基于三参数Logistic模型Gibbs抽样方法的敏感度分析

Sensitivity analysis of Gibbs sampling for 3PL model

通过蒙特卡罗(Monte Carlo,MC)方法研究了三参数Logistic(three-parameter Logistic,3PL)模型的Gibbs抽样方法的估计效果。首先,介绍了3PL模型的定义和参数的先验分布;其次,介绍了潜变量的引进及Gibbs抽样过程;最后,进行了模拟实验,考虑了不同的测试长度n=10,20和40,不同的样本容量N=1000,2000和5000,以及项目参数取不同的先验假设下的实验情况。对于结果的评价指标为均方根误差(root mean squared error,RMSE)和偏差(bias)。实验结果表明,随着测试长度或样本容量的增大,RMSE逐渐减小,当项目参数的先验分布方差取值较小时,获得的RMSE比较小。因此,对于3PL模型,当样本容量不是很大或者是测试长度不够长时,项目参数采用方差较小的先验分布可以得到比较准确的估计结果。

The estimation performance of the Gibbs sampling method for the three-parameter logistic(3PL)model is studied using Monte Carlo(MC)method.Firstly,the definition of the 3PL model and the prior distribution of parameters are introduced.Secondly,it explains the introduction of latent variables and the Gibbs sampling procedure.Finally,a simulation experiment is carried out,which considered three influencing factors:different test lengths n=10,20,and 40,various sample sizes N=1000,2000,and 5000,and all kinds of the prior assumptions of item parameters.The evaluation indicators for the results are root mean square error(RMSE)and bias.Experimental results show that RMSE decreases gradually with the increase of test length or sample size.When the variance of the prior distribution of item parameters is small,the RMSE obtained is relatively smaller.Therefore,for the 3PL model,when the sample sizes are not large or the test lengths are not long enough,the priors distribution with small variances can obtain more accurate estimation results.