论文标题:GA在IRT中2PLM参数估计中的应用研究
The Applied Study on Genetic Algorithm in Parameter Estimation of Two Parameters Logistic Model on Item Response Theory
论文作者
论文导师 田振清,论文学位 硕士,论文专业 教育技术学
论文单位 内蒙古师范大学,点击次数 30,论文页数 62页File Size1040K
2007-06-05论文网 http://www.lw23.com/lunwen_670896392/
Item response theory;;Two parameters logistic model;;Genetic algorithm;;Genetic operators;;Precocity
本研究就项目反应理论(IRT)二参逻辑斯蒂克模型(2PLM)的参数估计问题为主要关注点,通过对IRT参数估计方法和GA进行了详细的探究,提出一种基于GA的2PLM参数估计方法,并且编制相应的算法程序对不同的项目参数进行估计。 IRT是一种现代教育与心理测量理论。参数估计是应用IRT的前提,将这些参数估计出来是建设题库、评价被试、评价考试质量等具体应用方面的需要。可以说,IRT的发展史也就是能力参数和项目参数估计的发展史。 相关文献中介绍的参数估计方法,基本都是采用极大似然估计法或贝叶斯方法,似然函数的获取、对待估参数初值的选取以及对待估参数求导是此类估计方法的主要特征。然而参数初值如果选取不恰当,在计算过程中“真值”可能不收敛,甚至会产生“振荡”现象,这显然不是施测者所期望的现象。同时对参数的求导乃至二阶偏导的计算将是非常繁杂的过程,而且每次的迭代必然会产生一定的误差,随着迭代次数的增多,误差有可能会变大,为克服上述缺点,笔者提出了一种新的参数估计的方法,即通过GA的思想来对参数进行估计,通过该方法进行参数估计时对参数初值的选取没有严格要求,而且不需要有待估参数的任何导数信息。 GA是一种寻优方法,它具有其它寻优算法所没有的自适应性、全局优化性和隐含并行性等特点。笔者通过对GA编码、遗传算子的分析和借鉴,提出了对遗传算子的改进策略和算法加速收敛策略,编制了算法验证程序并通过一定量的数据资料与国外流行的BILOG软件进行了对比,结果表明,在一定的误差范围内,文中所提出的估计算法能够收敛到较好的最优解。
Having thoroughly studied the item response theory, the two parameters logistic model, this article proposes a kind of parameter estimation method based on the genetic algorithm and the two parameters logistic model methods, and also works out a relevant arithmetic program to estimate the different item parameters. Item response theory is one of the modern educational and psychological measure theories. Parameter estimation is the premise of utilizing the item response theory, it is necessary to estimate these parameters out for the application of establishing question base, evaluating the subject and evaluating the quality of examination, etc. It can be said that the developing history of item response theory is the developing history of capability parameter and item parameters. Recent parameter estimation methods are mainly the maximum likelihood method and Bayer’s method, the important parts of these methods are to obtain the likelihood function, select the initial value of the parameter estimation and the derivative on unknown parameters. However, if the initial value is not proper, the real value could not be convergence, and even surge, this is not the phenomenon the administrator expected. In the meanwhile, the calculation of both parameter seeking differential coefficient and second order partial derivative are very difficult process. Each iteration must bring some errors, with the increase of the iterative times,errors would be larger, therefore , this article put forward a new kind of parameter estimation methods according to those disadvantages mentioned above. That is to say, to estimate the parameter by the thinking of genetic algorithm, this method is not strict in the parameter initial value, and it doesn’t necessarily need any data of unevaluated parameter. Genetic algorithm is a premium seeking method,with the characters of self-adaptation, whole optimization, and concealed parallel processing .The author proposes the improving strategies of genetic operators and the speedup constringency strategies and work out the arithmetic validating program through the analysis and research of coding and genetic operators on genetic algorithm. Compared with the popular foreign software BILOG, and to some extent, the estimation method just mentioned can make a better constricted answer.
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