Multiple-to-multiple path analysis model

Abstract

One-to-multiple path analysis model describes the regulation mechanism of multiple independent variables to one dependent variable by dividing the correlation coefficient and the determination coefficient. How to analyse more complex regulation mechanisms of multiple independent variables to multiple dependent variables? Similarly, according to multiple-to-multiple linear regression analysis, multiple-to-multiple path analysis model was proposed in this paper and it demonstrated more complex regulation mechanisms among multiple independent variables and multiple dependent variables by dividing the generalized determination coefficient. Differently, three other types of paths were generated in multiple-to-multiple path analysis model in that the correlation among multiple dependent variables was considered. Then, the decision coefficient of each independent variable was constructed for dependent variables system, and its hypothesis testing statistics were given. Finally, the research example of the wheat breeding rules in arid area demonstrated that the multiple-to-multiple path analysis considering more correlation information can get better results.