We propose new methods for identifying and classifying aberrant response patterns (ARPs) by means of functional data analysis. These methods take the person response function (PRF) of an individual and compare it with the pattern that would correspond to a generic individual of the same ability according to the item-person response surface. ARPs correspond to atypical difference functions. The ARP classification is done with functional data clustering applied to the PRFs identified as ARP. We apply these methods to two sets of simulated data (the first is used to illustrate the ARP identification methods and the second demonstrates classification of the response patterns flagged as ARP) and a real data set (a Grade 12 science assessment test, SAT, with 32 items answered by 600 examinees). For comparative purposes, ARPs are also identified with three nonparametric person-fit indices (Ht, Modified Caution Index, and ZU3). Our results indicate that the ARP detection ability of one of our proposed methods is comparable to that of person-fit indices. Moreover, the proposed classification methods enable ARP associated with either spuriously low or spuriously high scores to be distinguished.

中文翻译：

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通过功能数据分析识别和分类异常响应模式

我们提出了通过功能数据分析来识别和分类异常响应模式（ARPs）的新方法。这些方法采用个人的人的反应功能（PRF），并将其与根据项目-人的反应面对应于具有相同能力的一般个体的模式进行比较。ARP对应于非典型差异函数。ARP分类是通过将功能数据聚类应用于标识为ARP的PRF来完成的。我们将这些方法应用于两组模拟数据（第一组用于说明ARP识别方法，第二组用于演示标记为ARP的响应模式的分类）和真实数据集（12年级科学评估测试SAT， 600名考生回答了32个问题）。出于比较目的，ARP还通过三个非参数的人员适应指数（Ht，修正谨慎指数和ZU3）进行标识。我们的结果表明，我们提出的方法之一的ARP检测能力与人体适应指数相当。此外，提出的分类方法使得能够区分与虚假的低分数或虚假的高分数相关联的ARP。