Modelo bayesiano da teoria de resposta ao item: uma abordagem generalizada para o traço latente via misturas

Abstract

The Item Response Theory (IRT) is a psychometric theory which aims to construct scales and estimate latent traits based on answers given to items that are directly in uenced by these traits. A common assumption of IRT models is to assume that the latent traits are random variables that follow a normal distribution. Although normal distributions are often observed and computationally convenient, it is unlikely that the latent traits are always well aproximated by the normal distribution. The aim of this dissertation is to propose a new IRT model that relaxes the assumption of normality by using mixtures of normal distributions. In particular, this approach provides a solution to modeling heavy-tails or asymmetry without the use of heavy-tailed or asymmetric distributions (e.g. t-Student or skew-normal). This dissertation also introduces a particular parametrisation of the 3 parameter Probit model using auxiliary variables to improve the MCMC algorithm used to make inference in the proposed model under a Bayesian approach. Finally, simulations and real data studies are presented to assess the eciency and applicability of the proposed model.