多维项目反应理论补偿性模型参数估计:基于广义回归神经网络集合

运用广义回归神经网络(GRNN)方法对小样本多维项目反应理论(MIRT)补偿性模型的项目参数进行估计,尝试解决传统参数估计方法样本数量要求较大的问题。MIRT双参数Logistic补偿模型被设置为二级计分的二维模型。首先,模拟二维能力参数、项目参数值与考生作答矩阵。其次,把通过主成分分析得到的前两个因子在每个题目上的载荷作为区分度的初始值以及题目通过率作为难度的初始值,这两个指标的初始值作为神经网络的输入。集成100个神经网络,其输出值的均值作为MIRT的项目参数估计值。最后,设置2×2种(能力相关水平:0.3和0.7; 两种估计方法:GRNN和MCMC方法)实验处理,对GRNN和MCMC估计方法的返真性进行比较。结果表明,小样本的情况下,基于GRNN集成方法的参数估计结果优于MCMC方法。

Compensatory MIRT Model Parameter Estimation:Based on Generalized Regression Neural Networks Ensemble

Estimating compensatory MIRT model item parameters with Generalized Regression Neural Networks Method(GRNN)under the condition of small sample.It is a tentative solution for the problem of conventional parameter estimation methods needing large sample.Multidimensional two-parameter logistic model is set the two-dimension binary model up.Firstly,latent traits parameters,item parameters and response matrices aregenerated examinees' based on two-dimension model with computer simulation.Then,the load of the first two factors obtained by principal component analysis on each topic is taken as the initial value of the item discrimination parameters and the passing rate as the initial value of the item difficulty parameters.And they are taken as the input of the neural network.Train 100 neural networks,and take the mean of their output as the estimated value of MIRT's item parameters.Finally,compare the parameter recovery of the GRNN and MCMC estimation methods by 2×2(latent traits correlation level:0.3 and 0.7; estimation methods:GRNN and MCMC)experimental design.The results show that GRNN ensemble method could get better parameter estimate than MCMC method in the case of small sample.