Bayesian inference for multidimensional graded response model using Pólya-Gamma latent variables

In the context of both cognitive and affective tests, items are usually designed to involve more than two responses, for which polytomous models are applicable. The purpose of this paper is to propose a highly effective Pólya-Gamma Gibbs sampling algorithm based on auxiliary variables to estimate the multidimensional graded response model that has been widely used in psychological, educational, and health-related assessment. The strategy is based on the Pólya Gamma family of distributions which provides a closed-form posterior distribution for logistic-based models. With the introduction of the two latent variables, the full conditional distributions are tractable, and consequently the Gibbs sampling is easy to implement. Nice features including empirical performance of the proposed methodology are demonstrated by simulation studies. Finally, two empirical data sets were analysed to demonstrate the efficiency and utility of the proposed method.