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

迄今发展起来的m-群回归分析技术存在两个主要问题。第一个问题是，模型总是假设模型中包含的所有回归系数都是可交换的。在这项研究中，我们开发了一种通用的方法，可以处理1)跨组通用回归系数，2)跨组可交换回归系数，以及3)不可交换回归系数的混合。开发了基于该模型的计算机程序。第二个问题是通常的组内回归分析仅限于线性模型。在这项研究中，我们研究了将原来的想法扩展到包括样条模型和神经网络模型在内的非线性模型的可能性。作为第一步，开发了一种高效的神经网络回归算法。对于效用函数的度量，在假设无差异概率服从贝塔分布的基础上，利用极大似然估计技术，编制了相应的计算机程序。

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.