数据存在共线性时采用主成分回归分析与投影寻踪回归分析的效果比较

摘要

目的 比较主成分回归分析与投影寻踪回归分析在数据存在共线性时效果之差别.方法 利用实际数据从拟合效果和预测效果两方面评价两种建模方法的优劣.结果 主成分回归模型的决定系数为0.8172,相对误差绝对值的平均值为6.42％,预测误差的均方为0.61;投影寻踪回归分析各模型的决定系数为0.8851～0.9944,相对误差绝对值的平均值为1.11％ ～4.81％,预测误差的均方为0.03 ～ 0.38.结论 本实例数据(存在一定共线性)分析结果表明,投影寻踪回归分析的拟合效果与预测效果均优于主成分回归分析.%Objective To compare the difference of effect between principal component regression analysis and projection pursuit regression analysis when collinearity exists in data.Methods Evaluating the advantages and disadvantages of the two modeling methods by using the actual data on two aspects:the fitting effect and the predicting effect.Results The principal component regression model showed that the coefficient of determination was 0.8172,the mean of absolute relative error was 6.42％ and the mean square of prediction error was 0.61.The projection pursuit regression model,on the other hand,showed that the coefficient of determination ranged from 0.8851 to 0.9944,the mean of absolute relative error ranged from1.11％ to 4.81％ and the mean square of prediction error ranged from 0.03 to 0.38.Conclusion The analysis results based on the actual data with collinearity indicate that the projection pursuit regression analysis outperforms the principal component regression analysis both in fitting and predicting effect.