2023 Fiscal Year Final Research Report
Development of Orthonormal principal component analysis for categorical data and its applications
| Project/Area Number |
20K03303
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 10010:Social psychology-related
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| Research Institution | Chukyo University |
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Principal Investigator |
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | 多重対応分析 / 主成分分析 / 因子の回転 / 心理測定 / 社会調査 / カテゴリカルデータ |
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| Outline of Final Research Achievements |
The main objective of this study was to improve Multiple Correspondence Analysis (MCA). Because interpretations of MCA results have mainly been based on graphical representations, reading the solution with more than three dimensions took a lot of work. We introduced the loading matrix and its independent cluster rotation to shift the main clue of interpretations from the diagrams to axes. Orthonormal polynomials and the design matrices transformed to orthonormality, used to give numerical values to response categories, were consistent with the traditional quantification in MCA. Several application studies using real psychometric and social survey data demonstrated the efficiency of our Orthonormal Principal Component Analysis (OPCA) for categorical data by giving some new findings and confirming a few theoretical hypotheses.
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| Free Research Field |
社会科学
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| Academic Significance and Societal Importance of the Research Achievements |
質的、あるいは順序的応答カテゴリーを用いる心理測定、社会調査は広く実施され、膨大なデータが得らつつある。そうしたデータの分析には、因子分析や各種の数量化の方法（多重対応分析はそのひとつ）が用いられてきた。心理測定データについては、項目反応理論や構造方程式モデルといった潜在変量を用いられた分析が近年台頭しているが、モデルの前提条件や複雑性が、心理測定モデルに不適合であることが多く、社会調査に関しては、本来心理測定以上に多次元性が想定されるデータの分析が、無理に少数の次元に落とし込まれる傾向があった。本研究は、それらの問題点を解決する一助となることが期待できる。
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