In recent years a number of articles have focused on the identifiability of the basic local independence model. The identifiability issue usually concerns two model parameter sets predicting an identical probability distribution on the response patterns. Both parameter sets are applied to the same knowledge structure. However, nothing is known about cases where different knowledge structures predict the same probability distribution. This situation is referred to as ʻempirical indistinguishabilityʼ between two structures and is the main subject of the present paper. Empirical indistinguishability is a stronger form of unidentifiability, which involves not only the parameters, but also the structural and combinatorial properties of the model. In particular, as far as knowledge structures are concerned, a consequence of empirical indistinguishability is that the existence of certain knowledge states cannot be empirically established. Most importantly, it is shown that model identifiability cannot guarantee that a certain knowledge structure is empirically distinguishable from others. The theoretical findings are exemplified in a number of different empirical scenarios.

中文翻译：

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论知识结构的经验不可区分性

近年来，许多文章都集中在基本本地独立模型的可识别性上。可识别性问题通常涉及预测响应模式上相同概率分布的两个模型参数集。两个参数集都应用于相同的知识结构。然而，对于不同知识结构预测相同概率分布的情况，我们一无所知。这种情况被称为两种结构之间的“经验不可区分性”，是本文的主要主题。经验不可区分性是不可识别性的一种更强形式，它不仅涉及模型的参数，还涉及模型的结构和组合属性。特别是，就知识结构而言，经验不可区分性的一个结果是某些知识状态的存在不能凭经验建立。最重要的是，它表明模型可识别性不能保证某个知识结构在经验上与其他知识结构是可区分的。理论发现在许多不同的经验情景中得到了例证。