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Study of Model Selection in Regression Analysis for Repeated Measurements

重复测量回归分析模型选择研究

基本信息

批准号：
09680312
负责人：
OHTAKI Megu
金额：
$ 2.11万
依托单位：
HIROSHIMA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09680312/
关键词：
Repeated measurements Growth curve models Model selection Hierarchical structure Random coefficient model Monotone missing data Sex ratio Interval estimation of RBE 成長曲線モデル変動効果モデル経時測定データモデル選択基準欠測値処理多次元データ構造

项目摘要

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 … More 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

1）研究了具有多个层次个体内设计矩阵的扩展增长曲线模型下的一些推理问题。该模型包括平均结构由不同程度的多项式增长曲线组成的模型。首先我们考虑协方差矩阵未知正定的情况。我们推导了 LR 检验，用于检查个体内设计矩阵的层次结构和模型选择标准。接下来，我们考虑在个体间设计矩阵的某些假设下假设随机系数协方差结构的情况。还考虑了类似的推理问题。基于扩展的生长曲线模型重新检查了牙科测量数据（参见例如 Potthoff 和 Roy (1964, Biometrika 51, 313-326)）。（Fujikoshi、Kanda 和 Ohtaki，正在出版）2）基于 k 步单调样本，研究了 p 变量正态总体 Np (mu, SIGMA) 的 MLE mu 和 SIGMA 的一些基本属性。对于k=2和3，我们得到了mu的精确均值和方差以及SIGMA的精确偏差。在样本量较大的情况下，也得到了这些估计量分布的渐近展开。对于一般的 k，mu 的 MLE 和 SIGMA 的常用变换矩阵 DELTA 以显式形式给出。还获得了一些类似的性质。 (Kanda and Fujikoshi, 1998)3) 统计考虑了1975-1994年0-4岁日本人口中女性比例是否存在增加的时间趋势的问题。根据全国人口普查数据，使用β二项式模型检验了使用二项式模型分析女性人口数量的有效性。通过检验女性比例相对于有序替代方案均相等的原假设，研究了女性比例增加的时间趋势。（Nakayama、Satoh 和 Ohtaki，提交）4) 开发了一种基于生长曲线分析、通过重复测量对相对生物有效性 (RBE) 进行区间估计的方法。 RBE 的时间相关估计可以通过我们的方法获得。利用一组小鼠实验数据，我们估算了中子或伽马射线照射后中子射线对体重的 RBE。（Satoh、Ohtaki 等人，1998）