An efficient PG-INLA algorithm for the Bayesian inference of logistic item response models

Xiaofan Lin and Yincai Tang

Statistical Theory and Related Fields, 2025, vol. 9, issue 1, 84-100

Abstract: In this paper, we propose a Bayesian PG-INLA algorithm which is tailored to both one-dimensional and multidimensional 2-PL IRT models. The proposed PG-INLA algorithm utilizes a computationally efficient data augmentation strategy via the Pólya-Gamma variables, which can avoid low computational efficiency of traditioanl Bayesian MCMC algorithms for IRT models with a logistic link function. Meanwhile, combined with the advanced and fast INLA algorithm, the PG-INLA algorithm is both accurate and computationally efficient. We provide details on the derivation of posterior and conditional distributions of IRT models, the method of introducing the Pólya-Gamma variable into Gibbs sampling, and the implementation of the PG-INLA algorithm for both one-dimensional and multidimensional cases. Through simulation studies and an application to the data analysis of the IPIP-NEO personality inventory, we assess the performance of the PG-INLA algorithm. Extensions of the proposed PG-INLA algorithm to other IRT models are also discussed.

Date: 2025
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DOI: 10.1080/24754269.2024.2442174

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