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The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability

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  • Alexander Shapiro
  • Jos Berge

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  • 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.
    • Handle: RePEc:spr:psycho:v:65:y:2000:i:3:p:413-425
    DOI: 10.1007/BF02296154
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    References listed on IDEAS

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    1. Louis Guttman, 1945. "A basis for analyzing test-retest reliability," Psychometrika, Springer;The Psychometric Society, vol. 10(4), pages 255-282, December.
    2. 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.
    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. 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.
    5. Alexander Shapiro, 1982. "Rank-reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 187-199, June.
    6. Giacomo Riccia & Alexander Shapiro, 1982. "Minimum rank and minimum trace of covariance matrices," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 443-448, December.
    7. Lee Cronbach, 1988. "Internal consistency of tests: Analyses old and new," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 63-70, March.
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    Citations

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    Cited by:

    1. Ke-Hai Yuan & Peter Bentler, 2002. "On robusiness of the normal-theory based asymptotic distributions of three reliability coefficient estimates," Psychometrika, Springer;The Psychometric Society, vol. 67(2), pages 251-259, June.
    2. Jos Berge & Gregor Sočan, 2004. "The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality," Psychometrika, Springer;The Psychometric Society, vol. 69(4), pages 613-625, December.
    3. Peter M. Bentler, 2021. "Alpha, FACTT, and Beyond," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 861-868, December.
    4. Jushan Bai & Serena Ng, 2017. "Principal Components and Regularized Estimation of Factor Models," Papers 1708.08137, arXiv.org, revised Nov 2017.
    5. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    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. Bai, Jushan & Ng, Serena, 2019. "Rank regularized estimation of approximate factor models," Journal of Econometrics, Elsevier, vol. 212(1), pages 78-96.
    8. Klaas Sijtsma, 2009. "On the Use, the Misuse, and the Very Limited Usefulness of Cronbach’s Alpha," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 107-120, March.
    9. 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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