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On the Bayesian estimation for Cronbach's alpha

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  • Amir T. Payandeh Najafabadi
  • Maryam Omidi Najafabadi

Abstract

This article considers the problem of estimating Cronbach's alpha under a Bayeisan framework. Such Bayes estimator arrives through out approximating distribution of the maximum likelihood estimator for Cronbach's alpha by an F distribution. Then, employing a noninformative prior distribution, Bayes estimator under squared-error and LINEX loss functions have been evaluated. Simulation studies suggest that the Bayes estimator under LINEX loss function reduce biasness of the ordinary maximum likelihood estimator. Moreover, The LINEX Bayes estimator does not sensitive with respect to choice of hyperparameters of prior distribution. R codes for readers to calculate Bayesian Cronbach's alpha have been given.

Suggested Citation

  • Amir T. Payandeh Najafabadi & Maryam Omidi Najafabadi, 2016. "On the Bayesian estimation for Cronbach's alpha," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(13), pages 2416-2441, October.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:13:p:2416-2441
    DOI: 10.1080/02664763.2016.1163529
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    References listed on IDEAS

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    1. Goldine Gleser & Lee Cronbach & Nageswari Rajaratnam, 1965. "Generalizability of scores influenced by multiple sources of variance," Psychometrika, Springer;The Psychometric Society, vol. 30(4), pages 395-418, December.
    2. J. Zyl & H. Neudecker & D. Nel, 2000. "On the distribution of the maximum likelihood estimator of Cronbach's alpha," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 271-280, September.
    3. Changyong Feng & Hongyue Wang & Yu Han & Yinglin Xia & Xin M. Tu, 2013. "The Mean Value Theorem and Taylor's Expansion in Statistics," The American Statistician, Taylor & Francis Journals, vol. 67(4), pages 245-248, November.
    4. Emily Kistner & Keith Muller, 2004. "Exact distributions of intraclass correlation and Cronbach's alpha with Gaussian data and general covariance," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 459-474, September.
    5. Payandeh Najafabadi, Amir T., 2010. "A new approach to the credibility formula," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 334-338, April.
    6. Leonard Feldt, 1965. "The approximate sampling distribution of Kuder-Richardson reliability coefficient twenty," Psychometrika, Springer;The Psychometric Society, vol. 30(3), pages 357-370, September.
    7. Adam Duhachek & Anne T. Coughlan & Dawn Iacobucci, 2005. "Results on the Standard Error of the Coefficient Alpha Index of Reliability," Marketing Science, INFORMS, vol. 24(2), pages 294-301, July.
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