Abstract The basic local independence model (BLIM) is one of the most widely applied probabilistic models in knowledge space theory. It is known that the BLIM is not identifiable in general and that its identifiability strictly depends on the properties of the knowledge structure to which it is applied. If the knowledge structure is either forward- or backward-graded in one or more items, then the BLIM is not identifiable. In such cases, there exist continuous transformations of the model’s parameters, named forward and backward transformations, that keep constant the value of the model’s prediction function. Under certain constraints on the model’s parameters, some of the transformations might lose this property. The type of constraints considered in this article consist of fixing the probability of a knowledge state to a constant value. The theoretical results contained in the article shed light on the role of the different state probabilities in reducing the collection of transformations and thus restoring the identifiability of the model’s parameters.

中文翻译：

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前后变换下BLIM的可识别性和参数不变性

摘要 基本局部独立模型（BLIM）是知识空间理论中应用最广泛的概率模型之一。众所周知，BLIM 通常是不可识别的，其可识别性严格取决于应用它的知识结构的属性。如果知识结构在一个或多个项目中向前或向后分级，则 BLIM 是不可识别的。在这种情况下，存在模型参数的连续变换，称为向前和向后变换，它们保持模型预测函数的值不变。在模型参数的某些约束下，某些转换可能会失去此属性。本文中考虑的约束类型包括将知识状态的概率固定为常数值。