BP神经网络估计IRT参数的比较研究

摘要

Objective : Compared with classical test theory, item response theory has more advantages, However, item response theory models are complex , the parameter estimates are often required a large sample ; Artificial neural network may provide methods for small sample to estimate item response theory parameters , The purpose of the article is to find a more accurate parameter estimation by Monte Carlo simulation of neural networks . Method:two parameters item response theory model as an example , MAB and RMSE as compared indicators , Comparison the differences of values by simulation data between percentage , point-biserial correlation coefficient, the average score in the Classical Test Theory and the converted value (IRT parameter estimation of initial value) as the neural network input values in neural network training network , compare two indicators RMSE and MAB index under different condition . Result : there is a difference between item percentage and bj=zj/rbj in estimating the item parameters b;there is a difference between point-biserial correlation coefficient and aj=rbj/ 1-r 2 bj in estimating item parameters a ; there is a difference between average score and ln[ x/(m-x) in estimating ability parameters ] theta. Conclusion:For the two-parameter item response model , error in item percentage is smaller than bj=zj/rbj in estimating item parameter b ; error in point-biserial correlation coefficient is larger than aj=rbj/ 1-r bj in 2 estimating item parameter a;error in average score is larger than ln[ x/(m-x) in estimating ability parameter theta.%　　目的：与经典测量理论相比，项目反应理论具有更多的优势，但由于项目反应理论模型的复杂性，进行参数估计时往往需要较大的被试样本；人工神经网络的出现为小样本被试估计项目反应理论的能力参数和项目参数提供了可能，文章的目的是通过神经网络的蒙特卡罗模拟研究寻找更精确的参数估计方法。方法：以项目反应理论的两参数模型为例，以MAB和RMSE为比较指标，通过模拟数据比较经典测量理论的通过率、点二列相关系数、平均得分作为神经网络的输入值与以经过转换的数值(IRT参数估计的初值)作为神经网络的输入值训练网络结果的差异，比较不同条件下MAB指标和RMSE指标的差异。结果：以通过率估计项目参数b与以bj=zj/rbj估计项目参数b存在差异；以点二列相关系数估计项目参数a与以aj=rbj/1-r 2bj估计项目参数a存在差异；以平均得分估计能力参数θ与以ln[ x/(m-x)估计能力参数θ存在差异。结论：对]于两参数项目反应模型，以通过率估计项目参数b比以bj=zj/rbj估计项目参数b误差更小，而以点二列相关系数估计项目参数a比以aj=rbj/1-r 2bj 估计项目参数a误差更大，以平均得分估计能力参数θ比以ln[ x/(m-x)估计能力参数θ误差更大。