Although a statistical model might fit well to a large proportion of the individuals of a random sample, some individuals might give ‘unusual’ responses that are not well explained by the hypothesized model. If individual responses are given as continuous response vectors, M‐distances can be used to produce real valued indicators of how well an individual's response vector corresponds to a covariance structure implied by a psychometric model. In this note, we focus on the so‐called one‐factor model. Two M‐distances, d_si and d_ri, which are sensitive to different aspects of the assumed factor model, have been proposed. While one of the M‐distances, d_ri, has been derived based on Bartlett factor scores, in this note we show that the second M‐distance, d_si, can be derived in an analogous fashion based on Thomson factor scores.

中文翻译：

---

有关识别异常响应模式的剩余M距离的说明。

尽管统计模型可能非常适合随机样本中的很大一部分个体，但某些个体可能会给出“异常”的响应，而该假设模型无法很好地解释该响应。如果将各个响应作为连续响应向量给出，则M距离可用于生成一个实值指标，用于指示一个人的响应向量与心理模型所隐含的协方差结构的对应程度。在本说明中，我们关注所谓的单因素模型。已经提出了对假设因子模型的不同方面敏感的两个M距离d _si和d _ri。当M距离之一时，d _ri，是根据巴特利特因子得分得出的，在此注释中，我们表明可以基于汤姆森因子得分以类似的方式得出第二个M距离d _si。