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

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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.