Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-01-07T19:28:02.219Z Has data issue: false hasContentIssue false

Reliability of Summed Item Scores Using Structural Equation Modeling: An Alternative to Coefficient Alpha

Published online by Cambridge University Press:  01 January 2025

Samuel B. Green*
Affiliation:
Arizona State University
Yanyun Yang
Affiliation:
Florida State University
*
Requests for reprints should be sent to Samuel B. Green, Arizona State University, P.O. Box 870611, Tempe, AZ, 85287-0611, USA. E-mail: samgreen@asu.edu

Abstract

A method is presented for estimating reliability using structural equation modeling (SEM) that allows for nonlinearity between factors and item scores. Assuming the focus is on consistency of summed item scores, this method for estimating reliability is preferred to those based on linear SEM models and to the most commonly reported estimate of reliability, coefficient alpha.

Type
Theory and Methods
Copyright
Copyright © 2008 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.)

References

Bentler, P.M. (2009). Alpha, dimension-free, and model-based internal consistency reliability. Psychometrika, 74, doi: 10.1007/s11336-008-9100-1.CrossRefGoogle Scholar
Bollen, K.A. (1989). Structural equations with latent variables, New York: Wiley.CrossRefGoogle Scholar
Curran, P.J., West, S.G., Finch, J.F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1, 1629.CrossRefGoogle Scholar
DiStefano, C. (2002). The impact of categorization with confirmatory factor analysis. Structural Equation Modeling, 9, 327346.CrossRefGoogle Scholar
Feldt, L.S., Brennan, R.L. (1989). Reliability. In Linn, R.L. (Eds.), Educational measurement (pp. 105146). (3rd ed.). New York: Macmillan.Google Scholar
Finney, S., DiStefano, C. (2006). Non-normal and categorical data in structural equation modeling. In Hancock, G.R., Mueller, R.O. (Eds.), Structural equation modeling: A second course (pp. 269314). Greenwich: Information Age.Google Scholar
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, 466491.CrossRefGoogle ScholarPubMed
Gorsuch, R.L. (1983). Factor analysis, Hillsdale: Erlbaum.Google Scholar
Green, S.B. (1983). Identifiability of spurious factors using linear factor analysis with binary items. Applied Psychological Measurement, 7, 139147.CrossRefGoogle Scholar
Green, S.B., Akey, T.M., Fleming, K.K., Hershberger, S.L., Marquis, J.G. (1997). Effect of the number of scale points on chi-square fit indices in confirmatory factor analysis. Structural Equation Modeling, 4, 108120.CrossRefGoogle Scholar
Green, S.B., Hershberger, S.L. (2000). Correlated errors in true score models and their effect on coefficient alpha. Structural Equation Modeling, 7, 251270.CrossRefGoogle Scholar
Green, S.B., & Yang, Y. (2009). Commentary on coefficient alpha: a cautionary tale. Psychometrika, 74, doi: 10.1007/s11336-008-9098-4.CrossRefGoogle Scholar
Jöreskog, K.G. (1971). Statistical analysis of sets of congeneric test. Psychometrika, 36, 109133.CrossRefGoogle Scholar
Lissitz, R.W., Green, S.B. (1975). Effect of the number of scale points on reliability: A Monte Carlo approach. Journal of Applied Psychology, 60, 1013.CrossRefGoogle Scholar
Lozano, L.M., García-Cueto, E., Muñiz, J. (2008). Effect of the number of response categories on the reliability and validity of rating scales. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 4, 73479.CrossRefGoogle Scholar
Maydeu-Olivares, A., Coffman, D.L., Hartmann, W.M. (2007). Asymptotically distribution-free (ADF) interval estimation of coefficient alpha. Psychological Methods, 12(2), 157176.CrossRefGoogle ScholarPubMed
McDonald, R.P. (1999). Test theory: A unified approach, Hillsdale: Erlbaum.Google Scholar
McDonald, R.P., Ahlawat, K.S. (1974). Difficulty factors in binary data. British Journal of Mathematical and Statistical Psychology, 27, 8299.CrossRefGoogle Scholar
Miller, M.B. (1995). Coefficient Alpha: A basic introduction from the perspectives of classical test theory and structural equation modeling. Structural Equation Modeling, 2, 255273.CrossRefGoogle Scholar
Muthén, L.K., Muthén, B.O. (2008). Mplus user’s guide, (5th ed.). Los Angeles: Authors.Google Scholar
Raykov, T., Shrout, P. (2002). Reliability of scales with general structure: Point and interval estimation using a structural equation modeling approach. Structural Equation Modeling, 9, 195212.CrossRefGoogle Scholar
Sijtsma, K. (2009). On the use, the misuse, and the very limited usefulness of Cronbach’s alpha. Psychometrika (to be published in the March).CrossRefGoogle Scholar