Uma solução bayesiana para se considerar a incerteza associada à calibração de itens na teoria de resposta ao item

Abstract

In the conventional methods of the Item Response Theory (IRT), the latent trait of the individuals is usually estimated based on a previously calibrated test, that is, it is assumed that the parameters of the items are known after the values are estimated through a pre-test, thus there is an uncertainty in the estimation since we use a sample to estimate them. Ignoring this uncertainty can lead to inferential errors of estimates of latent traits, particularly when the calibration sample is not large enough. This paper proposes a Bayesian approach to deal with the problem of estimating the ability taking into account the uncertainty regarding the parameters of the pre-calibrated items. An algorithm that approximates the posterior distribution of an individual submitted to the pre-calibrated test from the sample of the posterior distribution of the parameters of the items obtained via MCMC is proposed. Finally, the discussed algorithm is extended to the context of adaptive tests, allowing the estimation of the ability to each item answered. In this context, new methods of item choices and stop rules are proposed. The proposed methodology is investigated in simulated data analysis and illustrated in the analysis of a data set related to the Enem.