A Bayesian approach to estimating variance components within a multivariate generalizability theory framework

In many behavioral research areas, multivariate generalizability theory (mG theory) has been typically used to investigate the reliability of certain multidimensional assessments. However, traditional mG-theory estimation—namely, using frequentist approaches—has limits, leading researchers to fail to take full advantage of the information that mG theory can offer regarding the reliability of measurements. Alternatively, Bayesian methods provide more information than frequentist approaches can offer. This article presents instructional guidelines on how to implement mG-theory analyses in a Bayesian framework; in particular, BUGS code is presented to fit commonly seen designs from mG theory, including single-facet designs, two-facet crossed designs, and two-facet nested designs. In addition to concrete examples that are closely related to the selected designs and the corresponding BUGS code, a simulated dataset is provided to demonstrate the utility and advantages of the Bayesian approach. This article is intended to serve as a tutorial reference for applied researchers and methodologists conducting mG-theory studies.     

Gibbs Samplers for Logistic Item Response Models via the Pólya–Gamma Distribution: A Computationally Efficient Data-Augmentation Strategy

Psychometrika - Fully Bayesian estimation of item response theory models with logistic link functions suffers from low computational efficiency due to posterior density functions that do not have...