偏最小二乘回归及其应用

目的：研究用于多重共线性严重，尤其解释变量个数多、样本量少数据资料的一种新的稳健统计分析方法：偏最小二乘(partial least square,PLS)．方法：采用实证方式比较PLS与一般最小二乘(ordinary least square,OLS)逐步回归的优劣．结果：实例分析表明，PLS对数据的拟合度和预测精度均优于另一个常用于处理多重共线性的统计方法：OLS逐步回归．结论：PLS是一种数据“软”建模的稳健统计方法．它无需剔除任何解释变量或样本点，具有简单稳健、易于定性解释、预测精度较高等优点，通常用于数据探索性分析，或处理多重共线性严重资料，尤其当解释变量个数宏、样本量小时很有效；其缺点主要是无法对解释变量与反应变量之间的关系作出精确的定量解释．

Partial least square and its application

AIM: To study partial least square (PLS), a new robust statistical analysis dealing with serious multicollinearity and a small sample with numerous predictor variables. METHODS: The discretion between PLS and OLS (ordinary least square) stepwise regression was shown by a case. RESULTS: It was illustrated by this case that in goodness of fit and prediction, PLS was better than OLS stepwise regression, another statistical technique dealing with multicollinearity. CONCLUSION: As a soft statistical modeling method, PLS is rather robust. It needs not exclude any predictor variable or observation at all. PLS has many advantages such as simplicity and robustness, highly predicted precision, clearly qualitative explanation. Usually it is used to explore data and cope with multicollinearity. It is particularly powerful when the number of predictor variables is large and the sample size is small. However, the principal disadvantage of PLS is that it cannot provide quantitative explanation for the relationship between predictor variables and response variables.