Two-parameter logistic模型的Gibbs抽样敏感度分析——基于Pólya-Gamma分布

A sensitivity analysis of Gibbs sampling for two-parameter logistic model——based on Pólya-Gamma distribution

项目反应理论(item response theory,IRT)在教育与心理测量中有着重要的应用价值,其主要针对被试者的能力及被试者对测试项目的“正确作答概率”进行建模。主要讨论了两参数logistic项目反应理论模型(two-parameter logistic item response model,2PL)下基于PólyaGamma分布的Gibbs抽样方法的贝叶斯估计效果。针对2PL模型,通过Monte Carlo模拟研究了基于Pólya-Gamma抽样方法的估计效果,并讨论了该抽样方法针对不同先验的敏感度。在模拟实验中,具体讨论了测验长度、被试样本及先验分布等因素,最终汇报了2个统计量——偏差(BIAS)和均方根误差(root mean squared error,RMSE)来检验参数的估计效果。模拟分析表明,基于Pólya-Gamma的抽样方法的参数估计结果是比较准确的。

Item Response Theory(IRT)plays an important role in education and psychological measurement.IRT is mainly based on the ability of the subjects and the“probability of correct answer”of the test items.The bayesian estimation effect of Gibbs sampling method based on Pólya-Gamma distribution under two-parameter logistic item Response model(2PL)is discussed.For 2PL model,the estimation effect based on Pólya-Gamma sampling method is studied by Monte Carlo simulation,and the sensitivity of the sampling method to different priors is discussed.In the simulation experiment,factors such as test length,subject sample and prior distribution are discussed in detail.Finally,two statistics-BIAS and Root Mean Squared Error(RMSE)are reported to test the effect of parameter estimation.Simulation analysis shows that the parameter estimation result based on Pólya-Gamma sampling method is relatively accurate.