Direct and Indirect Effects

Abstract

The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and prac­ tical difficulties (in nonlinear models), be­ cause they cannot be isolated by holding cer­ tain variables constant. This paper presents a new way of defining the effect transmit­ ted through a restricted set of paths, without controlling variables on the remaining paths. This permits the assessment of a more nat­ ural type of direct and indirect effects, one that is applicable in both linear and nonlinear models and that has broader policy-related interpretations. The paper establishes con­ ditions under which such assessments can be estimated consistently from experimen­ tal and nonexperimental data, and thus ex­ tends path-analytic techniques to nonlinear and nonparametric models. The distinction between total, direct, and indirect ef­ fects is deeply entrenched in causal conversations, and attains practical importance in many applications, in­ cluding policy decisions, legal definitions and health care analysis. Structural equation modeling (SEM) (Goldberger 1972), which provides a methodology of defining and estimating such effects, has been re­ stricted to linear analysis, and no comparable method­ ology has been devised to extend these capabilities to models involving nonlinear dependencies,1 as those 1 A notable exception is the counterfactual analysis of Robins and Greenland (1992) which is applicable to non­ linear models, but does not incorporate path-analytic tech­ niques. The causal relationship that is easiest to interpret, define and estimate is the total effect. Written as P(Y"' = y), the total effect measures the probability that response variable Y would take on the value y when X is set to x by external intervention.2 This probability function is what we normally assess in a controlled experiment in which X is randomized and in which the distribution of Y is estimated for each level x of X. In many cases, however, this quantity does not ade­ quately represent the target of investigation and at­ tention is focused instead on the direct effect of X on Y. The term "direct effect" is meant to quantify an influence that is not mediated by other variables in the model or, more accurately, the sensitivity of Y to changes in X while all other factors in the analysis are held fixed. Naturally, holding those factors fixed would sever all causal paths from X to Y with the exception of the direct link …

Extracted Key Phrases

Showing 1-7 of 7 references

Statistical evidence in discrimination cases

  • Gastwirth
  • 1997

Hagenaars, 1993) J. Hagenaars. Loglinear Models with Latent Variables

  • 1993

Discussion: Two notes on the probabilistic approach to causality

  • G Hesslow, Hesslow
  • 1976
1 Excerpt

Identifiability and for direct and indirect effects Estimating causal effects of treatments in randomized and nonrandomized stud­ ies

  • Robins, Greenland
  • 1974

Structural equa­ tion models in the social sciences

  • Goldberger
  • 1972
2 Excerpts
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