等级反应模型的Gibbs抽样方法

Gibbs sampling method in the graded response model

探讨了MCMC算法在多级评分项目反应模型参数估计中的实现及其估计精度.针对等级反应模型,基于数据扩充技术,提出了一种高效灵活的Gibbs抽样方法,得到了各个参数的Markov链.随着潜在变量的引入,每个参数的满条件分布为相应参数的先验分布的截断分布.这种抽样方法适用于任何类型的先验分布,不受先验分布形式的约束.对应每个待估参数,去掉所得Markov链前面的一些迭代值,用后面的迭代结果作估计,得到相应参数的Bayes后验估计.并通过随机模拟实验验证了该方法的有效性.

This paper demonstrates the Markov Chain Monte Calro（MCMC） method,which is now widely used in parameter estimation in the item response theory（IRT） model abroad and discusses its application in the parameter estimation of polytomous IRT models.Gibbs sampling is the simplest,and the most popular MCMC method.Based on a data augmentation scheme using the Gibbs sampler,this article proposes a Bayesian procedure to estimate the Graded response model（GRM）,and get the markov chains of the corresponding parameters.With the introduction of latent variable,the full conditional distributions are tuncated distribution of the coresponding prior distribution.This method is apropriate for any type prior distribution.For each markov chain,discarding the values of the earlier part,and using the rest to make inference and get the Bayesian estimates.Finally,the technique is illustrated by using the simulated data.