, C. W. Some Rao-Guttman relationships. Psychometrika, 1962, 27, 247–264CrossRefGoogle Scholar
Horst, P. Matrix Algebra for Social Scientists, 1964, New York: Holt, Rinehart and WinstonGoogle Scholar
Jöreskog, K. G. Efficient estimation in image factor analysis. Psychometrika, 1969, 34, 51–75CrossRefGoogle Scholar
Kaiser, H. F. The varimax criterion for analytic rotation in factor analysis. Psychometrika, 1958, 23, 187–200CrossRefGoogle Scholar
MacDonald, R. P. A unified treatment of the weighting problem. Psychometrika, 1968, 33, 351–381CrossRefGoogle Scholar
Thurstone, L. L. Multiple Factor Analysis, 1947, Chicago: University of Chicago PressGoogle Scholar
Tucker, L. R, Cooper, L. G. and Meredith, W. Obtaining squared multiple correlations from a correlation matrix which may be singular. Psychometrika, 1972, 37, 143–148CrossRefGoogle Scholar
Tucker, L. R, Koopman, R. F. and Linn, R. L. Evaluation of factor analytic research procedures by means of simulated correlation matrices. Psychometrika, 1969, 34, 421–459CrossRefGoogle Scholar