Study of Model Selection in Regression Analysis for Repeated Measurements

1)研究了具有多个层次的个体内设计矩阵的扩展生长曲线模型下的一些推理问题。模型包括均值结构由不同程度的多项式生长曲线组成的模型。首先考虑了协方差矩阵为未知正定的情况。我们推导了一个LR测试，用于检查个体内设计矩阵的层次结构和模型选择标准。其次，在个体间设计矩阵的一定假设下，考虑随机系数协方差结构的情况。还考虑了类似的推理问题。根据扩展生长曲线模型重新检查牙齿测量数据（例如，见Potthoff和Roy (1964, Biometrika 51,313 -326)）。（Fujikoshi, Kanda and Ohtaki, in press）2)研究了基于k步单调样本的p变量正态总体Np （mu， SIGMA）的MLE的mu和SIGMA的一些基本性质。更多内容。对于k=2和3，我们得到了mu的确切均值和方差以及SIGMA的确切偏差。在样本量较大的情况下，得到了这些估计量分布的渐近展开式。对于一般的k，以显式形式给出了mu的MLE和SIGMA的变换矩阵DELTA。还得到了一些类似的性质。（Kanda and Fujikoshi, 1998）3)统计学上考虑了1975-1994年日本0-4岁人口中女性比例是否有上升的时间趋势。以全国人口普查数据为基础，采用β -二项模型检验二项模型分析女性种群数量的有效性。通过检验有序方案下女性比例均相等的零假设，研究了女性比例增加的时间趋势。（Nakayama, Satoh and Ohtaki，提交）4)提出了一种基于生长曲线分析的重复测量相对生物有效性（RBE）区间估计方法。我们的方法可以得到随时间变化的RBE估计。利用一组小鼠实验数据，估计了中子或伽马射线辐照后中子射线对体重的RBE。(Satoh, Ohtaki et al., 1998

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