Entropy-Based Path Analysis

Abstract

First, in recursive path systems of variables, the systems are described by path diagrams, and decompositions of the joint distributions of the variables are made according to the path diagrams. Usual path analysis of continuous variables based on linear regression models is reviewed. Second, path analysis based on generalized linear models (GLMs) is discussed by using log odds ratios, in order to use both continuous and categorical variable path systems. A method for calculating the total, direct, and indirect effects of parent variables on the descendant variables is provided, and the method is demonstrated for path systems based on GLMs with canonical links. Third, in order to summarize the effects computed with log odds ratios, the effects are summarized according to the entropy coefficient determination (ECD). The path analysis is demonstrated by using two numerical examples. Finally, a general method for calculating the summary total, direct, and indirect effects is given.