Bayesian estimation of the multidimensional graded response model with nonignorable missing data

Abstract

A Bayesian approach is developed for analysing item response models with nonignorable missing data. The relevant model for the observed data is estimated concurrently in conjunction with the item response model for the missing-data process. Since the approach is fully Bayesian, it can be easily generalized to more complicated and realistic models, such as those models with covariates. Furthermore, the proposed approach is illustrated with item response data modelled as the multidimensional graded response models. Finally, a simulation study is conducted to assess the extent to which the bias caused by ignoring the missing-data mechanism can be reduced.

Keywords:

• Bayesian estimation
• data augmentation
• Gibbs sampling
• item response theory
• nonignorable missing data

AMS Classification :

• Primary: 62F15
• Secondary: 65C60
• 62M05

Acknowledgements

This work is supported by NSFC (10431010, 10828102, and 10871037) and Training Fund of NENU'S Scientific Innovation Project (NENU-STC07002).