Study of Model Selection in Regression Analysis for Repeated Measurements

1)研究了具有多个层次个体内设计矩阵的扩展生长曲线模型下的若干推理问题。该模型包括均值结构由不同次数的多项式增长曲线组成的模型。首先我们考虑协方差阵未知正定的情况。我们推导出一个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，我们考虑的情况下，假设一个随机系数协方差结构，在一定的假设下，个体间的设计矩阵。类似的推理问题也被考虑。牙科测量数据（参见，例如，Potthoff和Roy（1964，Biometrika 51，313-326））基于扩展的生长曲线模型进行了重新检查。（Fujikoshi，Kanda and Ohtaki，in press）2）研究了p-变量正态总体Np（mu，SIGMA）基于k步单调样本的MLE的mu和SIGMA的一些基本性质。 ...更多信息 对于k=2和3，我们得到了μ的精确均值和方差以及SIGMA的精确偏差，并在大样本情况下得到了这些估计量分布的渐近展开式。对于一般k，给出了μ的极大似然估计和SIGMA变换矩阵DELTA的显式表达式。还得到了一些类似的性质。（Kanda and Fujikoshi，1998）3）对1975-1994年日本0-4岁人口中女性比例是否有增加的时间趋势进行了统计学研究。基于全国人口普查数据，采用β-二项模型检验了二项模型用于分析女性人口数量的有效性。通过对有序方案的女性比例相等的零假设检验，研究了女性比例的时间增长趋势。（Nakayama，Satoh and Ohtaki，submitted）4）建立了基于生长曲线分析的重复测量相对生物学效应（Relative Biological Effectiveness，RBE）区间估计方法。利用我们的方法可以得到RBE的时变估计。利用一组小鼠实验数据，估算了中子或γ射线照射后，中子射线对体重的相对生物效应。（Satoh，Ohtaki等人，减

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