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

Abstract

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.

Keywords:

• Data augmentation
• Gibbs sampling
• multidimensional graded response model
• Pólya-Gamma distribution

Mathematics Subject Classifications:

• 62F15
• 62-08

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Multi-unidimensional IRT model is a special case of MIRT model. It is usually adopted when a test consists of several subtests with each focussing on one specific ability and the items in a particular subtest designed to measure one ability in common.

2 The data were retrieved from an online personality testing website (http://personality testing.info/).

Additional information

Funding

This work was supported by National Social Science Fund of China [grant number 21BTJ036].