| Project/Area Number |
12640106
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | TOKYO GAKUGEI UNIVERSITY |
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Principal Investigator |
YOKOYAMA Takahisa Tokyo Gakugei University, Faculty of Education, Associate Prof., 教育学部, 助教授 (20240864)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIKOSHI Yosunori Hiroshima University, Faculty of Science, Prof., 理学研究科, 教授 (40033849)
NAKAMURA Tadashi Okayama University of Science, Faculty of Informatics, Prof., 総合情報学部, 教授 (20069074)
TAKADA Yoshikazu Kumamoto University, Faculty of Engineering, Prof., 工学部, 教授 (70114098)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2001: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2000: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Repeated Measures / Random Effects / Covariance Structure / Growth Curve Model |
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| Research Abstract |
First weconsider a multivariatc growth curve model with covaria'tcs and random effects. The model is a mixed MANOVA-GMANOVA model which has multivariatc random-effects covariance structures. Test statistics for a general hypothesis concerning the adequacy of a family of the covariance structures arc proposed. A modified LR statistic for the hypothesis and its asymptotic expansion arc obtained. The MLE's of unknown mean parameters arc obtained under the covariance structures. The efficiency of the MLE is discussed (Kumamoto J. Math. 13 (2000), Hiroshima Math. J. 30 (2000)). Next we consider profileanalysis in two extended growth curve models. The first is a growth curve model with parallel mean profiles, which has a random effects covariance structure based on a single response variable ; the second is a multivariatc growth curve model with parallel mean profiles, which has a multivariate random effects covariance structure based on several response variables. For testing "no condition variation" and "level" hypotheses concerning parallel mean profiles of several groups, we obtain the Wald's criteria and their asymptotic non-null distributions. We also consideran extended grswth curve model with two hierarchical within-individuals design matrices, which is useful in analyzing mean profiles of several groups with parallel polynomial growth curves. The covariance structure based on a random effects model is assumed. The MLE's arc obtained under the random effects covariance structure. The efficiency of the MLE is discussed. A numerical example is also given (Amer. J. Math. ManagementSci. 20 (2000), Hiroshima Math. J. 31 (2001)).
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