Luo Guanzhong, Andrich David
Research Division, Hong Kong Examinations and Assessment Authority, 130 Hennessy Road, Wan Chai, Hong Kong.
J Appl Meas. 2005;6(2):128-46.
A category with a frequency of zero is called a null category. When null categories are present in polytomous responses, then in the Rasch model for such responses, the thresholds that define the categories are inestimable with the commonly used joint maximum likelihood, marginal maximum likelihood, or standard conditional maximum likelihood estimation algorithms. The reason for this situation is that in principle, these estimation algorithms involve frequencies of each category. Andrich and Luo (2003) describe an algorithm in which the thresholds are reparameterized into their principal components and in which the estimate of any threshold is based on a function of the frequencies of all categories of the item rather than the frequency of a particular category. This algorithm works in the presence of null categories. However, in situations where the null categories are at the extremes of a set of categories, the estimates themselves can become too extreme. This paper describes a procedure in which the solution algorithm described by Andrich and Luo is further adapted in the presence of null categories by using their expected frequencies. The procedure is demonstrated with simulated and real data.
频率为零的类别称为空类别。当多分类响应中存在空类别时，在针对此类响应的拉施模型中，使用常用的联合极大似然估计、边际极大似然估计或标准条件极大似然估计算法无法估计定义类别的阈值。出现这种情况的原因是，原则上这些估计算法涉及每个类别的频率。安德里奇和罗（2003年）描述了一种算法，其中阈值被重新参数化为其主成分，并且任何阈值的估计基于项目所有类别的频率函数，而不是特定类别的频率。该算法在有空类别时有效。然而，在空类别处于一组类别的极端位置的情况下，估计值本身可能会变得过于极端。本文描述了一种程序，其中在有空类别存在的情况下，通过使用安德里奇和罗描述的求解算法，并利用其预期频率对其进行进一步调整。该程序通过模拟数据和实际数据进行了演示。
