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.
Highlights
The regression analysis, as one of the most widely used statistical methodologies, focuses on studying the relations between dependent variables and independent variables
The path diagram is a pictorial representation of a system of simultaneous equations, which presents the picture of the relationships that are assumed and is more clearly than the equations [4]
We attempt to propose the multiple-to-multiple path analysis model according to the multiple-to-multiple linear regression analysis, including multiple independent variables and multiple dependent variables and no latent variables
Summary
The regression analysis, as one of the most widely used statistical methodologies, focuses on studying the relations between dependent variables and independent variables. The decision coefficient was constructed in the specified path analysis model with no latent variables, which included one dependent variable (as result) and multiple independent variables (as causes), based on the decomposition of total determination coefficient [21]. The one-to-multiple path analysis model can be used to analyse the importance of each independent variable to one dependent variable and the regulations among multiple independent variables. We attempt to propose the multiple-to-multiple path analysis model according to the multiple-to-multiple linear regression analysis, including multiple independent variables and multiple dependent variables and no latent variables. The decomposition of the generalized determination coefficient showed the regulation mechanisms among the multiple independent variables and multiple dependent variables along these five types of paths. The effectiveness of the model was verified by an example of the wheat breeding rules in arid area
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