基于递阶偏最小二乘回归的数据分析

Data Analysis Based on Hierarchical Partial Least-squares Regression

针对最小二乘法难以克服因子多重共线性对回归模型精度影响的不足和大坝观测数据分析中因变量较多的特征,引进递阶偏最小二乘法,对大坝安全监测变量及其影响因子进行递阶偏最小二乘回归分析,将建模预测分析方法通过递阶分层处理,可同时实现回归建模和数据结构简化,所建立的大坝安全监控模型精度可通过交叉有效性检验来控制.工程应用实例和模型对比分析研究表明,递阶偏最小二乘回归模型能有效克服由于各类因子变量间的多重共线性和因子变量数目较多而对模型拟合精度及其预测能力的影响,相对于传统回归模型有更好的解释能力,因而具有一定的实用价值.

The hierarchical partial least-squares regression （Hi-PLSR） method is introduced to analyze the variables of dam safety monitoring model and the factors affecting them, such as the large number of variables and multiple-collinearity among them. This method combines the establishment of model and simplification of data structure by means of hierarchical regression. The accuracy of the dam safety monitoring model is controlled by the cross validation test. The result of practical project with model forecasting shows that the proposed method can effectively overcome the effects of multiple-collinearity among variables and the large number of variables on fitting accuracy and forecasting capability of the safety monitoring model with a better explanatory ability; thus it has a certain practicability.