多个预测因子组的PLS回归的多协方差方法：结构方程探索性回归
A multiple covariance approach to PLS regression with several predictor groups: Structural Equation Exploratory Regression
摘要：
假设变量组Y依赖于R个主题变量组X1，>...，X R .我们假设Y中的分量线性依赖于Xr中的分量。在这项工作中，我们提出了一个多协方差标准，扩展了PLS回归到这个多个预测组的情况。在此基础上，我们建立了一个PLS型的探索性方法-结构方程探索性回归（SEER）-允许同时进行组中的降维和调查的线性模型的组件。SEER使用每个组的多维结构。最后给出了应用实例。
英文摘要：
A variable group Y is assumed to depend upon R thematic variable groups X 1, >..., X R . We assume that components in Y depend linearly upon components in the Xr's. In this work, we propose a multiple covariance criterion which extends that of PLS regression to this multiple predictor groups situation. On this criterion, we build a PLS-type exploratory method - Structural Equation Exploratory Regression (SEER) - that allows to simultaneously perform dimension reduction in groups and investigate the linear model of the components. SEER uses the multidimensional structure of each group. An application example is given.
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