Equivalence of the Mediation, Confounding and Suppression Effect
Abstract
This paper describes the statistical similarities among mediation, confounding, and suppression. Each is quantified by measuring the change in the relationship between an independent and a dependent variable after adding a third variable to the analysis. Mediation and confounding are identical statistically and can be distinguished only on conceptual grounds. Methods to determine the confidence intervals for confounding and suppression effects are proposed based on methods developed for mediated effects. Although the statistical estimation of effects and standard errors is the same, there are important conceptual differences among the three types of effects.
Once a relationship between two variables has been established, it is common for researchers to consider the role of a third variable in this relationship (Lazarsfeld, 1955). This paper will examine three types of third variable effects—mediation, confounding, and suppression—in which an additional variable may clarify the nature of the relationship between an independent and a dependent variable. These three concepts have largely been developed within different areas of inquiry, and although the three types of effects are conceptually distinct, they share considerable statistical similarities. Some aspects of the similarity of these concepts have been mentioned in several different articles (Olkin & Finn, 1995; Robins, 1989; Spirtes, Glymour, & Scheines, 1993; Tzelgov & Henik, 1991). In this paper, we demonstrate that mediation, confounding, and suppression effects can each be considered in terms of a general third variable model, and that point and interval estimates of mediation effects can be adapted for use in confounding and suppression frameworks. The paper focuses on a three variable system containing an independent variable (X), a dependent variable (Y), and a third variable that may be a mediator (M), a confounder (C), or a suppressor (S).
Footnotes
Here we are not referring to confounding discussed in the analysis of variance for incomplete designs (see Winer, Brown, & Michels, 1991 and Kirk, 1995).
A simulation study of suppression and confounding models confirmed that the statistics typically used to assess mediation are generally unbiased in assessing confounder and suppressor effects. Point estimates of mediator, suppressor, and confounder effects and their standard errors were quite accurate for sample sizes of 50 or larger for the model in Fig. 1 and multivariate normal data. Information regarding the simulation study results can be found at the following website: www.public.asu.edu/~davidpm/ripl
J.L.K. is currently at the Department of Psychology, University of Missouri-Columbia.