KERNEL SMOOTHING APPROACHES TO NONPARAMETRIC ITEM CHARACTERISTIC CURVE ESTIMATION
KERNEL SMOOTHING APPROACHES TO NONPARAMETRIC ITEM CHARACTERISTIC CURVE ESTIMATION
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DOI：
10.1007/bf02294494
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发表时间：
1991-12-01
期刊：
影响因子：
3
通讯作者：
RAMSAY, JO
中科院分区：
文献类型：
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作者：
RAMSAY, JO
选择特征曲线，即为测试项目选择特定选项的能力和概率之间的关系，可以通过非参数平滑技术来估计。被平滑的是估计的考生能力排名的一些函数与指示选项是否被选择的二元变量之间的关系。本文探讨了使用核平滑，这是特别适合这种应用程序。实例表明，在快速傅立叶变换的帮助下，估计数的计算速度大约是使用常用参数方法（如使用三参数logistic分布的最大边际似然估计）的500倍。模拟表明，即使人口曲线是三参数逻辑斯谛曲线，也没有效率损失。这种方法有几个有趣的扩展。
The option characteristic curve, the relation between ability and probability of choosing a particular option for a test item, can be estimated by nonparametric smoothing techniques. What is smoothed is the relation between some function of estimated examinee ability rankings and the binary variable indicating whether or not the option was chosen. This paper explores the use of kernel smoothing, which is particularly well suited to this application. Examples show that, with some help from the fast Fourier transform, estimates can be computed about 500 times as rapidly as when using commonly used parametric approaches such as maximum marginal likelihood estimation using the three-parameter logistic distribution. Simulations suggest that there is no loss of efficiency even when the population curves are three-parameter logistic. The approach lends itself to several interesting extensions.