Bayesian Inference For Multidimensional Graded Response Models Based On Pólya-Gamma Latent Variables

Fully Bayesian estimation of graded response model with logistic link functions suffers from low computational efficiency due to posterior density functions that do not have known forms.In order to improve algorithmic computational efficiency,this paper proposes a Gibbs sampling algorithm based on data augmentation strategy for uni-and multi-dimensional graded response models.The proposed algorithm uses the Polya-Gamma distribution family to provide a closed posterior distribution for the logistic model,which converts the complex posterior density into a full-condition distribution that is easy to sample,and overcomes the shortcomings of the traditional Metropolis-Hastings algorithm such as sensitivity to adjusting parameter.This reduces the computational burden and makes the Gibbs sampling algorithm easy to implement.In order to verify the effectiveness and practicability of the proposed algorithm,simulation research and empirical analysis are carried out.In simulation research,it is verified that the proposed algorithm is slightly superior to HMC algorithm and MHRM algorithm from the aspects of convergence diagnosis,parameter estimation and computational efficiency.In empirical analysis,the proposed algorithm is applied to MTF and FPS datasets using uni-and multi-dimensional graded response models,respectively,to verify the good performance of the proposed algorithm in real datasets.