2013 Fiscal Year Final Research Report
New Developments in Factor Analysis Underlain by Fixed Models
| Project/Area Number |
23500347
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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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| Research Field |
Statistical science
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| Research Institution | Osaka University |
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Principal Investigator |
ADACHI Kohei 大阪大学, その他の研究科, 教授 (60299055)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 行動計量分析 / 多変量解析 / 因子分析 / 母数モデル / 同時因子分析 / 高階数近似 |
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| Research Abstract |
I developed a factor analysis (FA) procedure underlain by a new fixed factor model in which common and unique factor scores are treated as fixed parameters. This procedure can be called joint FA (JFA), as all parameters are estimated jointly. I presented an algorithm for minimizing the least squares function of JFA. A feature of the algorithm is that the optimal loadings and unique variances can be estimated only if inter-variable covariances are available. Simulation studies showed that the true loadings and unique variances are recovered well, and the usefulness of JFA was illustrated in real data examples. A property of JFA interesting theoretically is that JFA can be regarded as higher rank approximation of a data matrix. I further used the property to give the explanation of the common and unique factor indeterminacy which is a generalized version of Mulaik's (1976) cone.
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