A comparison of objective priors for Cronbach’s coefficient alpha using a balanced random effects model

In this article, the reference and probability matching priors for Cronbach’s alpha will be derived. The performance of these two priors will be compared to that of the well-known Jeffreys prior and a divergence prior. Cronbach’s alpha is a measure used to assess the reliability of a set of test items. A simulation study will be considered to compare the performance of the priors, where the coverage rates, average interval lengths, and standard deviations of the interval lengths will be computed. A second simulation study will be considered where the mean relative error will be compared for the various priors using three different loss functions. The following loss functions will be considered, Squared error loss, Absolute error loss, and Linex loss. An illustrative example will also be considered. Throughout the article, the random effects approach will be used.