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Planning a Study for Testing the Rasch Model given Missing Values due to the use of Test-booklets

机译:由于使用测试手册,计划在给出缺失值的情况下测试Rasch模型的研究

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摘要

Though calibration of an achievement test within a psychological and educational context is very often carried out by the Rasch model, data sampling is hardly designed according to statistical foundations. However, Kubinger, Rasch, and Yanagida (2009, 2011) suggested an approach for the determination of sample size according to a given Type-Ⅰ- and Type-Ⅱ-risk and a certain effect of model contradiction when testing the Rasch model. The approach uses a three-way analysis of variance design with mixed classification. For the while, their simulation studies deal with complete data, meaning every examinee is administered with all of the items of an item pool. The simulation study now presented in this paper deals with the practical relevant case, in particular for large-scale assessments, that item presentation happens to use several test-booklets. As a consequence, there are missing values by design. Therefore, the question to be considered is, whether this approach works in this case as well. Besides the fact, that data are not normally distributed but there is a dichotomous variable (an examinee either solves an item or fails to solve it), only a single entry for each cell exists in the given three-way analysis of variance design - if at all, due to missing values. Hence, the obligatory test-statistic's distribution may not be retained, in contrast to the case of having no missing values. The result of our simulation study, despite applying only to a very special scenario, is that this approach works, indeed: Whether test-booklets were used or every examinee is administered all of the items changes nothing in respect to the actual Type-Ⅰ-risk or to the power of the test, given almost the same amount of information of examinees per item. However, as the results are limited to a special scenario, we currently recommend any interested researcher to simulate the appropriate one in advance by him-/herself.
机译:尽管在心理和教育背景下对成就测验进行校准通常是由Rasch模型进行的,但很难根据统计基础来设计数据采样。然而,Kubinger,Rasch和Yanagida(2009,2011)提出了一种根据给定的Ⅰ型和Ⅱ型风险以及在测试Rasch模型时存在一定的模型矛盾效应来确定样本量的方法。该方法使用混合分类的方差设计的三向分析。一段时间以来,他们的模拟研究处理的是完整的数据,这意味着每个应试者都需要管理一个项目库中的所有项目。现在在本文中进行的模拟研究涉及实际的相关案例,特别是对于大规模评估而言,项目演示恰好使用了几本测试手册。结果,设计上存在缺失值。因此,要考虑的问题是这种方法在这种情况下是否也适用。除了事实,数据不是正态分布的,而是存在一个二分变量(应试者解决了一个问题或未能解决一个问题),在给定的方差设计三向分析中,每个单元格仅存在一个条目-如果完全是因为缺少值。因此,与没有缺失值的情况相比,强制检验统计量的分布可能不会保留。我们的模拟研究结果尽管仅适用于非常特殊的情况,但这种方法确实有效:无论是使用测试手册还是对每位应试者进行管理,所有项目相对于实际的Ⅰ型都不会改变。假设每个项目的考生信息量几乎相同,则可能会降低测试的风险或功效。但是,由于结果仅限于特殊情况,我们目前建议任何有兴趣的研究人员预先自己模拟合适的研究人员。

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  • 来源
    《Journal of applied measurement》 |2015年第4期|432-442|共11页
  • 作者单位

    School of Applied Health and Social Studies,University of Applied Sciences Upper Austria, Garnisonstrabe 21,4020 Linz, Austria,;

    University of Vienna;

    University of Natural Resources and Applied Life Sciences, Vienna;

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  • 正文语种 eng
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