Tanaka Y
Environ Health Perspect. 1979 Oct;32:113-23. doi: 10.1289/ehp.7932113.
In order to analyze qualitative observations, methods of quantification or optimal scaling have been proposed by Fisher, Guttman, and Hayashi. According to these methods, scores are assigned optimally in some objective and operational sense to the qualitative categories. The present paper mainly reviews Hayashi's four methods of quantification from the mathematical point of view. They are widely used, especially in Japan, in various fields such as social and marketing surveys, psychological research, medical research, etc., where information is obtained mainly in the form of qualitative categories. The first and second methods are applied to the case where an external criterion is present, and are used to predict the external criterion or to analyze the effects of factors. On the other hand, the third and fourth methods are applied to the case where no external criterion is present, and are used to construct a spatial configuration so as to grasp the mutual relationship of the data. After reviewing Hayashi's four methods, we discuss two topics which have been pointed out as the problems to be solved in applying the methods of quantification. One is quantification for ordered categories and the other is statistical consideration. With respect to these topics we review some recently developed methods including the studies due to the present author. Finally we mention briefly several computer programs available in Japan.
为了分析定性观察结果，费希尔、古特曼和林提出了量化方法或最优尺度法。根据这些方法，在某种客观和可操作的意义上，分数被最优地分配给定性类别。本文主要从数学角度回顾林的四种量化方法。它们被广泛应用，尤其是在日本，应用于社会和市场调查、心理学研究、医学研究等各个领域，在这些领域中，信息主要以定性类别的形式获取。第一种和第二种方法应用于存在外部标准的情况，用于预测外部标准或分析因素的影响。另一方面，第三种和第四种方法应用于不存在外部标准的情况，用于构建空间配置以把握数据之间的相互关系。在回顾了林的四种方法之后，我们讨论两个被指出在应用量化方法时需要解决的问题。一个是有序类别的量化，另一个是统计考量。关于这些主题，我们回顾了一些最近发展的方法，包括作者本人的研究。最后，我们简要提及日本现有的几个计算机程序。
