判别分析、Logistic回归和BP神经网络在二分类问题中的模拟对比

Simulated Comparison of Discriminatory Analysis,Logistic Regression and BP Neural Network in Binary Classification

采用随机模拟的方法,模拟出不同的样本量,不同的随机扰动方差,不同的解释变量个数的样本数据,采用判别分析、Logistic回归和BP神经网络三种方法进行判别,计算200次模拟的平均回判率。模拟发现:三种方法的效果都与解释变量呈正相关关系;随机扰动方差对判别分析、Logistic回归有一定影响,误差水平低时,Logistic回归优于判别分析,反之,Logistic回归劣于判别分析,但对BP神经网络无影响;随着样本量增大,Logistic回归与判别分析变化较小,且最终效果趋于一致,但BP神经网络的效果显著提高,超越Logistic回归与判别分析。

By using the stochastic simulation method and simulating the data with different sample sizes,random disturbance variances and different numbers of explanatory variables,this paper distinguishes the data with discriminatory analysis,logistic regression and BP neural network respectively.After 200 simulations,it calculates the average back-contracting rate.According to the average back-contracting rate,and the comparison of the results of these effects on the discrimination,it shows: the effects of the three methods are positively correlated with the number of explanatory variables that the more the explanatory variables are,the higher the rateis; random disturbance variances have an effect on discriminatory analysis and logistic regression; logistic regression is superior to discriminatory analysis when the error level is low; vice versa,logistic regression is inferior to the discriminatory analysis.Random disturbance variances have no effect on BP neural network.With the increased sample size,logistic regression and discriminatory analysis are of small changes,and the final results consistent,but in a large number of samples,the effect of the BP neural network is significant.