心理与教育测验中异常反应侦查新技术：变点分析法

doi:10.3724/SP.J.1042.2020.01462

摘要/Abstract

摘要：

变点分析法(change point analysis, CPA)近些年才引入心理与教育测量学, 相较于传统方法, CPA不仅可以侦查异常作答被试, 还能自动精确地定位变点位置, 高效清洗作答数据。其原理在于：判断作答序列中是否存在可将该序列划分为具有不同统计学属性两部分的点(即变点), 并且需使用被试拟合统计量(person-fit statistic, PFS)来量化两个子序列之间的差异。未来可将单变点分析拓展至多变点, 结合反应时等信息, 构建非参数化指标以及将现有指标拓展至多级计分或多维测验, 以提高CPA的适用广度及效力。

关键词: 异常反应, 变点分析法, 累积和法, 被试拟合统计量

Abstract:

The change point analysis (CPA), as one of the most widely used methods for statistical process control, is introduced to psychological and educational measurement for detection of aberrant response patterns in recent years. CPA outperforms the traditional method as follows: In addition to detecting aberrant response patterns, it can also pinpoint the locations of change points, contributing to efficient cleansing of response data. The method is employed to determine whether there is a point so that the complete sequence can be divided into two parts with different statistical properties, where person-fit statistics (PFS) is needed for quantifying the difference between two sub-sequences. Future researchers should pay more attention to multiple change points detection, making full use of other effective information like response time data, developing non-parametric indices as well as reforming the exiting person-fit statistics for polytomous and multidimensional tests, so as to enhance its applicability and power.

Key words: aberrant responses, change point analysis, cumulative summation, person-fit statistics

中图分类号:

B841

张龙飞, 王晓雯, 蔡艳, 涂冬波. (2020). 心理与教育测验中异常反应侦查新技术：变点分析法. 心理科学进展 , 28(9), 1462-1477.

ZHANG Longfei, WANG Xiaowen, CAI Yan, TU Dongbo. (2020). Change point analysis: A new method to detect aberrant responses in psychological and educational testing. Advances in Psychological Science, 28(9), 1462-1477.

图/表 2

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	CUSUM	CPA
主要思想	按照题目顺序依次将各题上观察与期望得分间的残差累积求和。	找到某个可将序列划分为具有不同统计学属性两部分的点。
PFS	基于题目平均加权残差的单侧指标$C_{j}^{+}$, $C_{j}^{-}$和双侧指标${{C}^{T}}$。	双侧指标：基于似然比检验的${{L}_{\max }}$, 基于Wald检验的${{W}_{\max }}$, 基于得分检验的${{S}_{\max }}$和基于加权残差的${{R}_{\max }}$, 以及各自的单侧形式。
单双侧指标	在侦测前已明确目标效应时用单侧指标, 未明确目标效应或对目标效应不作具体要求时用双侧指标。
优点	输出图像, 可用于过程监控。	自动精确定位变点。
缺点	需人工检查图像来定位变点, 准确性较低。	当变点位于序列最前或最后几题时难以定位。
适用情境	变点前后模型参数已知。	变点前后模型参数未知。其中${{L}_{\max }}$、${{W}_{\max }}$和${{S}_{\max }}$适用于高风险(教育)测验, ${{R}_{\max }}$适用于低风险(心理)测验。

	CUSUM	CPA
主要思想	按照题目顺序依次将各题上观察与期望得分间的残差累积求和。	找到某个可将序列划分为具有不同统计学属性两部分的点。
PFS	基于题目平均加权残差的单侧指标$C_{j}^{+}$, $C_{j}^{-}$和双侧指标${{C}^{T}}$。	双侧指标：基于似然比检验的${{L}_{\max }}$, 基于Wald检验的${{W}_{\max }}$, 基于得分检验的${{S}_{\max }}$和基于加权残差的${{R}_{\max }}$, 以及各自的单侧形式。
单双侧指标	在侦测前已明确目标效应时用单侧指标, 未明确目标效应或对目标效应不作具体要求时用双侧指标。
优点	输出图像, 可用于过程监控。	自动精确定位变点。
缺点	需人工检查图像来定位变点, 准确性较低。	当变点位于序列最前或最后几题时难以定位。
适用情境	变点前后模型参数已知。	变点前后模型参数未知。其中${{L}_{\max }}$、${{W}_{\max }}$和${{S}_{\max }}$适用于高风险(教育)测验, ${{R}_{\max }}$适用于低风险(心理)测验。