Abstract: Computerized adaptive testing (CAT) is based on item response theory (IRT) ,which requires a large-scale item bank, and each item in item bank needs item parameters, the item bank of CAT needs to be constantly updated, the item parameters are very important when the bank is constructed and updated. At the present, statistical methods are used for estimating the item parameters, which need to have enough items and examinees, otherwise, it may lack of precision or lead to failure. These limitations are the motivation behind some research to use other adaptive approach to estimate the parameters. Some researchers proposed a novel solution based on back-propagation(BP) neural network to solve the above mentioned limitations. Based on dichotomous model, the parameters were estimated with BP neural network, their study results showed that, for small samples, there are higher precision of the item parameters estimated by neural network than that by statistical methods. Polytomous items can provide more information than dichotomous items, and adopting polytomous items in test is a research direction of CAT. In this paper, the BP neural network and dimension reduction method are adopted to estimate items parameters and examinees ability based on Graded Response Model( GRM) model. First of all, MATLAB toolbox is used to design network, and some factors such as the number of the BP neural network layers, the number of neurons in each layer, and optimal activation function are discussed. In this paper, three layers of the BP neural network is used; each layer neuron number is 4, 12, 1;and s type function ‘Tansig' is used in the first and second layer, the third layer used linear 'purelin' function. Then, Monte Carlo simulation are employed to simulate the response matrixes, and the dimensions of response matrixes are reduced as following: the mean score rate of examinee is used to estimate the examinee’s ability, the passing rate of every grade of each item is used to estimate the difficulty parameters, and the correlation coefficient of score between each item and all items is used to estimate discrimination parameter. The vector of input parameters processed by means of reducing dimensions can improve the speed and the precision of estimation. Monte Carlo simulation results show that: (1) in small sample, whether examinees more than items or examinees less than items (such as the 50 examinees 20 items or the 20 examinees 30 items),which is difficult to work well for statistical estimation method, but the BP neural network method can obtain better results, and the training sample is larger, the precision is higher, the result of parameters estimation can be applied in practice. (2) it can be used to estimate more than 15 levels of polytomous item, which are not applicable for traditional estimation methods. (3)the calculation time is greatly reduced, comparing with traditional methods. By reducing dimensions, the new method decreases the inputs of a neural network from a high dimension to a low dimension ,which accelerates the speed of computation and enhances the precision of estimation.

Key words: parameter estimation,graded response model,back-propagation neural network,reduction of dimension,monte carlo simulation

摘要： 目前参数估计多采用统计方法，存在耗时长、要求被试样本容量大和项目数多等缺点。本文将BP神经网络和降维法相结合，对GRM的项目参数和考生能力参数进行估计。蒙特卡洛模拟结果显示：（1）不管是人多题少还是题多人少，该网络设计下的参数估计精度都较高；（2）可以应用到多个不同等级评分的参数估计中，甚至是超过15个等级的项目参数，估计精度也较高，这是其他参数估计方法所不可比拟的；（3）运行的时长和统计估计方法相比大大缩减。

关键词: 参数估计 GRM模型 BP神经网络 降维法 蒙特卡洛模拟