Studies on Properties of the Data-Fitting Solution in Factor Analysis

2021 Fiscal Year Final Research Report

• Project/Area Number: 18K11191
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60030:Statistical science-related
• Research Institution: Osaka University
• Principal Investigator: Adachi Kohei 大阪大学, 人間科学研究科, 教授 (60299055)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Keywords: 統計学 / 多変量解析 / 因子分析 / 行列代数

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.

Free Research Field

統計科学

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．