Item response theory (IRT): bayesian estimation of the ability of individuals

Abstract

This article presents a simulation study for the estimation of ability measurements () of individuals subjected to a test designed according to the methodology of Item Response Theory (IRT). We used a bayesian approach and the Markov Chain Monte Carlo (MCMC) procedure to obtain the simulated posterior samples via OpenBUGS. The procedure was implemented in the R language and used the R2WinBUGS and BRUGS libraries. The performance of the Bayes estimator for individual abilities was evaluated by comparison with the corresponding true values which were used to simulate the test result data. The method performs well in terms of coverage by be posterior credibility sets. Basic notions about IRT as a new method to grade education tests, and possible other applications for the methods are also included.