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Psychometric Studies on Quantification and Simple Structure Analysis of Multivariate Categorical Data

多元分类数据量化和简单结构分析的心理测量研究

基本信息

批准号：
13610176
负责人：
ADACHI Kohei
金额：
$ 1.22万
依托单位：
Koshien University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

项目摘要

The purpose of this project was to study the rotation of the solution in multiple correspondence analysis (MCA). We first proposed an orthogonal rotation method for giving simple structure to a variables by dimensions matrix of indices to be interpreted. Here, the Orthomax criterion is used for defining simplicity. The method is classified into a category option and an item option, according whether the entities regarded as variables are categories or items. In the former option, category scores are used as indices, while discrimination measures are used in the latter option.The solution can be rotated obliquely, if MCA is formulated as a method for the low-rank approximation of indicator matrices. Thus, we next proposed an oblique rotation method using the Promax criterion. This method is also classified into the two options. In the category option, the cosines between category data vectors and object score vectors are used as the indices to be interpreted, whereas the cosines between the sub-spaces for items and object score vectors are used in the item option. We found the usefulness of the above orthogonal and oblique rotation methods in their applications to real data.Additionally, we studied goodness-of-fit (GOF) measures of the MCA solution and proposed to use a correct classification rate (CCR) as the measure. CCR is defined as the proportion of the cases where objects are classified into correct categories according to the solution. Simulation analysis showed the superiority of CCR to other eigenvalue-based GOF measures.

本计画的目的是研究多重对应分析（MCA）中解的旋转。本文首先提出了一种正交旋转方法，它可以使待解释的变量的维数矩阵具有简单的结构。这里，正交最大准则用于定义简单性。根据被视为变量的实体是类别还是项目，将该方法分为类别选项和项目选项。在前一种选择中，类别分数被用作指标，而在后一种选择中，歧视措施被使用。如果MCA被制定为一种方法，用于低秩近似的指标矩阵，解决方案可以被旋转倾斜。因此，我们接下来提出了一种使用Promax准则的倾斜旋转方法。这种方法也分为两种选择。在类别选项中，类别数据向量和对象得分向量之间的余弦被用作要解释的索引，而项目的子空间和对象得分向量之间的余弦被用在项目选项中。我们发现上述正交和斜旋转方法在应用于真实的数据时是有用的。此外，我们研究了MCA解的拟合优度（GOF）度量，并提出使用正确分类率（CCR）作为度量。CCR被定义为根据解将对象分类为正确类别的情况的比例。仿真分析表明，CCR优于其他基于特征值的GOF措施。