A Didactic Presentation of Snijders’s lz* Index of Person Fit With Emphasis on Response Model Selection and Ability Estimation
A Didactic Presentation of Snijders’s lz* Index of Person Fit With Emphasis on Response Model Selection and Ability Estimation
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Snijders lz* 人适合度指数的教学演示，重点是响应模型选择和能力估计
DOI：
10.3102/1076998610396894
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发表时间：
2012
影响因子：
2.4
通讯作者：
Sébastien Béland
中科院分区：
文献类型：
--
作者：
D. Magis;Gilles Raîche;Sébastien Béland
本文重点关注两个基于似然性的人物适合度指数，即指数 lz 和 Snijders 修正指数 lz *。第一个通常用于人员适合度的实际评估，尽管当真实能力被样本能力估计取代时，其渐近标准正态分布无效。 lz * 索引是 lz 的概括，它纠正了这种采样变异性。令人惊讶的是，它在心理测量和教育评估界尚未流行。此外，关于哪种类型的项目响应模型和能力估计方法可用于计算 lz * 指数还存在一些模糊性。本文的目的是以一种简单且具有指导性的方式呈现索引 lz *。从lz和lz*之间的关系出发，我们根据逻辑项目响应理论（IRT）模型的类型和基于可能性的能力估计量开发了框架。通过分析真实的语言技能评估数据集来说明lz*的实际计算。
This paper focuses on two likelihood-based indices of person fit, the index lz and the Snijders’s modified index lz *. The first one is commonly used in practical assessment of person fit, although its asymptotic standard normal distribution is not valid when true abilities are replaced by sample ability estimates. The lz * index is a generalization of lz , which corrects for this sampling variability. Surprisingly, it is not yet popular in the psychometric and educational assessment community. Moreover, there is some ambiguity about which type of item response model and ability estimation method can be used to compute the lz * index. The purpose of this article is to present the index lz * in a simple and didactic approach. Starting from the relationship between lz and lz *, we develop the framework according to the type of logistic item response theory (IRT) model and the likelihood-based estimators of ability. The practical calculation of lz * is illustrated by analyzing a real data set about language skill assessment.