Gibbs sampling method in multidimensional two parameter logistic item response model
FU Zhihu · Journal of Shenyang Normal University · 2014
Item response theory(IRT)is based on three assumptions:unidimensionality,local independence and monotonicity.However these assumption has some defects need to be improved.Research shows that use unidimensional model to fit multidimensional data will increase measurement error and make wrong inference to students'ability.Just because of this researchers extend the unidimensional IRT to the multidimensional IRT from different perspectives.Since the multidimensional model has more parameters need to be estimated,traditional methods such as marginal maximum likelihood and Bayes modal estimation procedures are not suitable.However,Gibbs sampler has a great potential to be an efficient and versatile estimation procedure in item response theory.In this article,based on a data augmentation scheme using the Gibbs sampler,we propose a Bayesian procedure to estimate the multidimensional two parameter logistic model(2PLM).With the introduction of latent variable,the full conditional distributions are tractable,and consequently the Gibbs sampling is easy to implement for any prior assumptions.