Exploratory factor analysis (EFA) is commonly employed to evaluate the factor structure of measures with dichotomously scored items. Generally, only the estimated factor loadings are provided with no reference to significance tests, confidence intervals, and/or estimated factor loading standard errors. This simulation study assessed factor loading estimation error under several experimental conditions and whether hypothesis testing and/or confidence intervals should be employed. Results revealed that the promax rotation performed well with small interfactor correlations and simple structure data, whereas varimax only performed well with orthogonal factors. Neither rotation method performed well with larger interfactor correlations or approximate simple structure data. An explanation of these results is provided.
Ackerman, T.A. ( 2005). Multidimensional item response theory modeling. In J. McArdle & A. Maydeu-Olivares (Eds.), Contemporary psychometrics (pp. 3-25). Mahwah, NJ: Lawrence Erlbaum.
Browne, M.W. ( 2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36, 111-150.
4.
Carroll, J.B. ( 1945). The effect of difficulty and chance success on correlations between items or between tests. Pschometrika, 10, 1-19.
5.
Cliff, N., & Hamburger, C.D. (1967). The study of sampling errors in factor analysis by means of artificial experiments. Psychological Bulletin, 68, 430-445.
6.
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.
7.
Finch, H. ( 2006). Comparison of the performance of varimax and promax rotations: Factor structure recovery for dichotomous items. Journal of Educational Measurement, 43, 39-52.
8.
Flora, D.B., & Curran P.J. ( 2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9, 466-491.
9.
Ford, J.K., MacCallum, R.C., & Tait, M. ( 1986). The application of exploratory factor analysis in applied psychology: A critical review and analysis. Personnel Psychology , 39, 291-314.
10.
Fraser, C. ( 1988). NOHARM: An IBM PC computer program for fitting both unidimensional and multidimensional normal ogive models of latent trait theory. Armidale, Australia: University of New England.
Greer, T., Dunlap, W.P., & Beatty, G.O. ( 2003). A Monte Carlo evaluation of the tetrachoric correlation coefficient. Educational and Psychological Measurement, 63, 931-950.
14.
Harman, H.H. ( 1976). Modern factor analysis (3rd ed.). Chicago: University of Chicago Press.
15.
Hayton, J.C., Allen, D.G., & Scarpello, V. ( 2004). Factor retention decisions in exploratory factor analysis: A tutorial on parallel analysis. Organizational Research Methods , 7, 191-205.
16.
Hogarty, K.Y., Hines, C.V., Kromrey, J.D., Ferron, J.M., & Mumford, K.R. ( 2005). The quality of factor solutions in exploratory factor analysis: The influence of sample size, communality, and overdetermination . Educational and Psychological Measurement, 65, 202-226.
17.
Jöreskog, K., & Moustaki, I. ( 2001). Factor analysis for ordinal variables: A comparison of three approaches. Multivariate Behavioral Research, 36, 347-387.
Maydeu-Olivares, A. ( 2001). Multidimensional item response theory modeling of binary data: Large sample properties of NOHARM estimates. Journal of Educational and Behavioral Statistics, 26, 49-69.
Nandakumar, R., & Ackerman, T. ( 2004). Test modeling. In D. Kaplan (Ed.), The Sage handbook of quantitative methodology for the social sciences (pp. 93-105). Thousand Oaks, CA: Sage.
25.
Nunnally, J.C. ( 1978). Psychometric theory. New York: McGraw-Hill.
26.
Stout, W., Habing, B., Douglas, J., Kim, H.R., Roussos, L., & Zhang, J. ( 1996). Conditional covariance-based nonparametric multidimensionality assessment. Applied Psychological Measurement, 20, 331-354.
27.
Takane, Y., & de Leeuw, J. ( 1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393-408.
28.
Thurstone, L.L. ( 1947). Multiple factor analysis. Chicago : University of Chicago Press.
29.
Wood, R., Wilson, D., Gibbons, R., Schilling, S., Muraki, E., & Bock, D. ( 2003). Testfact4. Chicago: Scientific Software International.
