Application Of The Bayes Factor In IRT Model Selection

Calculating posterior probabilities and related Bayes factors for a collection of compet-ing models has been a difcult and challenging problem for Bayesian statisticians．Bayesianmodel selection is to select a model correspond to reality through observation data froma number of competitive models. In this paper, we consider the single-parameter,two-parameter, three-parameter item response models as a set of competitive models.We usethe Bayes factors based on actual observation data to select a model from the three com-petitive models.We know that the use of Bayes factor to select models is an important application ofcomputing normalizing constants in statistics, but for complex or high-dimensional model,the calculation is more difcult.However, for nested hypothesis in Bayesian statistical test,we can use the Savage-Dickey methods combined with the Gibbs sampling to efectivelyestimates the Bayes factor, which simplifes the calculation of the Bayes factors. The Savage-Dickey density ratio provides a conceptually simple approach to computing Bayes factor.Here, we review methods for computing the Savage-Dickey density ratio, and highlight animproved method. The improved method is based on conditional quantities, which maybe integrated by Markov chain Monte Carlo sampling to estimate Bayes factors. Theseconditional quantities efciently utilize all the information in the MCMC chains, leading toaccurate estimation of Bayes factors.This paper frst introduces the three models of item response theory, in addition, alsodescribes the related concept of the Bayes factor and the basic idea of the model selectionusing Bayes factors; Secondly, we do the model selection simulations on the three itemresponse models; Then, we illustrates the signifcance of the simulation results;Finally, tosummarize the work done.