Hypotheses involving mediation are common in the behavioral sciences. Mediation exists when a predictor affects a dependent variable indirectly through at least one intervening variable, or mediator. Methods to assess mediation involving multiple simultaneous mediators have received little attention in the methodological literature despite a clear need. We provide an overview of simple and multiple mediation and explore three approaches that can be used to investigate indirect processes, as well as methods for contrasting two or more mediators within a single model. We present an illustrative example, assessing and contrasting potential mediators of the relationship between the helpfulness of socialization agents and job satisfaction. We also provide SAS and SPSS macros, as well as Mplus and LISREL syntax, to facilitate the use of these methods in applications.

https://link.springer.com/content/pdf/10.3758/BRM.40.3.879.pdf

Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models

Researchers often conduct mediation analysis in order to indirectly assess the effect of a proposed cause on some outcome through a proposed mediator. The utility of mediation analysis stems from its ability to go beyond the merely descriptive to a more functional understanding of the relationships among variables. A necessary component of mediation is a statistically and practically significant indirect effect. Although mediation hypotheses are frequently explored in psychological research, formal significance tests of indirect effects are rarely conducted. After a brief overview of mediation, we argue the importance of directly testing the significance of indirect effects and provide SPSS and SAS macros that facilitate estimation of the indirect effect with a normal theory approach and a bootstrap approach to obtaining confidence intervals, as well as the traditional approach advocated by Baron and Kenny (1986). We hope that this discussion and the macros will enhance the frequency of formal mediation tests in the psychology literature. Electronic copies of these macros may be downloaded from the Psychonomic Society's Web archive at www.psychonomic.org/archive/.

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SPSS and SAS procedures for estimating indirect effects in simple mediation models.

Mediation is said to occur when a causal effect of some variable X on an outcome Y is explained by some intervening variable M. The authors recommend that with small to moderate samples, bootstrap methods (B. Efron & R. Tibshirani, 1993) be used to assess mediation. Bootstrap tests are powerful because they detect that the sampling distribution of the mediated effect is skewed away from 0. They argue that R. M. Baron and D. A. Kenny's (1986) recommendation of first testing the X --> Y association for statistical significance should not be a requirement when there is a priori belief that the effect size is small or suppression is a possibility. Empirical examples and computer setups for bootstrap analyses are provided.

/pdf/mediation-in-experimental-and-nonexperimental-studies-new-36pi5vkg4y.pdf

Mediation in experimental and nonexperimental studies: New procedures and recommendations.

A Monte Carlo study compared 14 methods to test the statistical significance of the intervening variable effect. An intervening variable (mediator) transmits the effect of an independent variable to a dependent variable. The commonly used R. M. Baron and D. A. Kenny (1986) approach has low statistical power. Two methods based on the distribution of the product and 2 difference-in-coefficients methods have the most accurate Type I error rates and greatest statistical power except in 1 important case in which Type I error rates are too high. The best balance of Type I error and statistical power across all cases is the test of the joint significance of the two effects comprising the intervening variable effect.

/pdf/a-comparison-of-methods-to-test-mediation-and-other-21xho8v2xm.pdf

A comparison of methods to test mediation and other intervening variable effects.

Baron and Kenny’s procedure for determining if an independent variable affects a dependent variable through some mediator is so well known that it is used by authors and requested by reviewers almost reflexively. Many research projects have been terminated early in a research program or later in the review process because the data did not conform to Baron and Kenny’s criteria, impeding theoretical development. While the technical literature has disputed some of Baron and Kenny’s tests, this literature has not diffused to practicing researchers. We present a nontechnical summary of the flaws in the Baron and Kenny logic, some of which have not been previously noted. We provide a decision tree and a step-by-step procedure for testing mediation, classifying its type, and interpreting the implications of findings for theory building and future research.

/pdf/reconsidering-baron-and-kenny-myths-and-truths-about-2nucg9g9ev.pdf

Reconsidering Baron and Kenny: Myths and Truths about Mediation Analysis

The most commonly used method to test an indirect effect is to divide the estimate of the indirect effect by its standard error and compare the resulting z statistic with a critical value from the standard normal distribution. Confidence limits for the indirect effect are also typically based on critical values from the standard normal distribution. This article uses a simulation study to demonstrate that confidence limits are imbalanced because the distribution of the indirect effect is normal only in special cases. Two alternatives for improving the performance of confidence limits for the indirect effect are evaluated: (a) a method based on the distribution of the product of two normal random variables, and (b) resampling methods. In Study 1, confidence limits based on the distribution of the product are more accurate than methods based on an assumed normal distribution but confidence limits are still imbalanced. Study 2 demonstrates that more accurate confidence limits are obtained using resampling methods, with the bias-corrected bootstrap the best method overall.

/pdf/confidence-limits-for-the-indirect-effect-distribution-of-2yv44tb6it.pdf

Confidence Limits for the Indirect Effect: Distribution of the Product and Resampling Methods.

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.

/pdf/equivalence-of-the-mediation-confounding-and-suppression-27x13bb1vg.pdf

Equivalence of the Mediation, Confounding and Suppression Effect

This article describes a program, PRODCLIN (distribution of the PRODuct Confidence Limits for INdirect effects), written for SAS, SPSS, and R, that computes confidence limits for the product of two normal random variables. The program is important because it can be used to obtain more accurate confidence limits for the indirect effect, as demonstrated in several recent articles (MacKinnon, Lockwood, & Williams, 2004; Pituch, Whittaker, & Stapleton, 2005). Tests of the significance of and confidence limits for indirect effects based on the distribution of the product method have more accurate Type I error rates and more power than other, more commonly used tests. Values for the two paths involved in the indirect effect and their standard errors are entered in the PRODCLIN program, and distribution of the product confidence limits are computed. Several examples are used to illustrate the PRODCLIN program. The PRODCLIN programs in rich text format may be downloaded from www.psychonomic.org/archive.

/pdf/distribution-of-the-product-confidence-limits-for-the-nis4utpf0u.pdf

Distribution of the product confidence limits for the indirect effect: Program PRODCLIN

Background An intermediate endpoint is hypothesized to be in the middle of the causal sequence relating an independent variable to a dependent variable. The intermediate variable is also called a s...

/pdf/the-intermediate-endpoint-effect-in-logistic-and-probit-159x0qbza5.pdf

Chondra M. Lockwood

Papers

A comparison of methods to test mediation and other intervening variable effects.

Confidence Limits for the Indirect Effect: Distribution of the Product and Resampling Methods.

Equivalence of the Mediation, Confounding and Suppression Effect

Distribution of the product confidence limits for the indirect effect: Program PRODCLIN

The intermediate endpoint effect in logistic and probit regression