Sage Journals: Discover world-class research

Abstract

This article is concerned with standard errors (SEs) and confidence intervals (CIs) for exploratory factor analysis (EFA) in different situations. The authors adapt a sandwich SE estimator for EFA parameters to accommodate nonnormal data and imperfect models, factor extraction with maximum likelihood and ordinary least squares, and factor rotation with CF-varimax, CF-quartimax, geomin, or target rotation. They illustrate the sandwich SEs and CIs using nonnormal continuous data and ordinal data. They also compare SE estimates and CIs of the conventional information method, the sandwich method, and the bootstrap method using simulated data. The sandwich method and the bootstrap method are more satisfactory than the information method for EFA with nonnormal data and model approximation error.

Keywords

factor analysis latent variable models factor rotation standard errors

Get full access to this article

View all access options for this article.

References

Asparouhov

Muthén

(2009). Exploratory structural equation modeling. Structural Equation Modeling, 16, 397-438. doi:10.1080/10705510903008204

Browne

M. W.

(2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36, 111-150. doi:10.1207/s15327906mbr3601_05

Browne

M. W.

Cudeck

(1993). Alternative ways of assessing model fit. In Bollen

K. A.

Long

J. S.

(Eds.), Testing structural equation models (pp. 136-162). Newbury Park, CA: Sage.

Browne

M. W.

Cudeck

Tateneni

Mels

(2010). CEFA 3.04: Comprehensive Exploratory Factor Analysis. Retrieved from http://faculty.psy.ohio-state.edu/browne/programs.htm

Browne

M. W.

Shapiro

(1986). The asymptotic covariance matrix of sample correlation coefficients under general conditions. Linear Algebra and Its Applications, 82, 169-176. doi:10.1016/0024-3795(86)90150-3

Cheung

F. M.

Leung

Fan

Song

Zhang

(1996). Development of the Chinese Personality Assessment Inventory. Journal of Cross-Cultural Psychology, 27, 181-199. doi:10.1177/0022022196272003

Cudeck

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. doi:10.1037//0033-2909.115.3.475

Gorsuch

R. L.

(1983). Factor analysis (2nd ed.). Mahwah, NJ: Lawrence Erlbaum. doi:10.4324/9780203781098

Hattori

Zhang

Preacher

K. J.

(2017). Multiple local solutions and geomin rotation. Multivariate Behavioral Research, 52, 720-731. doi:10.1080/00273171.2017.1361312

10.

Ichikawa

Konishi

(1995). Application of the bootstrap methods in factor analysis. Psychometrika, 60, 77-93. doi:10.1007/bf02294430

11.

Jennrich

R. I.

(1973). Standard errors for obliquely rotated factor loadings. Psychometrika, 38, 593-604. doi:10.1007/bf02291497

12.

Jennrich

R. I.

(1974). Simplified formulae for standard errors in maximum-likelihood factor analysis. British Journal of Mathematical and Statistical Psychology, 27, 122-131. doi:10.1111/j.2044-8317.1974.tb00533.x

13.

John

O. P.

Donahue

E. M.

Kentle

R. L.

(1991). The Big Five Inventory—Versions 4a and 54. Berkeley, CA: University of California, Berkeley, Institute of Personality and Social Research. doi:10.1037/t07550-000

14.

Lee

C.-T.

Zhang

Edwards

M. C.

(2012). Ordinary least squares estimation of parameters in exploratory factor analysis with ordinal data. Multivariate Behavioral Research, 47, 314-339. doi:10.1080/00273171.2012.658340

15.

Luo

(2005). Personality and relationship satisfaction. Unpublished studies.

16.

Luo

Chen

Yue

Zhang

Zhaoyang

(2008). Predicting marital satisfaction from self, partner, and couple characteristics: Is it me, you, or us?Journal of Personality, 76, 1231-1266. doi:10.1111/j.1467-6494.2008.00520.x

17.

MacCallum

R. C.

(2003). Working with imperfect models. Multivariate Behavioral Research, 38, 113-139. doi:10.1207/s15327906mbr3801_5

18.

Olsson

(1979). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika, 44, 443-460. doi:10.1007/bf02296207

19.

SAS Institute. (2006). SAS/STAT 9.2 user’s guide. Cary, NC: Author.

20.

Tateneni

(1998). Use of automatic and numerical differentiation in the estimation of asymptotic standard errors in exploratory factor analysis (Doctoral dissertation). The Ohio State University, Columbus.

21.

White

(1981). Consequences and detection of misspecified nonlinear regression models. Journal of the American Statistical Association, 76, 419-443. doi:10.1080/01621459.1981.10477663

22.

Yuan

K.-H.

Bentler

P. M.

(1997). Generating multivariate distributions with specified marginal skewness and kurtosis. In Bandilla

Faulbaum

(Eds.), Softstat’97 advances in statistical software 6 (pp. 385-391). Stuttgart, Germany: Lucius & Lucius.

23.

Yuan

K.-H.

Hayashi

(2003). Bootstrap approach to inference and power analysis based on three test statistics for covariance structure models. British Journal of Mathematical and Statistical Psychology, 56, 93-110. doi:10.1348/000711003321645368

24.

Yuan

K.-H.

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, 95-121. doi:10.1007/bf02294711

25.

Yuan

K.-H.

Schuster

(2013). Overview of statistical estimation methods. In Little

T. D.

(Ed.), The Oxford handbook of quantitative methods (pp. 361-387). New York, NY: Oxford University Press.

26.

Zhang

Jiang

Hattori

Trichtinger

(2018). Utility functions for exploratory factor analysis (Version 1.2.2) [Computer software manual]. Retrieved from https://cran.r-project.org/web/packages/EFAutilities/EFAutilities.pdf

27.

Zhang

Preacher

K. J.

Jennrich

R. I.

(2012). The infinitesimal jackknife with exploratory factor analysis. Psychometrika, 77, 634-648. doi:10.1007/s11336-012-9281-5

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.22 MB

A Sandwich Standard Error Estimator for Exploratory Factor Analysis With Nonnormal Data and Imperfect Models

Abstract

Keywords

Get full access to this article

References

Supplementary Material