| Project/Area Number |
62530014
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
統計学
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| Research Institution | Otemon Gakuen University |
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Principal Investigator |
MASASHI OKAMOTO Otemon Gakuen Univ., School of Economics, Professor, 経済学部, 教授 (80029389)
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| Co-Investigator(Kenkyū-buntansha) |
YUTAKA KANO Osaka Univ., Fac. of Engin. Sciences, Research Assistant, 基礎工学部, 助手 (20201436)
HIROSHI NAKAMICHI Otemon Gakuen Univ., School of Economics, Professor, 経済学部, 教授 (70079341)
TAKUO OHTA Otemon Gakuen Univ., School of Economics, Assoc. Professor, 経済学部, 助教授 (20079354)
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| Project Period (FY) |
1987 – 1988
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| Project Status |
Completed (Fiscal Year 1988)
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| Budget Amount *help |
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1988: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1987: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | AIC method / Early-step estimator / Gauss-Newton algorithm / Least-squares factor analysis / Monte Carlo experiment / Non-iterative estimator / Number-of-factors problem / ランダム負荷モデル / 1段推定量 / AIC / 部分ガラス・ニュートン法 / 尤度比法 |
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| Research Abstract |
This project is a continuation of the project "A theoretical and experimental study of factor analysis" supported by the Grant-in-Aid for Scientific Research (c), 1983-1984. In between the two projects the author published a book "Inshi-Bunseki no Kiso", JUSE Publ. 1986, and a survey paper "Recent developments in factor analysis" (ed. Suzuki ＆ Takeuchi, Quantitative Analysis in Social Sciences, Univ. Of Tokyo Press, 1987, Chap. 1).
1. Study of early-step estimators The author carried out a Monte Carlo experiment on early-step estimators obtained after a few (j) iterations starting from an initial value in order to reduce the estimation error due to an improper solution. A fixed loading model based on Emmett's data was abopted as a numerical model and the final estimator F was considered as a control. It was found that one-step estimator J(j=1) fared best.
2. Proposal of a random loading model and the number-of-factors problem A new construction method of the random loading model was proposed in order to evade an enevitable bias of the fixed loading model. It is determined by a few parameters and so is more objective than a fixed one. As methods to deal with the number-of-factors problem, Guttman-Kaiser method, likelihood ratio method and AIC method were compared with each other. On the whole, AIC method based on F was optimal. On the other hand, J was found better than F in reducing the estimation error of the unknown parameter.
3. Non-iterative estimator by Kano Kano proposed a method to obtain a non-iterative estimator using a g-inverse matrix. It has a merit of being consistent and seems to be worthy of further investigation.
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