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Alpha, FACTT, and Beyond

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  • Peter M. Bentler

    (University of California, Los Angeles)

Abstract

Sijtsma and Pfadt (Psychometrika, 2021) provide a wide-ranging defense for the use of coefficient alpha. Alpha is practical and useful when its limitations are acceptable. This paper discusses several methodologies for reliability, some new here, that go beyond alpha and were not emphasized by Sijtsma and Pfadt. Bentler’s (Psychometrika 33:335–345, 1968. https://doi.org/10.1007/BF02289328 ) combined factor analysis (FA) and classical test theory (CTT) model. FACTT provides a key conceptual foundation.

Suggested Citation

  • Peter M. Bentler, 2021. "Alpha, FACTT, and Beyond," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 861-868, December.
    • Handle: RePEc:spr:psycho:v:86:y:2021:i:4:d:10.1007_s11336-021-09797-8
    DOI: 10.1007/s11336-021-09797-8
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    References listed on IDEAS

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    1. P. Bentler & J. Woodward, 1980. "Inequalities among lower bounds to reliability: With applications to test construction and factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 45(2), pages 249-267, June.
    2. Klaas Sijtsma & Julius M. Pfadt, 2021. "Part II: On the Use, the Misuse, and the Very Limited Usefulness of Cronbach’s Alpha: Discussing Lower Bounds and Correlated Errors," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 843-860, December.
    3. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
    4. P. Bentler & J. Woodward, 1985. "On the greatest lower bound to reliability," Psychometrika, Springer;The Psychometric Society, vol. 50(2), pages 245-246, June.
    5. Peter M. Bentler, 2016. "Covariate-free and Covariate-dependent Reliability," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 907-920, December.
    6. Peter Bentler, 2009. "Alpha, Dimension-Free, and Model-Based Internal Consistency Reliability," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 137-143, March.
    7. P. Bentler, 1968. "Alpha-maximized factor analysis (alphamax): Its relation to alpha and canonical factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 33(3), pages 335-345, September.
    8. Alexander Shapiro & Jos Berge, 2000. "The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 413-425, September.
    9. Louis Guttman, 1945. "A basis for analyzing test-retest reliability," Psychometrika, Springer;The Psychometric Society, vol. 10(4), pages 255-282, December.
    10. Brian Woodhouse & Paul Jackson, 1977. "Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: II: A search procedure to locate the greatest lower bound," Psychometrika, Springer;The Psychometric Society, vol. 42(4), pages 579-591, December.
    11. P. Bentler & David Weeks, 1980. "Linear structural equations with latent variables," Psychometrika, Springer;The Psychometric Society, vol. 45(3), pages 289-308, September.
    12. Jos Berge & Tom Snijders & Frits Zegers, 1981. "Computational aspects of the greatest lower bound to the reliability and constrained minimum trace factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 46(2), pages 201-213, June.
    13. Ke-Hai Yuan & Peter M. Bentler, 2017. "Improving the convergence rate and speed of Fisher-scoring algorithm: ridge and anti-ridge methods in structural equation modeling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 571-597, June.
    14. Tyler Hunt & Peter Bentler, 2015. "Quantile Lower Bounds to Reliability Based on Locally Optimal Splits," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 182-195, March.
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