Hostname: page-component-6898cfcb55-kwdml Total loading time: 0 Render date: 2026-11-11T18:50:43.678Z Has data issue: false hasContentIssue false
  • English
  • Français

The Infinitesimal Jackknife with Exploratory Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Guangjian Zhang,
Kristopher J. Preacher and
Robert I. Jennrich
Guangjian Zhang*
Affiliation:
University of Notre Dame
Kristopher J. Preacher
Affiliation:
Vanderbilt University
Robert I. Jennrich
Affiliation:
University of California at Los Angeles
*
Requests for reprints should be sent to Guangjian Zhang, Psychology Department, Haggar Hall, University of Notre Dame, Notre Dame, IN 46556, USA. E-mail: gzhang3@nd.edu
Get accessRights & Permissions [Opens in a new window]

Abstract

The infinitesimal jackknife, a nonparametric method for estimating standard errors, has been used to obtain standard error estimates in covariance structure analysis. In this article, we adapt it for obtaining standard errors for rotated factor loadings and factor correlations in exploratory factor analysis with sample correlation matrices. Both maximum likelihood estimation and ordinary least squares estimation are considered.

Keywords

exploratory factor analysisstandard errorEFAinfinitesimal jackknifeIJKnonparametric standard error estimatesmodel misspecificationnonnormal dataminimum deviance methods

Information

Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 4 , October 2012, pp. 634 - 648
Copyright
Copyright © 2012 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.)

Article purchase

Temporarily unavailable

References

Archer, C.O., & Jennrich, R.I. (1973). Standard errors for orthogonally rotated factor loadings. Psychometrika, 38, 581–592.CrossRefGoogle Scholar
Browne, M.W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical & Statistical Psychology, 37, 62–83.CrossRefGoogle ScholarPubMed
Browne, M.W. (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36, 111–150.CrossRefGoogle Scholar
Browne, M.W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In Bollen, K.A., & Long, J.S. (Eds.), Testing structural equation models (pp. 136–162). Newbury Park: Sage.Google Scholar
Browne, M.W., Cudeck, R., Tateneni, K., & Mels, G., (2008). CEFA: comprehensive exploratory factor analysis. Retrieved from http://faculty.psy.ohio-state.edu/browne/.Google Scholar
Browne, M.W., & Tateneni, K., (2008). Standard errors for OLS estimates in exploratory factor analysis. Annual meeting of the society of multivariate experimental psychology, Montreal, Canada.Google Scholar
Clarkson, D.B. (1979). Estimating the standard errors of rotated factor loadings by jackknifing. Psychometrika, 44, 297–314.CrossRefGoogle Scholar
Clarkson, D.B., & Jennrich, R.I. (1988). Quartic rotation criteria and algorithm. Psychometrika, 53, 251–259.CrossRefGoogle Scholar
Crawford, C.B., & Ferguson, G.A. (1970). A general rotation criterion and its use in orthogonal rotation. Psychometrika, 35, 321–332.CrossRefGoogle Scholar
Cudeck, R., & O’Dell, L.L. (1994). Applications of standard error estimates in unrestricted factor analysis: significance tests for factor loadings and correlations. Psychological Bulletin, 115, 475–487.CrossRefGoogle ScholarPubMed
Harman, H.H. (1960). Modern factor analysis. Chicago: University of Chicago Press.Google Scholar
Hayashi, K., & Yung, Y.F. (1999). Standard errors for the class of orthomax-rotated factor loadings: some matrix results. Psychometrika, 64, 451–460.CrossRefGoogle Scholar
Ichikawa, M., & Konishi, S. (1995). Application of the bootstrap methods in factor analysis. Psychometrika, 60, 77–93.CrossRefGoogle Scholar
Jennrich, R.I. (1973). Standard errors for obliquely rotated factor loadings. Psychometrika, 38, 593–604.CrossRefGoogle Scholar
Jennrich, R.I. (1974). Simplified formulae for standard errors in maximum-likelihood factor analysis. British Journal of Mathematical & Statistical Psychology, 27, 122–131.CrossRefGoogle Scholar
Jennrich, R.I. (2008). Nonparametric estimation of standard errors in covariance analysis using the infinitesimal jackknife. Psychometrika, 73, 579–594.CrossRefGoogle Scholar
Jennrich, R.I., & Clarkson, D.B. (1980). A feasible method for standard errors of estimate in maximum likelihood factor analysis. Psychometrika, 45, 237–247.CrossRefGoogle Scholar
Lambert, Z.V., Wildt, A.R., & Durand, R.M. (1991). Approximating confidence intervals for factor loadings. Multivariate Behavioral Research, 26, 421–434.CrossRefGoogle ScholarPubMed
Luo, S., Chen, H., Yue, G., Zhang, G., Zhaoyang, R., & Xu, D. (2008). Predicting marital satisfaction from self, partner, and couple characteristics: is it me, you, or us?. Journal of Personality, 76, 1231–1266.CrossRefGoogle ScholarPubMed
Mardia, K.V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519–530.CrossRefGoogle Scholar
Ogasawara, H. (1998). Standard errors of several indices for unrotated and rotated factors. Econ. Rev. Otaru Univ. Commer., 49 12169.Google Scholar
Ogasawara, H. (2007). Asymptotic expansion of the distributions of the estimators in factor analysis under non-normality. British Journal of Mathematical & Statistical Psychology, 60, 395–420.CrossRefGoogle ScholarPubMed
Ogasawara, H. (2007). Higher-order approximations to the distributions of fit indexes under fixed alternatives in structural equation models. Psychometrika, 72, 227–243.CrossRefGoogle Scholar
R Development Core Team (2007). R: a language and environment for statistical computing [computer software manual]. (ISBN 3-900051-07-0). Vienna, Austria. Available form http://www.R-project.org.Google Scholar
Satorra, A. (1989). Alternative test criteria in covariance structure analysis: a unified approach. Psychometrika, 54, 131–151.CrossRefGoogle Scholar
Shapiro, A. (1983). Asymptotic distribution theory in the analysis of covariance structures. South African Statistical Journal, 17, 33–81.Google Scholar
Steiger, J.H., & Lind, J.C., (1980, June). Statistically based tests for the number of common factors. Paper presented at the annual meeting of the psychometric society, Iowa City, IA. .Google Scholar
Tateneni, K., (1998). Use of automatic and numerical differentiation in the estimation of asymptotic standard errors in exploratory factor analysis. Doctoral dissertation, Ohio State University, Columbus, OH. .Google Scholar
Yuan, K., Marshall, L.L., & Bentler, P.M. (2002). A unified approach to exploratory factor analysis with missing data, nonnormal data, and in the presence of outliers. Psychometrika, 67, 95–122.CrossRefGoogle Scholar
Yung, Y.F., & Hayashi, K. (2001). A computationally efficient method for obtaining standard error estimates for the promax and related solutions. British Journal of Mathematical & Statistical Psychology, 54, 125–138.CrossRefGoogle ScholarPubMed
Zhang, G., Preacher, K.J., & Luo, S. (2010). Bootstrap confidence intervals for ordinary least squares factor loadings and correlations in exploratory factor analysis. Multivariate Behavioral Research, 45, 104–134.CrossRefGoogle ScholarPubMed