Development of Computer Software for Analyzing Growth Curve Date.

Fujikoshi和Satoh在平衡设计下导出了扩展生长曲线模型未知参数的极大似然估计，并研究了其若干统计性质。他们用修正后的AIC和C发展了新的模型选择方法，并证明了这些方法具有良好的小样本性质（Fujikoshi和Satoh，广岛数学J.26，1996，Biometrika in press，J.Multivariate Analysis，in press）.Kanda和Seo研究了多重比较，通过推广多元方差分析模型，和均匀协方差结构。他们用改进的二次近似法给出了同时置信区间。在协方差结构模型下，导出了两变量Hotelling T^2型变量联合概率的渐近展开式（J.Japan Statistical Society 26，1996），Ohtaki与Satoh和Katou合作，开发了一套适用于非平衡设计生长曲线数据的计算机程序Growth2（Ver.3.2）。所用算法是基于Vonesh&Carter（1984）理论的扩展结果，在估计过程中不需要任何迭代，并适用于均值参数存在线性约束的情况。在程序设计中，采用Fortran 77和Pascal进行数值处理，并采用德尔菲（Ver.2.0J）建立图形用户界面，提高了程序的可操作性（放射生物医学研究所学报37期，1996）。

Fujikoshi and Satoh derived the maximum likelihood estimates of unknown parameters under the extended growth curve model with a balanced design, and studied the several statistical properties. They developed new methods for model selection with corrected versions of AIC and C,and proved that those methods have good small sample properties (Fujikoshi and Satoh, Hiroshima Mathematical J.26,1996, Biometrika in press, J.Multivariate Analysis, in press).Kanda and Seo studied a multiple comparison by original of generalizing the Multivariate Analysis of Variance model with, a positive definite, serial, and uniform covariance structures. They gave the simultaneous confidence intervals using modified second approximation procedure. They also derived the asymptotic expansions for the joint probability of bivariate Hotelling T^2-type variates under the model with the covariance structures (J.Japan Statistical Society 26,1996).Cooperating with Satoh and Katou, Ohtaki developed a package of computer programs referred to as Growth2 (Ver.3.2) which is applicable to the growth curve data with the unbalanced design. The algorithm used is based on the result of expanded version of the theory due to Vonesh&Carter (1984) which needs not any iteration in the estimating procedure, and is applicable to the cases where linear restriction exists in the mean parameters. In the programming, Fortran77 and Pascal were used for a numeric processing, and Delphi (Ver.2.0J) was also used for constructing the graphic user interface, which improves the operativeness of the program (Proc.of the Research Institute for Radiation Biology and Medicine 37,1996).