On the Bayesian estimation for Cronbach's alpha

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.

KEYWORDS:

• Parameter estimation
• Bayes estimator
• squared-error and LINEX loss functions
• approximation
• reliability of tests and measurements

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 62F10
• 62F15
• 62E17

Acknowledgments

The support of Shahid Beheshti University gratefully acknowledged by authors. Authors would like to anonymous reviewers for their constructive comments which improve theory, presentation, and simulation study of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.