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Influential Observations in Principal Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Yutaka Tanaka  and
Yoshimasa Odaka
Yutaka Tanaka*
Affiliation:
Department of Statistics, Okayama University
Yoshimasa Odaka
Affiliation:
Information Processing Center, Okayama University of Science
*
Request for reprints should be sent to Yutaka Tanaka, Department of Statistics, Okayama University, 2-1-1 Tsushima-naka, Okayama 700. JAPAN.
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Abstract

We propose a method for detecting influential observations in iterative principal factor analysis. For this purpose we derive the influence functions I(x; LLT) and I(x; Δ) for the common variance matrix T =LLT and the unique variance matrix Δ, respectively, in the common factor decomposition Σ =LLT + Δ. A numerical example is given for illustration.

Keywords

influential observationsinfluence functioninfluence on the subspace spanned by eigenvectorsprincipal factor analysisperturbation theory of eigenvalue problems
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 3 , September 1989 , pp. 475 - 485
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

The authors are grateful to Tomoyuki Tarumi and Atsuhiro Hayashi for their kind permission to use their software Seto/B for drawing Figures 1 and 2 and to anonymous reviewers for comments on the paper.

References

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