IRT模型参数估计的GRNN方法研究
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摘要
项目反应理论所估计出的项目参数不受被试者能力分布的影响,即具有参数不变性的优点.项目反应理论中的参数估计是应用项目反应理论的前提,常用参数估计方法有极大似然法、贝叶斯法等建立在数理统计基础上的方法,一般要求较大的样本,对于小样本缺乏合适的参数估计方法.本文提出一种广义回归神经网络(GRNN)的参数估计方法,以二值记分的测验结果作为样本,通过实验与数理统计方法进行对比,分析不同样本量下参数估计结果的误差.与传统数理统计方法相比,基于GRNN参数估计方法在小样本下对参数估计的精度较高.
Item parameters estimated by the Item Response Theory are not affected by the ability distribution of the subjects,that is,the advantages of parameter invariance. The parameter estimation in the theory is the premise of applying the theory. The method of maximum likelihood,Bayesian and others based on mathematical statistics is commonly used. It often requires large samples and lacks appropriate parameter estimation methods for small samples. In this paper,a generalized regression neural netw ork (GRNN) parameter estimation method is proposed. The test results of binary scores are taken as samples. The experimental and mathematical statistics methods are compared to analyze the error of parameter estimation results under different sample sizes. Compared w ith the traditional mathematical statistics method,the GRNN parameter estimation method has higher accuracy for parameter estimation under small samples.
Item parameters estimated by the Item Response Theory are not affected by the ability distribution of the subjects,that is,the advantages of parameter invariance. The parameter estimation in the theory is the premise of applying the theory. The method of maximum likelihood,Bayesian and others based on mathematical statistics is commonly used. It often requires large samples and lacks appropriate parameter estimation methods for small samples. In this paper,a generalized regression neural netw ork (GRNN) parameter estimation method is proposed. The test results of binary scores are taken as samples. The experimental and mathematical statistics methods are compared to analyze the error of parameter estimation results under different sample sizes. Compared w ith the traditional mathematical statistics method,the GRNN parameter estimation method has higher accuracy for parameter estimation under small samples.
引文
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[12]Zheng Zhi-yun,Jiang Guo-lin,Zhang Xing-jin,et al.Research on the prediction algorithm for sina popular micro blog based on multi-features[J].Journal of Chinese Computer Systems,2017,38(3):494-498.
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[16]Wang Jian-fang,Li Xiao,Wu Wen-qi,et al.An algorithm of collaborative filtering based on SVD and trust factors[J].Journal of Chinese Computer Systems,2017,38(6):1290-1293.
[8]余嘉元.项目反应理论及其应用[M].南京:江苏教育出版社,1992.
[11]赵宏伟,申德荣,田力威.云计算环境下资源需求预测与调度方法的研究[J].小型微型计算机系统,2016,37(4):659-663.
[12]郑志蕴,江国林,张行进,等.基于多特征的热门微博预测算法研究[J].小型微型计算机系统,2017,38(3):494-498.
[13]柳建,孙胜军,毛国平,等.蒙特卡洛模拟的并行实现及并行效率研究[J].计算机应用与软件,2018,35(1):295-297.
[16]王建芳,李骁,武文琪,等一种SVD和信任因子相结合的协同过滤算法[J].小型微型计算机系统,2017,38(6):1290-1293.
1 http://langtest. jp.(2015)
[2]Baker F B,Kim S H.Item response theory:parameter estimation techniques[M].CRC Press,2004.
[3]Van d L W J,Klein Entink R H,Fox J P.IRT parameter estimation w ith response times as collateral information[J].Applied Psychological M easurement,2010,34(5):327-347.
[4]Tay L,Ali U S,Drasgow F,et al.Fitting IRT models to dichotomous and polytomous data:assessing the relative model-data fit of ideal point and dominance models[J].Applied Psychological M easurement,2011,35(4):280-295.
[5]Yegnanarayana B.Artificial neural networks[M].PHI Learning Pvt.Ltd.,2009.
[6]Wang Cun-you,Yu Jia-yuan.New model of IRT item parameter estimation based on neural netw orks[J].Journal of Computer Applications,2006,26(4):992-994.
[7]Specht D F.A general regression neural network[J].IEEE Transactions on Neural Netw orks,1991,2(6):568-576.
[8]Yu Jia-yuan.IRT and appliance[M].Nanjing:Jiangsu Education Press,1992.
[9]Samejima F.Estimation of latent ability using a response pattern of graded scores[J].Psychometrika,1969,34(1):1-97.
[10]Yao S B,Guo D L,Yang G W.Three-dimensional aerodynamic optimization design of high-speed train nose based on GA-GRNN[J].Science China Technological Sciences,2012,55(11):3118-3130.
[11]Zhao Hong-wei,Shen De-rong,Tian Li-wei.Research on resources forecasting and scheduling method in cloud computing environment[J].Journal of Chinese Computer Systems,2016,37(4):659-663.
[12]Zheng Zhi-yun,Jiang Guo-lin,Zhang Xing-jin,et al.Research on the prediction algorithm for sina popular micro blog based on multi-features[J].Journal of Chinese Computer Systems,2017,38(3):494-498.
[13]Liu Jian,Sun Sheng-jun,Mao Guo-ping,et al.Research on parallel implementation and parallel efficiency of M onte Carlo simulation[J].Computer Applications and Software,2018,35(1):295-297.
[14]Specht D F.Probabilistic neural networks and the polynomial adaline as complementary techniques for classification[J].IEEETransactions on Neural Netw orks,2002,1(1):111-121.
[15]Mizumoto A,Plonsky L.R as a lingua franca:advantages of using R for quantitative research in applied linguistics[J].Applied Linguistics,2016,37(2):284-291.
[16]Wang Jian-fang,Li Xiao,Wu Wen-qi,et al.An algorithm of collaborative filtering based on SVD and trust factors[J].Journal of Chinese Computer Systems,2017,38(6):1290-1293.
[8]余嘉元.项目反应理论及其应用[M].南京:江苏教育出版社,1992.
[11]赵宏伟,申德荣,田力威.云计算环境下资源需求预测与调度方法的研究[J].小型微型计算机系统,2016,37(4):659-663.
[12]郑志蕴,江国林,张行进,等.基于多特征的热门微博预测算法研究[J].小型微型计算机系统,2017,38(3):494-498.
[13]柳建,孙胜军,毛国平,等.蒙特卡洛模拟的并行实现及并行效率研究[J].计算机应用与软件,2018,35(1):295-297.
[16]王建芳,李骁,武文琪,等一种SVD和信任因子相结合的协同过滤算法[J].小型微型计算机系统,2017,38(6):1290-1293.
1 http://langtest. jp.(2015)