The Regression Analysis of Causal Paths

The purpose of this presentation is to acquaint biologists and biometricians with an important tool, path analysis. This tool can be of help in dealing with complex causal networks. These often, though not always, prove amenable to common regression technics. Path analysis, originated by Sewall Wright 1918, is a convenient approach to regression problems involving two or more regression equations. For those unskilled in statistics, path analysis provides one method of depicting regression problems by simple diagram. The path diagram, commonly representing the flow of cause and effect, often permits one to write estimators of parameters immediately upon inspection. Path analysis thus facilitates the process of abstraction for both mathematician and biologist. The analytic process is here explained, two computational algorithms (rules-of-thumb) are given, and an example involving feedback is detailed. Inclusion of feedback, and thus homeostasis, is an important feature of this presentation. Since Wright's early work 1918, 1921, 1924, 1934, and others the treatment of multiple equations has been extensively developed in econometrics (see especially Hood and Koopmans, 1953) but generally without use of the standardized regression coefficients used by Wright or of the path diagrams and algorithms which characterize Wright's technic. Wright himself 1921 used unstandardized coefficients and the term path regression, but in general 1954 has favored the standardized form. Tukey 1954 in a critical review pointed out advantages in working with unstandardized regression coefficients. Recently Kemp-