Abstract Invariant item ordering refers to the statement that if one item is harder than another for one person, then it is harder for all people. Whether item ordering holds is a psychological statement because it describes how people may qualitatively vary. Yet, modern item response theory (IRT) makes an a priori commitment to item ordering. The Rasch model, for example, posits that items must order. Conversely, the 2PL model posits that items never order. Needed is an IRT model where item ordering or its violation is a function of the data rather than an a priori commitment. We develop two-parameter shift-scale models for this purpose, and find that the two-parameter uniform offers many advantages. We show how item ordering may be assessed using Bayes factor model comparison, and discuss computational issues with shift-scale IRT models.

中文翻译：

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物品订购吗？IRT 模型中的心理学

摘要 不变项排序是指如果一项对一个人来说比另一项更难，那么对所有人来说都更难。物品订购是否成立是一种心理陈述，因为它描述了人们如何在质量上有所不同。然而，现代项目反应理论 (IRT) 对项目订购做出了先验承诺。例如，Rasch 模型假定项目必须排序。相反，2PL 模型假定物品从不订购。需要的是 IRT 模型，其中项目订购或其违规是数据的函数，而不是先验承诺。我们为此目的开发了双参数移位尺度模型，并发现双参数统一模型提供了许多优点。我们展示了如何使用贝叶斯因子模型比较来评估项目排序，并讨论使用移位尺度 IRT 模型的计算问题。