A Full Bayesian Implementation of A Generalized Partial Credit Model with an Application to an International Disability Survey

Abstract

Generalized partial credit models (GPCMs) are ubiquitous in many applications in the health and medical sciences that use item response theory. Such polytomous item response models have a great many uses ranging from assessing and predicting an individual's latent trait to ordering the items to test the effectiveness of the test instrumentation. By implementing these models in a full Bayesian framework, computed through the use of Markov chain Monte Carlo methods implemented in the efficient STAN software package, the paper exploits the full inferential capability of GPCMs. The GPCMs include explanatory covariate effects which allow simultaneous estimation of regression and item parameters. The Bayesian methods for ranking the items by using the Fisher information criterion are implemented by using Markov chain Monte Carlo sampling. This allows us to propagate fully and to ascertain uncertainty in the inferences by calculating the posterior predictive distribution of the item-specific Fisher information criterion in a novel manner that has not been exploited in the literature before. Lastly, we propose a new Monte Carlo method for predicting the latent trait score of a new individual by approximating the relevant Bayesian predictive distribution. Data from a model disability survey carried out in Sri Lanka by the World Health Organization and the World Bank are used to illustrate the methods. The approaches proposed are shown to provide simultaneous model-based inference for all aspects of disability which can be explained by environmental and socio-economic factors.