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The Manifest Association Structure of the Single-Factor Model: Insights from Partial Correlations

Published online by Cambridge University Press:  01 January 2025

Maria de Fátima Salgueiro ,
Peter W. F. Smith  and
John W. McDonald
Maria de Fátima Salgueiro*
Affiliation:
ISCTE Business School
Peter W. F. Smith
Affiliation:
University of Southampton
John W. McDonald
Affiliation:
University of Southampton
*
Requests for reprints should be sent to Maria de Fátima Salgueiro, Departamento Métodos Quantitativos, ISCTE Business School, Lisboa, Portugal. E-mail: [email protected]
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Abstract

The association structure between manifest variables arising from the single-factor model is investigated using partial correlations. The additional insights to the practitioner provided by partial correlations for detecting a single-factor model are discussed. The parameter space for the partial correlations is presented, as are the patterns of signs in a matrix containing the partial correlations that are not compatible with a single-factor model.

Keywords

anti-image correlation matrixelliptical tetrahedronfactor analysisfactor partial correlationmanifest partial correlation
Type
Theory and Methods
Information
Psychometrika , Volume 73 , Issue 4 , December 2008 , pp. 665 - 670
Copyright
Copyright © 2007 The Psychometric Society

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Footnotes

The research of the first author was supported by the Fundaçāo para a Ciência e a Tecnologia and by the Southampton Statistical Sciences Research Institute.

The authors thank the Editor, the Associate Editor and three Reviewers for their constructive comments which helped to improve the paper.

References

Anderson, T.W., & Rubin, H. (1956). Statistical inference in factor analysis. Proceedings of the third Berkeley symposium on mathematical statistics and probability (pp. 111–150). Berkeley: University of California Press.Google Scholar
Guttman, L. (1953). Image theory for the structure of quantitative variates. Psychometrika, 18, 277–296.CrossRefGoogle Scholar
Hadley, G. (1961). Linear algebra, Reading: Addison-Wesley.Google Scholar
Kaiser, H.F. (1970). A second generation Little Jiffy. Psychometrika, 35, 401–415.CrossRefGoogle Scholar
Rousseeuw, P.J., & Molenberghs, G. (1994). The shape of correlation matrices. The American Statistician, 48(4), 276–279.CrossRefGoogle Scholar
Salgueiro, M.F. (2003). Distributions of test statistics for edge exclusion for graphical models. PhD thesis, University of Southampton.Google Scholar
Salgueiro, M.F., Smith, P.W.F., & McDonald, J.W. (2005). Power of edge exclusion tests in graphical Gaussian models. Biometrika, 92(1), 173–182.CrossRefGoogle Scholar
Whittaker, J. (1990). Graphical models in applied multivariate statistics, Chichester: Wiley.Google Scholar
Yanai, H., & Mukherjee, B.N. (1987). A generalized method of image analysis from an intercorrelation matrix which may be singular. Psychometrika, 52(4), 555–564.CrossRefGoogle Scholar