Pacific Metrics Corporation, Princeton, NJ, USA.
Educational Testing Service, Princeton, NJ, USA.
Psychometrika. 2017 Dec;82(4):1149-1161. doi: 10.1007/s11336-016-9531-z. Epub 2016 Oct 21.
Tests for a change point (e.g., Chen and Gupta, Parametric statistical change point analysis (2nd ed.). Birkhuser, Boston, 2012; Hawkins et al., J Qual Technol 35:355-366, 2003) have recently been brought into the spotlight for their potential uses in psychometrics. They have been successfully applied to detect an unusual change in the mean score of a sequence of administrations of an international language assessment (Lee and von Davier, Psychometrika 78:557-575, 2013) and to detect speededness of examinees (Shao et al., Psychometrika, 2015). The differences in the type of data used, the test statistics, and the manner in which the critical values were obtained in these papers lead to questions such as "what type of psychometric problems can be solved by tests for a change point?" and "what test statistics should be used with tests for a change point in psychometric problems?" This note attempts to answer some of these questions by providing a general overview of tests for a change point with a focus on application to psychometric problems. A discussion is provided on the choice of an appropriate test statistic and on the computation of a corresponding critical value for tests for a change point. Then, three real data examples are provided to demonstrate how tests for a change point can be used to make important inferences in psychometric problems. The examples include some clarifications and remarks on the critical values used in Lee and von Davier (Psychometrika, 78:557-575, 2013) and Shao et al. (Psychometrika, 2015). The overview and the examples provide insight on tests for a change point above and beyond Lee and von Davier (Psychometrika, 78:557-575, 2013) and Shao et al. (Psychometrika, 2015). Thus, this note extends the research of Lee and von Davier (Psychometrika, 78:557-575, 2013) and Shao et al. (Psychometrika, 2015) on tests for a change point.
近年来，用于检测序列数据中均值变化的变点检验（例如，Chen 和 Gupta, Parametric statistical change point analysis (2nd ed.). Birkhuser, Boston, 2012; Hawkins 等人, J Qual Technol 35:355-366, 2003）因其在心理计量学中的潜在应用而备受关注。这些检验已经成功地应用于检测国际语言评估序列中异常的均值变化（Lee 和 von Davier, Psychometrika 78:557-575, 2013）以及检测被试的速度（Shao 等人, Psychometrika, 2015）。这些论文中使用的数据类型、检验统计量以及临界值的获取方式的差异，引发了一些问题，如“变点检验可以解决哪些类型的心理计量问题？”以及“心理计量问题中应使用哪种检验统计量？”本文通过提供一个变点检验的概述，并重点介绍其在心理计量问题中的应用，试图回答其中的一些问题。文中讨论了适当检验统计量的选择以及变点检验的相应临界值的计算，并提供了三个真实数据示例，以演示变点检验如何用于在心理计量问题中做出重要推断。这些示例包括对 Lee 和 von Davier（Psychometrika, 78:557-575, 2013）和 Shao 等人（Psychometrika, 2015）中使用的临界值的一些澄清和说明。本文的概述和示例提供了对变点检验的深入理解，超越了 Lee 和 von Davier（Psychometrika, 78:557-575, 2013）和 Shao 等人（Psychometrika, 2015）的研究。因此，本文扩展了 Lee 和 von Davier（Psychometrika, 78:557-575, 2013）和 Shao 等人（Psychometrika, 2015）关于变点检验的研究。
