Applications of Asymptotic Expansion in Item Response Theory Linking
Applications of Asymptotic Expansion in Item Response Theory Linking
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渐近展开在项目反应理论链接中的应用
DOI：
10.1007/978-0-387-98138-3_16
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
H. Ogasawara
中科院分区：
文献类型：
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作者：
H. Ogasawara
本章的目的是利用项目反应理论（IRT；参见，例如，Bock & Moustaki, 2007）在公共项目非等效群体设计中对连接系数估计量的分布进行渐近展开式。在IRT链接中，通常项目参数仅作为其估计值可用。因此，IRT连接中的参数，即连接系数，会受到抽样变化的影响。因此，考虑到这种变化，看到估计的大小是很重要的。估计其大小的典型方法之一是利用连接系数估计量的渐近标准误差（ase）。Ogasawara（2000）推导了使用项目参数矩的方法（以下简称矩法；Loyd & Hoover, 1980; Mislevy & Bock, 1990; Marco, 1977；另见Kolen & Brennan， 2004，第6章）的系数估计的熵值。Ogasawara （2001b）获得了使用响应函数的方法的相应ase （Haebara, 1980; Stocking & Lord, 1983；另见Kolen & Brennan， 2004，第6章）。Lord （1982a）和Ogasawara （2001a, 2003）获得了真实分数和观察分数相等方法中的ase，而Tsai， Hanson， Kolen和Forsyth（2001）研究了bootstrap的标准误差；另见Kolen & Brennan， 2004，第7章)。Liou, Cheng, and Johnson（1997）和von Davier等人通过不同的方法得到了核方程ase（见von Davier， Holland, & Thayer, 2004b）。
The purpose of this chapter is to have asymptotic expansions of the distributions of the estimators of linking coefficients using item response theory (IRT; see, e.g., Bock & Moustaki, 2007) in the common-item nonequivalent groups design. In IRT linking, usually item parameters are available only as their estimates. Consequently, the parameters in IRT linking, that is, linking coefficients, are subject to sampling variation. So, it is important to see the magnitudes of the estimates considering this variation. One of the typical methods to evaluate their sizes is using the asymptotic standard errors (ASEs) of the estimators of linking coefficients. The ASEs of the coefficient estimators bythe methods using moments of item parameters(hereafter referred to asmoment methods; Loyd & Hoover, 1980; Mislevy & Bock, 1990; Marco, 1977; see also Kolen & Brennan, 2004, Ch. 6) were derived by Ogasawara (2000). The corresponding ASEs for the methods using response functions (Haebara, 1980; Stocking & Lord, 1983; see also Kolen & Brennan, 2004, Ch. 6) were obtained by Ogasawara (2001b). The ASEs in equating methods for true and observed scores were obtained by Lord (1982a) and Ogasawara (2001a, 2003), whereas the standard errors by the bootstrap were investigated by Tsai, Hanson, Kolen, and Forsyth (2001; see also Kolen & Brennan, 2004, Ch. 7). The ASEs by kernel equating (see von Davier, Holland, & Thayer, 2004b) were obtained by Liou, Cheng, and Johnson (1997) and von Davier et al. by different methods.