Studies on Properties of the Data-Fitting Solution in Factor Analysis
| Project/Area Number |
18K11191
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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 60030:Statistical science-related
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| Research Institution | Osaka University |
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Principal Investigator |
Adachi Kohei 大阪大学, 人間科学研究科, 教授 (60299055)
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 統計学 / 多変量解析 / 因子分析 / 行列代数 / データ近似定式化 / 因子と誤差の相関 / 行列分解 / 主成分分析 / 線形代数 / 高階数近似 |
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| Outline of Final Research Achievements |
Factor analysis is a statistical procedure for extracting a few common factors that cause a number of variables. For example, the variables and common factors are the scores for test items and intelligence properties; they are also exemplified by behavioral patters and personality properties. I focused on the matrix-algebraic solution of the factor analysis to elucidate the following properties of the solution. [1] The solution for the multiplication of the common factors and the other (unique) factors multiplicated by coefficients can be uniquely determined. [2] Imposing an additional condition into the solution allows us to obtain the solution, in which the common factors, unique factors, and errors are completely decomposed. [3] The inequalities exist that elucidate the differences between factor analysis and principal component analysis, with the latter similar to the former.
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| Academic Significance and Societal Importance of the Research Achievements |
多変量解析と総称される統計解析法の中でも，因子分析は，創案から100年以上の歴史を持ち，かつ，現在普及する統計ソフトウェアに常備されるポピュラーな手法であるが，その解の性質の細部が明確でなかったが，本研究で明らかになった．
因子分析は，心理学をはじめとした人文・社会科学から，自然科学に渡って広く利用される統計解析法であるため，本研究成果は，因子分析を利用する人文社会・自然科学の研究者，さらには，企業のデータサイエンティストに，因子分析の結果を解釈するための指針を与えることができる．
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Report
(5 results)
Research Products
(41 results)
