多元成分数据的对数衬度偏最小二乘通径分析模型

Logcontrast PLS Path modeling of Multiple Compositional Data

本文研究多元成分数据的路径关联关系的建模问题,提出多元成分数据的对数衬度PLS通径分析模型.将中心化对数比变换与PLS通径分析方法相结合建立模型,其主要优势在于:①PLS通径分析模型对数据没有严格的分布假设要求,特别适于成分数据这类分布复杂的数据建模;②成分数据中心化对数比变换后的变量完全多重相关,PLS方法能够有效解决这一问题;③PLS通径分析模型特别适于多元成分数据这类具有层次关系的数据结构的建模,通过结构模型揭示多元成分数据之间的整体性路径关联关系,通过测量模型揭示成分数据与其成分分量之间的构成关系.更重要的是,本文的方法研究遵循成分数据所特有的代数基本理论,推导出模型的成分数据对数衬度隐变量的表达形式,从理论上证明了该建模方法的科学合理性.最后,将本方法用于北京市三次产业的投资结构、GDP结构、就业结构的路径关联关系的分析中,通过实证研究验证模型的可行性和应用价值.

This paper proposed logcontrast PLS （partial leest-squares） path modeling of multiple compositional data, analyzing the structural relationships between multiple compositional data. By combining centered logratio transformation with PLS path modeling, the following three difficulties are preferably overcome： 1） PLS path modeling is not demanding in distribution assumption to the original data set, which is valuable in the modeling of compositional data with complex distributions; 2） the centered logratio transformed variables are totally multilinearity where PLS can tackle the difficulty; 3） PLS path modeling is especially suitable to multiple composition data with hierarchical characteristic, for the structural models show the integrate relations between multiple compositional data and the measurement models explain the formative relations of compositional data with their corresponding compositions, respectively. Moreover, our methodology study is based on the special algebraic theoretical system of compositional data and the formula expression of logcontrast latent variables of compositional data are derived from the model, which theoretically justifies the proposed method. Finally, the method is applied to analyze the structural relationship of the investment, GDP and employment structures of Beijing＇s three industries, and the empirical results verified the validity and practicability of the model.