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

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 known forms. To improve algorithmic computational efficiency, this paper proposes a Bayesian estimation method by adopting a new data-augmentation strategy in uni- and multidimensional IRT models. The strategy is based on the Pólya-Gamma family of distributions which provides a closed-form posterior distribution for logistic-based models. In this paper, an overview of Pólya-Gamma distributions is described within a logistic regression framework. In addition, we provide details about deriving conditional distributions of IRT, incorporating Pólya-Gamma distributions into the conditional distributions for Bayesian samplers' construction, and random drawing from the samplers such that a faster convergence can be achieved. Simulation studies and applications to real datasets were conducted to demonstrate the efficiency and utility of the proposed method.