数量化Ⅱ类弓形效应修正方法及应用

Revision Method of the Arch Effect of QuantificationⅡand Its Application

对应分析在对定性数据进行数量化处理过程中出现了"弓形效应",关于对应分析的"弓形效应"的修正方法已经有了丰富的研究成果,避免了可能错误的分析结果,对理论界和应用领域都有重要意义。数量化Ⅱ类是关于定性数据的一种判别分析方法,在国内外已被广泛应用。本文通过大量模拟数据研究发现,数量化Ⅱ类在对定性数据进行数量化过程中出现了"弓形效应",降低了正判别率,同时不能正确再现原始数据信息,得出与原始数据信息不符的错误分析结果,为修正"弓形效应",提出了二阶段判别分析法,并从正判别率和对原始数据再现程度两个方面对数量化Ⅱ类与二阶段判别分析法进行了比较,同时将二阶段判别分析法运用到个人信用评级中,发现二阶段判别分析法的判别性能优于数量化Ⅱ类。

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.QuantificationⅡis 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 quantificationⅡ.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 quantificationⅡand 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 quantificationⅡ.