An efficient MCMC-INLA algorithm for Bayesian inference of logistic graded response models

This paper proposes a Bayesian MCMC-INLA algorithm specifically designed for both unidimensional and multidimensional logistic graded response models (LGRMs). The algorithm incorporates a computationally efficient data augmentation approach by introducing Pólya-Gamma variables and latent variables, thereby addressing the limitations of traditional Bayesian MCMC methods in handling item response theory (IRT) models with logistic link functions. By integrating the advanced and efficient integrated nested Laplace approximation (INLA) framework, the MCMC-INLA algorithm achieves both high computational efficiency and estimation accuracy. The paper provides detailed derivations of the posterior and conditional distributions for IRT models, outlines the incorporation of Pólya-Gamma and latent variables within the Gibbs sampling procedure, and presents the implementation of the MCMC-INLA algorithm for both unidimensional and multidimensional cases. The performance of the proposed algorithm is evaluated through extensive simulation studies and an empirical application to the IPIP-NEO dataset. Potential extensions of the MCMC-INLA framework to other IRT models are also discussed.