Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-08T09:44:12.559Z Has data issue: false hasContentIssue false
  • English
  • Français

Solving Implicit Equations in Psychometric Data Analysis

Published online by Cambridge University Press:  01 January 2025

J. O. Ramsay
J. O. Ramsay*
Affiliation:
McGill University
Get access Rights & Permissions [Opens in a new window]

Abstract

Many data analysis problems in psychology may be posed conveniently in terms which place the parameters to be estimated on one side of an equation and an expression in these parameters on the other side. A rule for improving the rate of convergence of the iterative solution of such equations is developed and applied to four problems: the principal axis communality problem, individual differences multidimensional scaling, LP norm multiple regression, and LP norm factor analysis of a data matrix. The rule results in substantially faster solutions or in solutions where none would be possible without the rule.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 3 , September 1975 , pp. 337 - 360
Copyright
Copyright © 1975 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

*

This work was supported by National Research Council of Canada grant APA 320 to the author.

References

Aitken, A. C.. On Bernoulli's numerical solution of algebraic equations. Proceedings of the Royal Society of Edinburgh, 1926, 46, 289–305.CrossRefGoogle Scholar
Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H., Tukey, J. W.. Robust estimates of location: Survey and advances, 1972, Princeton: Princeton University Press.Google Scholar
Blum, E. K.. Numerical analysis and computation: Theory and practice, 1972, Reading, Mass.: Addison-Wesley.Google Scholar
Browne, M. W.. A comparison of factor analytic techniques. Psychometrika, 1968, 33, 267–334.CrossRefGoogle ScholarPubMed
Carroll, J. D., Chang, J.. Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition. Psychometrika, 1970, 35, 283–319.CrossRefGoogle Scholar
Guilford, J. P.. The nature of human intelligence, 1967, New York: McGraw-Hill.Google Scholar
Guttman, L.. A general nonmetric technique for finding the smallest coordinate space for a configuration of points. Psychometrika, 1968, 33, 469–506.CrossRefGoogle Scholar
Harman, H. H.. Modern factor analysis, 2nd ed, Chicago: University of Chicago Press, 1967.Google Scholar
Isaacson, E., Keller, H. B.. Analysis of numerical methods, 1966, New York: Wiley.Google Scholar
Jöreskog, K. G.. Some contributions to maximum likelihood factor analysis. Psychometrika, 1967, 32, 443–482.CrossRefGoogle Scholar
Jöreskog, K. G.. A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 1969, 34, 183–202.CrossRefGoogle Scholar
Ortega, J. M., Rheinboldt, W. C.. Iterative solution of nonlinear equations in several variables, 1970, New York: Academic Press.Google Scholar
Rao, C. R.. Estimation and test of significance in factor analysis. Psychometrika, 1955, 20, 93–111.CrossRefGoogle Scholar
Ramsay, J. O., Case, B.. Attitude measurement and the linear model. Psychological Bulletin, 1970, 74, 185–192.CrossRefGoogle Scholar
Ramsay, J. O. A quadratically convergent algorithm for discrete linear approximation by minimizing the L P norm. Unpublished manuscript, 1974.Google Scholar
Wilkinson, J. H., Reinsch, C.. Handbook for automatic computation Vol. 2. Linear algebra, 1971, Berlin: Springer-Verlag.CrossRefGoogle Scholar