This article examines the Fisher information functions, , and explores implications for scoring of binary ideal point item response models. These models typically appear to have that are bimodal and identically equal to 0 at the ideal point. The article shows that this is an inherent property of ideal point IRT models, which either have this property or are indeterminate and thus violate the likelihood regularity conditions. For some models, the indeterminacy can be resolved, generating an effectively unimodal , albeit with violated regularity conditions. In other cases, diverges. All reasonable ideal point IRT models exhibit this behaviour. Users should exercise caution when relying on asymptotics, particularly for shorter assessments. Use of simulated plausible values or prediction from a fully Bayesian estimation is recommended for scoring.

中文翻译：

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二元理想点项目响应模型中的 Fisher 信息函数和评分：一个警示故事

本文检查了 Fisher 信息函数，并探讨了对二元理想点项目响应模型评分的影响。这些模型通常看起来是双峰的，并且在理想点处完全等于 0。文章表明，这是理想点 IRT 模型的固有属性，它要么具有此属性，要么是不确定的，因此违反了似然规律性条件。对于某些模型，可以解决不确定性，生成有效的单峰，尽管违反了规律性条件。在其他情况下，分歧。所有合理的理想点 IRT 模型都表现出这种行为。用户在依赖渐近线时应谨慎行事，尤其是对于较短的评估。建议使用模拟的合理值或完全贝叶斯估计的预测进行评分。