A method of scaling qualitative data is proposed, which is useful for discriminant analysis with more than two populations. In this method, values are assigned to categories within each variable so as to maximize the Rao's V statistic. Since the method proposed here makes much use of the information about a variable as a set of categories, the usual procedure of variable selection can be easily applicable to discrete variables by employing the maximized V statistic as a measure of discrimination. As an example, the method is applied to medical data of patients suffering from four kinds of diseases. The analysis shows that the use of the V statistic is efficient as a criterion for the selection of discrete predictor variables, although this procedure of selection is somewhat heuristic and done in a backward elimination manner. Furthermore, a comparison of the proposed method with the Hayashi's quantification theory of the second type is discussed.
The present paper uses the voting power analysis, and proposes two criteria for evaluating the effectiveness of coalition formation in a weighted voting body. They are called the“ criterion of effectiveness of coalition body(El)” and the“ criterion of effectiveness of coalitional members(E2)”. Introducing the Banzhaf measure as an index of voting power we have three theoretical results: (1)The criteria are independent each other, i. e., one does not include the other and vice versa. (2)The expected frequency that a coalition satisfies El is inversely proportional to the number of members in it, but the expected frequency that it satisfies E2 is directly proportional to that. (3)Defining the well-known concepts of veto holder and dummy on the index we prove the necessary condition that a coalition satisfies the two criteria, that is all members in a coalition are not veto holders and at least two members are not dummies. Finally, by using the proposed two criteria we evaluate the effectiveness of all possible coalitions in the House of Representatives of Japan.
A systematic approach for the analysis of ship accidents is presented. A simple stochasticmodel as to the process of accident occurrence is provided, in which vulnerable behavior is involved as the state prior to the accident. Vulnerable behavior is human error in the ship navigation that has the possibility of resulting in an accident. Therefore, reducing the behavior has the effect on preventing accidents, and it requires understandings of the latent factors causing the behavior. Based on the concepts, an accident analysis and a vulnerable behavior analysis are made using the data of actual accident cases and those obtained through the questionnaire to ship captains. The results of these analyses demonstrate the vulnerable behaviors that have to be reduced corresponding to each accident category and reveal five factors that are concerned in the occurrence of such behaviors. It is concluded that improving the situations indicated by the factors is useful for preventing ship accidents.
In the earlier paper, we surveyed the strategies for modeling the two-way contingency tables having ordered categories. Especially, Goodman's association models(1979)were discussed by reanalyzing the well-known sets of data. This manuscript presents the comparisons of the results by use of association models with those obtained using the canonical correlation analysis to locate the association models in the analysis of ordered categorical data. The examination of the agreement of the association models and Plackett's model(1965)with the bivariate normal may clarify the utility of association models. Then, the inference in contingency tables with ordered categories is mentioned based on Plackett's coefihcient of association. Furthermore, the association models may be generalized tomultiway contingency tables. Some examples are illustrated in the context of potential application of the association models to analyze the various types of ordered categorical data.