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
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摘要
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。
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.
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.
引文
关潮辉,丁树良.(2014).基于IRT模型的BP神经网络参数估计的进一步研究.江西师范大学学报(自然科学版),(4),434-436.
罗照盛.(2012).项目反应理论基础(pp.8-9).北京师范大学出版社.
汪存友,余嘉元.(2006).一种新的基于神经网络的IRT项目参数估计模型.计算机应用,26(4),992-994.
汪存友.(2007).运用ANN估计小样本的IRT参数研究(硕士学位论文).南京师范大学.
王鹏,朱新立,王芳.(2015).多维项目反应理论的计量模型、参数估计及应用.心理学进展,05(6),365-375.
严娟.(2014).MIRT补偿模型与非补偿模型的比较研究及其应用(硕士学位论文).江西师范大学.
余嘉元.(2009).基于神经网络集成的irt参数估计.江南大学学报(自然科学版),8(5),505-508.
Babcock,B.(2011).Estimating a noncompensatory irt model using metropolis within gibbs sampling.Applied Psychological Measurement,35(4),317-329.
Baker,F.B.(2004).Item response theory:Parameter estimation techniques(2nd,pp.8-9,158-169).New York:Marcel Dekker.
Béguin,A.A.,& Glas,C.A.W.(2001).Mcmc estimation and some model-fit analysis of multidimensional irt models.Psychometrika,66(4),541-561.
Bolt,D.M.,& Lall,V.F.(2003).Estimation of compensatory and noncompensatory multidimensional item response models using markov chain monte carlo.Applied Psychological Measurement,27(6),395-414.
Breiman,L.(1996).Bagging predictors.Kluwer Academic Publishers.
Chib,S.,& Greenberg,E.(1995).Understanding the metropolis-hastings algorithm.The American Statistician,49(4),327-335.
Christoffersson,A.(1975).Factor analysis of dichotomized variables.Psychometrika,40(1),5-32.
Jiang,Y.L.(2005).Estimating parameters for multidimensional item response theory models by MCMC methods.Unpublished doctoral dissertation,Michigan State University.
Laura,L.B.,Barnes,& Steven,L.W.(1991).The utility of a modified one-parameter irt model with small samples.Applied Measurement in Education,4(2),143-157.
Mcdonald,R.P.(1997).Normal-Ogive Multidimensional Model.Handbook of Modern Item Response Theory.Springer New York.
Mcdonald,R.P.(2000).A basis for multidimensional item response theory.Applied Psychological Measurement,24(2),99-114.
Metropolis,N.,Rosenbluth,A.W.,Rosenbluth,M.N.,Teller,A.H.,& Teller,E.(1953).Equation of state calculations by fast computing machines.The Journal of Chemical Physics,21(6),1087-1092.
Mordelet,F.,& Vert,J.P.(2014).A bagging SVM to learn from positive and unlabeled examples.Pattern Recognition Letters,37,201-209.
Reckase,M.D.(2009).18 multidimensional item response theory.Handbook of Statistics,26(06),607-642.
Specht,D.F.(1991).A general regression neural network.IEEE Trans Neural Netw,2(6),568-576.
Thissen,D.,& Wainer,H.(1982).Some standard errors in item response theory.Psychometrika,47(4),397-412.
Yao,L.(2003).BMIRT:Bayesian multivariate item response theory [Software].Monterey,CA:Defense Manpower Data Center.
Yao,L.,& Schwarz,R.D.(2006).A multidimensional partial credit model with associated item and test statistics:An application to mixed-format tests.Applied Psychological Measurement,30(6),469-492.
Yao,L.(2013).The bmirt toolkit.http://www.bmirt.com/.
罗照盛.(2012).项目反应理论基础(pp.8-9).北京师范大学出版社.
汪存友,余嘉元.(2006).一种新的基于神经网络的IRT项目参数估计模型.计算机应用,26(4),992-994.
汪存友.(2007).运用ANN估计小样本的IRT参数研究(硕士学位论文).南京师范大学.
王鹏,朱新立,王芳.(2015).多维项目反应理论的计量模型、参数估计及应用.心理学进展,05(6),365-375.
严娟.(2014).MIRT补偿模型与非补偿模型的比较研究及其应用(硕士学位论文).江西师范大学.
余嘉元.(2009).基于神经网络集成的irt参数估计.江南大学学报(自然科学版),8(5),505-508.
Babcock,B.(2011).Estimating a noncompensatory irt model using metropolis within gibbs sampling.Applied Psychological Measurement,35(4),317-329.
Baker,F.B.(2004).Item response theory:Parameter estimation techniques(2nd,pp.8-9,158-169).New York:Marcel Dekker.
Béguin,A.A.,& Glas,C.A.W.(2001).Mcmc estimation and some model-fit analysis of multidimensional irt models.Psychometrika,66(4),541-561.
Bolt,D.M.,& Lall,V.F.(2003).Estimation of compensatory and noncompensatory multidimensional item response models using markov chain monte carlo.Applied Psychological Measurement,27(6),395-414.
Breiman,L.(1996).Bagging predictors.Kluwer Academic Publishers.
Chib,S.,& Greenberg,E.(1995).Understanding the metropolis-hastings algorithm.The American Statistician,49(4),327-335.
Christoffersson,A.(1975).Factor analysis of dichotomized variables.Psychometrika,40(1),5-32.
Jiang,Y.L.(2005).Estimating parameters for multidimensional item response theory models by MCMC methods.Unpublished doctoral dissertation,Michigan State University.
Laura,L.B.,Barnes,& Steven,L.W.(1991).The utility of a modified one-parameter irt model with small samples.Applied Measurement in Education,4(2),143-157.
Mcdonald,R.P.(1997).Normal-Ogive Multidimensional Model.Handbook of Modern Item Response Theory.Springer New York.
Mcdonald,R.P.(2000).A basis for multidimensional item response theory.Applied Psychological Measurement,24(2),99-114.
Metropolis,N.,Rosenbluth,A.W.,Rosenbluth,M.N.,Teller,A.H.,& Teller,E.(1953).Equation of state calculations by fast computing machines.The Journal of Chemical Physics,21(6),1087-1092.
Mordelet,F.,& Vert,J.P.(2014).A bagging SVM to learn from positive and unlabeled examples.Pattern Recognition Letters,37,201-209.
Reckase,M.D.(2009).18 multidimensional item response theory.Handbook of Statistics,26(06),607-642.
Specht,D.F.(1991).A general regression neural network.IEEE Trans Neural Netw,2(6),568-576.
Thissen,D.,& Wainer,H.(1982).Some standard errors in item response theory.Psychometrika,47(4),397-412.
Yao,L.(2003).BMIRT:Bayesian multivariate item response theory [Software].Monterey,CA:Defense Manpower Data Center.
Yao,L.,& Schwarz,R.D.(2006).A multidimensional partial credit model with associated item and test statistics:An application to mixed-format tests.Applied Psychological Measurement,30(6),469-492.
Yao,L.(2013).The bmirt toolkit.http://www.bmirt.com/.