Abstract:

Recently Cognitive Diagnosis(CD) was attached more and more importance internationally. But the realization of CD must utilize a special psychometrical model called Cognitive Diagnosis Model(CDM). This paper is focused on the HO-DINA model. With this model this paper investigated it’s parameter estimation and it’s properties that can be the inference of users. Research Method: To explore the feasibility of MCMC algorithm and the estimated precision, and to probe the properties of HO-DINA model, Monte Carlo method is used here. There are two experiments: Experiment 1: Fixed the number of cognitive attributes(5), of test items(60) and of examinees (1000). The target of this experiment is to explore the feasibility of MCMC algorithm and the estimated precision. Experiment 2: This experiment intent to study the properties of HO-DINA model, particularly the correctness rate of diagnosis. There are two factors was considered: the number of test items varied with possible values of 20, 40, 60, 80, 100, 120. And the number of cognitive attributes varied with possible values of 4, 5, 6, 7, 8. The number of examinees is fixed as 1000. Conclusions: (1) The estimation method of MCMC algorithm holds fairly robustness, and it’s precision of item and ability parameters are preferably great. Which indicates the MCMC algorithm method is feasible. (2) With the number of attribute fixed, the increasing of the number of text items can enhance the pattern correctness rate effectively. When the number of test items is varied from 20 to 40, the extent of increasing is the greatest. While the number is varied from 40 to 60, the degree of increasing is less. In real work, if we want to obtain a pattern correctness rate higher than 80%, then the number of test items needs to be 20 with the number of attribute is 4, 40 with the number of attributes is 5, 6, 7 possibly, 60 with the number of attribute is 8. (3) With the number of test items fixed, the increasing of the number of attribute will decrease the pattern correctness rate. The extent of decreasing is the greatness with the number of test items is 20, while the degree of decreasing is the least with the number of test items is 120. When the number of attribute is varied from 5 to 7, the degree of deceasing is less. Thus seven attributes is the turning point. So in real work, the number of attributes is suggested not greater than seven.

Key words: Cognitive Diagnosis, High Order DINA Model, MCMC Algorithm, Monte Carol Simulation

摘要：

认知诊断目前在国内外越来越受到重视，而要真正实现认知诊断，需借助一定的计量学模型即认知诊断模型。国际上，目前已开发近60种认知诊断模型，不同模型又各具特点。本研究重点分析国外研究较成熟的模型——HO-DINA/DINA模型，具体探讨该模型参数估计的实现及模型性能，采用Monte Carlo模拟方法进行，研究发现：(1)本研究对项目参数、属性参数和被试参数估计返真性较好、稳健性较强、HO-DINA模型具有较高的判断率，MCMC算法可行；（2）诊断的属性个数越多，诊断的模式正确率越低，建议实际使用该模型时，诊断的属性个数不宜超过7个；（3）用于诊断的项目数越多，诊断的模式正确率越高，在实际工作中，若要保证有80%以上的模式判准率，则4个属性的至少需20题，5个、6个和7个属性的至少需要40题，8个属性至少需60题。实际运用者应根据实际情况考虑适当的项目数及属性数。

关键词: 认知诊断, HO-DINA模型, MCMC算法, Monte Carlo模拟