Andrew F. Hayes

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

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.

SPSS and SAS procedures for estimating indirect effects in simple mediation 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 atwww.psychonomic.org/archive/.

Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions

This article provides researchers with a guide to properly construe and conduct analyses of conditional indirect effects, commonly known as moderated mediation effects. We disentangle conflicting definitions of moderated mediation and describe approaches for estimating and testing a variety of hypotheses involving conditional indirect effects. We introduce standard errors for hypothesis testing and construction of confidence intervals in large samples but advocate that researchers use bootstrapping whenever possible. We also describe methods for probing significant conditional indirect effects by employing direct extensions of the simple slopes method and Johnson-Neyman technique for probing significant interactions. Finally, we provide an SPSS macro to facilitate the implementation of the recommended asymptotic and bootstrapping methods. We illustrate the application of these methods with an example drawn from the Michigan Study of Adolescent Life Transitions, showing that the indirect effect of intrinsic student interest on mathematics performance through teacher perceptions of talent is moderated by student math self-concept.

Beyond Baron and Kenny: Statistical Mediation Analysis in the New Millennium

Understanding communication processes is the goal of most communication researchers. Rarely are we satisfied merely ascertaining whether messages have an effect on some outcome of focus in a specif...

Answering the Call for a Standard Reliability Measure for Coding Data

In content analysis and similar methods, data are typically generated by trained human observers who record or transcribe textual, pictorial, or audible matter in terms suitable for analysis. Conclusions from such data can be trusted only after demonstrating their reliability. Unfortunately, the content analysis literature is full of proposals for so-called reliability coefficients, leaving investigators easily confused, not knowing which to choose. After describing the criteria for a good measure of reliability, we propose Krippendorffs alpha as the standard reliability measure. It is general in that it can be used regardless of the number of observers, levels of measurement, sample sizes, and presence or absence of missing data. To facilitate the adoption of this recommendation, we describe a freely available macro written for SPSS and SAS to calculate Krippendorffs alpha and illustrate its use with a simple example.

Computational procedures for probing interactions in OLS and logistic regression: SPSS and SAS implementations

Researchers often hypothesize moderated effects, in which the effect of an independent variable on an outcome variable depends on the value of a moderator variable. Such an effect reveals itself statistically as an interaction between the independent and moderator variables in a model of the outcome variable. When an interaction is found, it is important to probe the interaction, for theories and hypotheses often predict not just interaction but a specific pattern of effects of the focal independent variable as a function of the moderator. This article describes the familiar pick-a-point approach and the much less familiar Johnson-Neyman technique for probing interactions in linear models and introduces macros for SPSS and SAS to simplify the computations and facilitate the probing of interactions in ordinary least squares and logistic regression. A script version of the SPSS macro is also available for users who prefer a point-and-click user interface rather than command syntax.

Statistical mediation analysis with a multicategorical independent variable.

Virtually all discussions and applications of statistical mediation analysis have been based on the condition that the independent variable is dichotomous or continuous, even though investigators frequently are interested in testing mediation hypotheses involving a multicategorical independent variable (such as two or more experimental conditions relative to a control group). We provide a tutorial illustrating an approach to estimation of and inference about direct, indirect, and total effects in statistical mediation analysis with a multicategorical independent variable. The approach is mathematically equivalent to analysis of (co)variance and reproduces the observed and adjusted group means while also generating effects having simple interpretations. Supplementary material available online includes extensions to this approach and Mplus, SPSS, and SAS code that implements it.

An Index and Test of Linear Moderated Mediation

I describe a test of linear moderated mediation in path analysis based on an interval estimate of the parameter of a function linking the indirect effect to values of a moderator—a parameter that I call the index of moderated mediation. This test can be used for models that integrate moderation and mediation in which the relationship between the indirect effect and the moderator is estimated as linear, including many of the models described by Edwards and Lambert (2007) and Preacher, Rucker, and Hayes (2007) as well as extensions of these models to processes involving multiple mediators operating in parallel or in serial. Generalization of the method to latent variable models is straightforward. Three empirical examples describe the computation of the index and the test, and its implementation is illustrated using Mplus and the PROCESS macro for SPSS and SAS.

The Relative Trustworthiness of Inferential Tests of the Indirect Effect in Statistical Mediation Analysis Does Method Really Matter

A content analysis of 2 years of Psychological Science articles reveals inconsistencies in how researchers make inferences about indirect effects when conducting a statistical mediation analysis. In this study, we examined the frequency with which popularly used tests disagree, whether the method an investigator uses makes a difference in the conclusion he or she will reach, and whether there is a most trustworthy test that can be recommended to balance practical and performance considerations. We found that tests agree much more frequently than they disagree, but disagreements are more common when an indirect effect exists than when it does not. We recommend the bias-corrected bootstrap confidence interval as the most trustworthy test if power is of utmost concern, although it can be slightly liberal in some circumstances. Investigators concerned about Type I errors should choose the Monte Carlo confidence interval or the distribution-of-the-product approach, which rarely disagree. The percentile bootstrap confidence interval is a good compromise test.

Using heteroskedasticity-consistent standard error estimators in OLS regression: An introduction and software implementation

Homoskedasticity is an important assumption in ordinary least squares (OLS) regression. Although the estimator of the regression parameters in OLS regression is unbiased when the homoskedasticity assumption is violated, the estimator of the covariance matrix of the parameter estimates can be biased and inconsistent under heteroskedasticity, which can produce significance tests and confidence intervals that can be liberal or conservative. After a brief description of heteroskedasticity and its effects on inference in OLS regression, we discuss a family of heteroskedasticity-consistent standard error estimators for OLS regression and argue investigators should routinely use one of these estimators when conducting hypothesis tests using OLS regression. To facilitate the adoption of this recommendation, we provide easy-to-use SPSS and SAS macros to implement the procedures discussed here.