中小企业破产模型的判别分析与Logistic回归分析

The Discriminant Analysis and Logistic Regression Analysis of SMEs Bankruptcy Model

摘要: 多元统计分析中，判别分析和Logistic回归分析都是用来预测和解释一个对象所属类别的分类方法。回归模型用于预测和解释度量变量，而判别分析和Logistic回归分析用来解决被解释变量是非度量变量的情况。被解释变量包含两类时，判别分析和Logistic回归分析都适用；而被解释变量包含两类以上时，只有判别分析适用。但是，只有解释变量满足多元正态性和相等协方差阵假设时，判别分析才适用。而Logistic回归不需要解释变量的一系列的假设，仍可以得到良好的结果。本文分别用判别分析和Logistic回归分析对中小企业的破产模型进行分析，并对比两种分类方法的异同。

Abstract: In multivariate statistical analysis, discriminant analysis and Logistic regression analysis are both used to predict and interpret the classification. Regression models are used to predict and interpret metric variables, while discriminant analysis and Logistic regression analysis are used to solve situations where explanatory variables are non-metric variables. When the explanatory variable contains two types, both discriminant analysis and Logistic regression analysis are applicable; when the explanatory variable contains more than two types, only discriminant analysis is applicable. However, discriminant analysis is only applicable when the explanatory variables satisfy the multivariate normality and the equivalent covariance matrix hypothesis. Logistic regression does not require a series of assumptions about explanatory variables, and good results can still be obtained. In this paper, the bankruptcy model of SMEs (Small and Medium Enterprises) was analyzed by discriminant analysis and Logistic regression analysis respectively, and the differences and similarities between the two classification methods were compared.