• Introduction
• General Overviews
• Path Analysis in the Social Sciences
• Innovations of Path Analysis
• Mediation
• Moderation and Conditional Process Modeling
• Graph Theory and the Structural Causal Model
• Causal Mediation Analysis
• Latent Variable Extensions and SEM Textbooks
• Computer Tools for SEM
• Books about SEM Computer Tools
• Computer Tools for Analyzing Directed Acyclic Graphs
• Computer Tools for Causal Mediation Analysis
• Best Practices

# Path ModelsbyRex B. KlineLAST REVIEWED: 08 November 2018LAST MODIFIED: 29 May 2015DOI: 10.1093/obo/9780199828340-0173

## Introduction

Path analysis belongs to the family of statistical techniques known as structural equation modeling (SEM). Path analysis is the original—and thus the oldest—SEM technique. It can be viewed as an extension of regression techniques to the analysis of directed (causal) effects among a set of variables. Presumed causal effects are specified according to a particular theory, and such hypotheses can be represented graphically in the form of a path model, also known as a structural model of observed variables. But unlike standard regression techniques where the roles of predictor versus criterion are theoretically interchangeable, path models represent directional effects between an outcome variable and its presumed causes, and such effects are not arbitrarily reversible, because they are viewed in a particular theory as properties of nature. The basic logic of path analysis was developed by the geneticist Sewall Wright beginning in the 1920s. For two reasons, Wright’s work on path analysis had relatively little impact in biology at the time. First, the very notion of causality as a scientific construct in biology was usurped by that of statistical association, owing to Karl Pearson’s elaboration on the method of correlation in the late 1890s and early 1900s. Second, Ronald Fisher’s statistical methods from the 1920s, based on the method of analysis of variance applied in the context of experimental designs, appeared to offer a more comprehensive framework for causal inference than Wright’s theory of path coefficients. Fisher also viewed randomization and experimental control as the only real basis for causal inference. The two schools of thought just mentioned no longer predominate, but at the time their proponents resisted Wright’s method.

## General Overviews

The basic rationale of path analysis was outlined in several key works by Sewall Wright (Wright 1920, Wright 1921, Wright 1934). An early critical work, Niles 1922, exemplifies the opposition in biology and genetics to path analysis at that time; see also Wright’s response, Wright 1923. Wolfle 1999 is an annotated bibliography that traces the early development of path analysis, and the same history is described in a more narrative form in Shipley 2000.

• Niles, Henry E. 1922. Correlation, causation and Wright’s theory of “path coefficients.” Genetics 7:258–273.

Criticized the philosophical notion of ascribing to causation any basis beyond that implied by statistical association; that is, causation is correlation in this perspective. Also objected to some of Wright’s equations in earlier works, but these formulae are actually correct.

• Shipley, Bill. 2000. Cause and correlation in biology: A user’s guide to path analysis, structural equations and causal inference. New York: Cambridge Univ. Press.

Reviews the history of path analysis from its development in genetics to its later adoption in the social sciences in the 1960–1970s. Also considers links between Wright’s path analysis method and more modern approaches to causal inference based on graph theory.

• Wolfle, Lee M. 1999. Sewall Wright on the method of path coefficients: An annotated bibliography. Structural Equation Modeling 6:280–291.

Traces Wright’s development of path analysis in works that date from 1918 through 1984, at which point path analysis was becoming well known in the social sciences.

• Wright, Sewall. 1920. The relative importance of heredity and environment in determining the piebald pattern of guinea-pigs. Proceedings of the National Academy of Sciences 6:320–332.

One of the first path diagrams is presented in this article, in which the basic rationale of the whole method is described.

• Wright, Sewall. 1921. Correlation and causation. Journal of Agricultural Research 20:557–585.

Demonstrated in this article are two applications of path analysis, one in the area of weight at weaning of guinea pigs, and the other about the rate of transpiration in plants.

• Wright, Sewall. 1923. The theory of path coefficients: A reply to Niles’s criticism. Genetics 8:239–255.

Wright responded to Nile’s criticisms by emphasizing the importance of a casual model or theory when estimating correlations between variables of interest.

• Wright, Sewall. 1934. The method of path coefficients. Annals of Mathematical Statistics 5:161–215.

An even more comprehensive statement of the method of path coefficients, with examples of application of the tracing rule, is offered in this work.