1998 Fiscal Year Final Research Report Summary
Study of Model Selection in Regression Analysis for Repeated Measurements
| Project/Area Number |
09680312
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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 |
Statistical science
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| Research Institution | HIROSHIMA UNIVERSITY |
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Principal Investigator |
OHTAKI Megu Hiroshima University, Research Institute for Radiation Biology and Medicine, professor, 原爆放射能医学研究所, 教授 (20110463)
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| Co-Investigator(Kenkyū-buntansha) |
OOTANI Keiko Hiroshima University, , Department of Dentistry, Research Associate, 歯学部, 助手 (20243587)
SATOH Ken-ichi Hiroshima University, Research Institute for Radiation Biology and Medicine, Res, 原爆放射能医学研究所, 助手 (30284219)
KANDA Takashi Hiroshima Institute of Technology, Department of Environmetrics, Professor, 環境学部, 教授 (40098679)
FUJIKOSHI Yasunori Hiroshima University, Faculty of Science, Professor, 理学部, 教授 (40033849)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Repeated measurements / Growth curve models / Model selection / Hierarchical structure / Random coefficient model / Monotone missing data / Sex ratio / Interval estimation of RBE |
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| Research Abstract |
1) Some inferential problems under an extended growth curve model with several hierarchical within-individuals design matrices were studied. The model includes the one whose mean structure consists of polynomial growth curves with different degrees. First we considered the case when the covariance matrix is unknown positive definite. We derive a LR test for examining the hierarchical structure for within-individuals design matrices and a model selection criterion. Next we considered the case when a random coefficients covariance structure is assumed, under certain assumption of between-individual design matrices. Similar inferential problems were also considered. The dental measurement data (see, e.g., Potthoff and Roy (1964, Biometrika 51, 313-326)) was reexamined, based on extended growth curve models. (Fujikoshi, Kanda and Ohtaki, in press)
2) Some basic properties of the MLE's mu and SIGMA for a p-variate normal population Np (mu, SIGMA), based on a k-step monotone sample were studi
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ed. For k=2 and 3, we obtained the exact means and variances of mu and the exact bias of SIGMA.Asymptotic expansions of the distributions of these estimators were also obtained in the situation when the sample size is large. For a general k, the MLE's of mu and the usual transformed matrix DELTA of SIGMA were given in explicit forms. Some analogous properties were also obtained. (Kanda and Fujikoshi, 1998)
3) The problem whether there is an increasing time-trend of female proportion or not among 0-4 years old Japanese population in 1975-1994 was statistically considered. Based on national census data, the validity of the use of binomial model for analyzing female population number was examined using a beta-binomial model. The increasing time-trend of female proportion was investigated by the means of testing the null hypothesis that female proportions are all equal against ordered alternatives. (Nakayama, Satoh and Ohtaki, submitted)
4) A method for making interval estimation of Relative Biological Effectiveness (RBE) with repeated measurements, based on growth curve analysis, was developed. Time-dependent estimate of RBE can be obtained from our method. Using a set of data of mice experiments, we estimated the RBE of neutron ray on body weights after irradiation of neutron or gamma ray. (Satoh, Ohtaki et al., 1998) Less
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Research Products
(6 results)
