Garner Mary, Engelhard George
Department of Mathematics and Statistics, Kennesaw State University, Kennesaw, GA 30144-5591, USA.
J Appl Meas. 2009;10(1):30-41.
The purpose of this paper is to describe a technique for estimating the parameters of a Rasch model that accommodates ordered categories and rater severity. The technique builds on the conditional pairwise algorithm described by Choppin (1968, 1985) and represents an extension of a conditional algorithm described by Garner and Engelhard (2000, 2002) in which parameters appear as the eigenvector of a matrix derived from paired comparisons. The algorithm is used successfully to recover parameters from a simulated data set. No one has previously described such an extension of the pairwise algorithm to a Rasch model that includes both ordered categories and rater effects. The paired comparisons technique has importance for several reasons: it relies on the separability of parameters that is true only for the Rasch measurement model; it works in the presence of missing data; it makes transparent the connectivity needed for parameter estimation; and it is very simple. The technique also shares the mathematical framework of a very popular technique in the social sciences called the Analytic Hierarchy Process (Saaty, 1996).
本文旨在描述一种用于估计Rasch模型参数的技术，该模型适用于有序类别和评分者的严重程度。该技术基于Choppin（1968年、1985年）描述的条件成对算法，并代表了Garner和Engelhard（2000年、2002年）描述的条件算法的扩展，其中参数作为从成对比较中得出的矩阵的特征向量出现。该算法已成功用于从模拟数据集中恢复参数。此前没有人描述过将成对算法扩展到包含有序类别和评分者效应的Rasch模型。成对比较技术之所以重要，有几个原因：它依赖于仅对Rasch测量模型成立的参数可分离性；它在存在缺失数据的情况下也能起作用；它使参数估计所需的连通性变得透明；而且它非常简单。该技术还与社会科学中一种非常流行的技术——层次分析法（Saaty，1996年）共享数学框架。
