Abstract
Bayesian estimation of reliability by MCMC is proposed as an alternative to coefficient alpha, regarded as a classic method of estimating reliability. However, coefficient alpha is derived from a structural factor model, various kinds of which are used in modern data analysis, e.g., SEM, sometimes used to analyze reliability. SEM emphasizes covariances to analyze categorical items that are estimated by polychoric correlations. The methods proposed in this study directly apply the MCMC algorithm to individual examinees responses. Thus, covariances are not estimated but implicitly represented by factor models. For categorical items, models for continuous items are modified and applied based on an ordinal probit regression. The performances of the proposed models and algorithms are investigated by simulations and successful results are obtained.
