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Application of the Bootstrap Methods in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Masanori Ichikawa  and
Sadanori Konishi
Masanori Ichikawa*
Affiliation:
Tokyo University of Foreign Studies
Sadanori Konishi
Affiliation:
Graduate School Department of Mathematics, Kyushu University
*
Requests for reprints should be sent to Masanori Ichikawa, Tokyo University of Foreign Studies, 4-51-21 Nishi-ga-Hara, Kita-Ku, Tokyo 114, JAPAN.
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Abstract

A Monte Carlo experiment is conducted to investigate the performance of the bootstrap methods in normal theory maximum likelihood factor analysis both when the distributional assumption is satisfied and unsatisfied. The parameters and their functions of interest include unrotated loadings, analytically rotated loadings, and unique variances. The results reveal that (a) bootstrap bias estimation performs sometimes poorly for factor loadings and nonstandardized unique variances; (b) bootstrap variance estimation performs well even when the distributional assumption is violated; (c) bootstrap confidence intervals based on the Studentized statistics are recommended; (d) if structural hypothesis about the population covariance matrix is taken into account then the bootstrap distribution of the normal theory likelihood ratio test statistic is close to the corresponding sampling distribution with slightly heavier right tail.

Keywords

factor analysisbootstrapmaximum likelihoodlikelihood ratio test statisticconfidence intervalMonte Carlo experiment
Type
Original Paper
Information
Psychometrika , Volume 60 , Issue 1 , March 1995 , pp. 77 - 93
Copyright
Copyright © 1995 The Psychometric Society

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Footnotes

This study was carried out in part under the ISM cooperative research program (91-ISM · CRP-85, 92-ISM · CRP-102). The authors would like to thank the editor and three reviewers for their helpful comments and suggestions which improved the quality of this paper considerably.

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