Develpooing data analytic techniques for the entrance examinations utilizing m-group regression analysis and decision theoretic apporach.

迄今为止发展起来的M-群回归分析技术有两个主要问题。第一个问题是模型总是假设模型中所有回归系数的互换性。在这项研究中，我们开发了一种通用的方法，可以处理1）跨组的共同回归系数，2）跨组的可交换回归系数，3）不可交换回归系数的混合。第二个问题是通常的组内回归分析局限于线性模型。在本研究中，我们探讨了将原始想法扩展到非线性模型包括样条模型和神经网络模型的可能性。作为第一步，提出了一种有效的神经网络回归算法。在效用函数的计算方面，本文在假设无差异概率服从贝塔分布的基础上，采用极大似然估计技术，编制了一个计算机程序。

M-group regression analysis technique so far developed has two major problems. The first one is that the model always assumes the exchangeability of all the regression coefficients included in the model. In this research, we developped a general method which can handle a mixture of 1) common regression coefficients across groups, 2) exchangeable regression coefficients across groups, and 3) non-exchangeable regression coefficients. A computer program based on this model was developped.The second problem is that the usual in-group regression analysis is restricted to the linear model. In this research, we investigated the possibility of extending the original idea to non-linear models including spline model and neural network model. As the first step, an efficient algorithm for neural netrowk regression was developped. We found that developping the m-group version of the newral network regression models seems promissing.As for measuring utility functions, a computer program was developped which uses the maximum likelihood estimation technique based on the assumption that the indifference probabilities have beta distribution.