On the boundary problems in diagnostic classification models
On the boundary problems in diagnostic classification models
复制标题
诊断分类模型中的边界问题
DOI：
10.1007/s41237-022-00187-7
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Yamaguchi Kazuhiro
中科院分区：
文献类型：
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作者：
Yamaguchi Kauzhiro;Fujita Kazuya;Yamaguchi Kazuhiro
在诊断分类模型中，参数估计有时会提供粘在参数空间边界上的估计，这被称为边界问题，并可能导致标准误差的极值。然而，边界问题和不规则的标准误差之间的关系还没有分析探讨。此外，以往的研究还没有表明如何最大后验估计避免边界问题，并影响估计的标准误差。为了分析这些关系，最大后验估计的期望最大化算法和一个完整的数据Fisher信息矩阵明确推导出饱和诊断分类模型的混合制剂。理论研究表明，属性掌握模式的空性导致边界问题和不准确的标准误估计。此外，不幸的边界问题没有空导致较短的标准误差。仿真研究表明，最大后验概率方法防止边界问题。此外，这种方法与单调约束估计改善标准误差估计比无约束的极大似然估计。
In diagnostic classification models, parameter estimation sometimes provides estimates that stick to the boundaries of the parameter space, which is called the boundary problem and may lead to extreme values of standard errors. However, the relationship between the boundary problem and irregular standard errors has not been analytically explored. In addition, prior research has not shown how maximum-a-posteriori estimates avoid the boundary problem and affect the standard errors of estimates. To analyze these relationships, the expectation–maximization algorithm for maximum-a-posteriori estimates and a complete data Fisher information matrix are explicitly derived for a mixture formulation of saturated diagnostic classification models. Theoretical considerations show that the emptiness of attribute mastery patterns causes both the boundary problem and the inaccurate standard error estimates. Furthermore, unfortunate boundary problem without emptiness causes shorter standard errors. A simulation study shows that the maximum-a-posteriori method prevents boundary problems. Moreover, this method with monotonicity constraint estimation improves standard error estimates more than unconstrained maximum likelihood estimates do.