名義尺度型データ処理の一方法 : 多次元属牲空間縮小の計量的手法
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概要
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1. 多次元属性空間の縮小2. 外的基準のある場合 : その1 : PSA3. 外的基準のある場合 : その2 : AID4. 外的基準のある場合 : その3 : AIDの修正5. 外的基準のない場合 : 関連分析6. 結論In the area of sociological measurement, it is one of the most fundamental problems how data consisting of a large number of nominal scales can be analyzed and reduced. For data collected in social research are usually obtained by forcing respondents to select one out of categories listed on questionaire. It seems to the present writer that there are two kinds of approach to this problem. They are the followings : 1) This type of data can be summarized by introducing the composite variable α, [numerical formula] w_jk=the value given to the k-th category of the j-th variable. When a criterion function of w_jk, which is to be maximized or minimized in terms of the purpose of analysis, is considered, the value of w_jk is calculated so that the given criterion function is optimized. This type of method, "the Hayashi quantification theory," is well known among behavioral scientists in Japan, which is named after the founder of this methodology. 2) This type of data can also be summarized by means of the new nominal scale, which is constructed i) by selecting a number of variables out of all given nominal scales, ii) by grouping some of categories which belong to the same variable selected, and iii) by combining categories which belong to the different variables. This is equivalent to grouping ultimate classes included in a multiple contingency table which shows interrelationships among nominal scales. This procedure is named "reduction of multidimensional attribute space," which was formulated by P.P. Lazarsfeld and H. Barton in 1951. Though they practiced this operation in an intuitive manner, some statistical methods which reduce a multidimensional attribute space have been developed in the last ten years. They are PSA (Polarized Subgroup Analysis), AID (Automatic Interaction Detector), association analysis and so on. These methods may be appropriately included under the label of "Optimal Tree-Structure Analysis." Since, the results analyzed by one of these techniques, are normally presented in dendrogram style.
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