Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-08T12:00:29.621Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear Factors in Two Dimensions

Published online by Cambridge University Press:  01 January 2025

W. A. Gibson
W. A. Gibson*
Affiliation:
Personnel Research Branch, Tago, Department of the Army
Get access Rights & Permissions [Opens in a new window]

Abstract

Intercorrelations among tests nonlinearly related to underlying dimensions require more linear factors than content would demand. For the case of two independent underlying content dimensions, a fictitious example is constructed and made to yield a transformation useful for the nonlinear analysis of certain empirical data. That transformation, when applied to a standard factorization (centroid or principal components if certain symmetries obtain) of the appropriate empirical correlations, yields parameters descriptive of plausible nonplanar regression surfaces for tests on the two underlying dimensions. An empirical example is presented and discussed.

Type
Original Paper
Information
Psychometrika , Volume 25 , Issue 4 , December 1960 , pp. 381 - 392
Copyright
Copyright © 1960 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

*

The opinions expressed are those of the author and are not to be construed as reflecting official Department of the Army policy.

References

Carroll, J. B. The effect of difficulty and chance success on correlations between items or between tests. Psychometrika, 1945, 10, 1–19.CrossRefGoogle Scholar
Dingman, H. F. The dependence of factorial analysis upon the correlation statistic. Unpublished doctoral dissertation, Univ. Southern California, 1955.Google Scholar
Ferguson, G. A. The factorial interpretation of test difficulty. Psychometrika, 1941, 6, 323–329.CrossRefGoogle Scholar
Gibson, W. A. Non-linear factor analysis, single factor case. Amer. Psychologist, 1955, 10, 438–438. (Abstract).Google Scholar
Gibson, W. A. Three multivariate models: factor analysis, latent structure analysis, and latent profile analysis. Psychometrika, 1959, 24, 229–252.CrossRefGoogle Scholar
Green, B. F. A general solution for the latent class model of latent structure analysis. Psychometrika, 1951, 16, 151–166.CrossRefGoogle ScholarPubMed
Green, B. F. The orthogonal approximation of an oblique structure in factor analysis. Psychometrika, 1952, 17, 429–440.CrossRefGoogle Scholar
Guilford, J. P. The difficulty of a test and its factor composition. Psychometrika, 1941, 6, 67–77.CrossRefGoogle Scholar
Guilford, J. P. and Zimmerman, W. S.. The Guilford-Zimmerman aptitude survey, Beverly Hills: Sheridan Supply Company, 1947.Google Scholar
Lazarsfeld, P. F. et al. The logical and mathematical foundation of latent structure analysis. In Stouffer, S. A. et al (Eds.), Measurement and prediction. Princeton: Princeton Univ. Press, 1950, 362–412.Google Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar
Wherry, R. J. and Gaylord, R. H. Factor pattern of test items and tests as a function of the correlation coefficient: content, difficulty, and constant error factors. Psychometrika, 1944, 9, 237–244.CrossRefGoogle Scholar