成分数据的多元回归建模方法研究

Multiple linear regression modeling method based on the compositional data

在社会、经济、技术等许多领域的数据分析中,成分数据(compositional data)是一种应用十分广泛的数据类型,可以被用来反映诸如投资结构、产业结构、居民消费结构等问题.将成分数据的logratio变换方法与偏最小二乘路径分析相结合,提出在因变量是成分数据,而与之相关的若干个自变量也都是成分数据的情况下,建立了多元线性回归模型的方法.该建模方法可以满足成分数据的定和约束,克服成分数据中完全多重共线性对建模的不良影响,并且突出成分数据主题含义在建模中的作用和意义.作为案例,应用所提出的方法,采用北京市三类产业的投资、GDP以及就业的结构数据,建立了三者之间的回归模型,进一步说明了多元成分数据回归建模的工作过程及其应用价值.

Compositional data consist of vectors of nonnegative values summing to a unit. In this paper the PLS path modeling is applied to the compositional data after logratio transformation and a method of multiple linear regression modeling is put forward when the dependent and independent variables are all correlated compositional data. For compositional data this modeling method can satisfy the unit-sum constraint and eliminate the harms that derive from the complete multicollinearity. By the case of a regression model built on Beijing＇ s three industries structure data of investment, GDP and employment, it is proved that the modeling can clarity the property that contained in the compositional data effectively.