关键词: 数量化Ⅱ类, 弓形效应, 二阶段判别分析法

Abstract: Correspondence analysis method shows an “arch effect” in the process of quantifying qualitative data. There are abundant research results on the revision method of the “arch effect". The revision helps avoid the possible erroneous analysis results, which is of great significance to both theoretical study and application. Quantification Ⅱ is a discriminant analysis method for qualitative data, which has been widely used at home and abroad. In this paper, through a large number of simulation data, we find that the “arch effect” appears in the quantitative process of qualitative data in quantification Ⅱ. The “arch effect” lowers the positive discrimination rate, and cannot faithfully reproduce the original data information, resulting in the erroneous analysis that does not match the original data information. In this paper, a two-stage discriminant analysis method is proposed to revise the “arch effect”. The quantification Ⅱ and two-stage discriminant analysis are compared in terms of the correct discrimination rate and the reproducibility of the original data. At the same time, when applied to the personal credit rating, the two-stage discriminant analysis method outperforms quantification Ⅱ.

Key words: Quantification Ⅱ, Arch Effect, Two Stage Discriminant Analysis Method