2002 Fiscal Year Final Research Report Summary
Psychometric Studies on Quantification and Simple Structure Analysis of Multivariate Categorical Data
| Project/Area Number |
13610176
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
教育・社会系心理学
|
|---|
| Research Institution | Koshien University |
|---|
Principal Investigator |
ADACHI Kohei Koshien University, Department of Psychology, Associate Professor, 人間文化学部, 助教授 (60299055)
|
|---|
| Project Period (FY) |
2001 – 2002
|
| Keywords | multivariate analysis / optimal quantification / correspondence analysis / orthogonal rotation / oblique rotation / categorical data / goodness-of fit / correct classification rates |
|---|
| Research Abstract |
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.
|
