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"Hayes, Andrew F"
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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.
Journal Article
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.
Journal Article
Statistical Methods for Communication Science
Statistical Methods for Communication Science is the only statistical methods volume currently available that focuses exclusively on statistics in communication research. Writing in a straightforward, personal style, author Andrew F. Hayes offers this accessible and thorough introduction to statistical methods, starting with the fundamentals of measurement and moving on to discuss such key topics as sampling procedures, probability, reliability, hypothesis testing, simple correlation and regression, and analyses of variance and covariance. Hayes takes readers through each topic with clear explanations and illustrations. He provides a multitude of examples, all set in the context of communication research, thus engaging readers directly and helping them to see the relevance and importance of statistics to the field of communication.
eBook
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.
Journal Article
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.
Journal Article
Mediation, Moderation, and Conditional Process Analysis: Concepts, Computations, and Some Common Confusions
This work provides a conceptual introduction to mediation, moderation, and conditional process analysis in psychological research. We discuss the concepts of direct effect, indirect effect, total effect, conditional effect, conditional direct effect, conditional indirect effect, and the index of moderated mediation index, while providing our perspective on certain analysis and interpretation confusions that sometimes arise in practice in this journal and elsewhere, such as reliance on the causal steps approach and the Sobel test in mediation analysis, misinterpreting the regression coefficients in a model that includes a product of variables, and subgroups mediation analysis rather than conditional process analysis when exploring whether an indirect effect depends on a moderator. We also illustrate how to conduct various analyses that are the focus of this paper with the freely-available PROCESS procedure available for SPSS, SAS, and R, using data from an experimental investigation on the effectiveness of personal or testimonial narrative messages in improving intergroup attitudes.
Journal Article
Questions of value, questions of magnitude: An exploration and application of methods for comparing indirect effects in multiple mediator models
Mediation analysis is widely used to test and inform theory and debate about the mechanism(s) by which causal effects operate, quantitatively operationalized as an
indirect effect
in a mediation model. Most effects operate through multiple mechanisms simultaneously, and a mediation model is likely to be more realistic when it is specified to capture multiple mechanisms at the same time with the inclusion of more than one mediator in the model. This also allows an investigator to compare indirect effects to each other. After an overview of the mechanics of mediation analysis, we advocate formally comparing indirect effects in models that include more than one mediator, focusing on the important distinction between questions and claims about
value
(i.e., are two indirect effects the same number?) versus
magnitude
(i.e., are two indirect effects equidistant from zero or the same in strength?). After discussing the shortcomings of the conventional method for comparing two indirect effects in a multiple mediator model—which only answers a question about magnitude in some circumstances—we introduce several methods that, unlike the conventional approach, always answer questions about difference in magnitude. We illustrate the use of these methods and provide code that implements them in popular software. We end by summarizing simulation findings and recommending which method(s) to prefer when comparing like- and opposite-signed indirect effects.
Journal Article
The moderating role of social ties on entrepreneurs' depressed affect and withdrawal intentions in response to economic stress
We explored whether contact with business-related social ties would buffer entrepreneurs against the potentially deleterious effects of economic stress. Our proposed stress-buffering model builds on the premise that social ties with similar others can serve as both a source of valuable information and a source of empathic support. Findings from a sample of 262 entrepreneurs revealed that the relation between economic stress and intentions to withdraw from entrepreneurial opportunities was stronger among individuals reporting less contact with social ties and weaker among those who reported more contact with social ties. We further examined the indirect effects of economic stress and contact with business-related social ties on entrepreneurs' future intentions through depressed affect. Results showed that among those reporting less contact with social ties, the indirect effect is positive, meaning greater economic stress leads to higher depressed affect, which in turn results in greater intentions to withdraw from entrepreneurship. Among those with more contact with social ties, there is no evidence of this process at work. We interpret this to mean that social ties serve to buffer the impact of economic stress on depressed affect, which in turn reduces an entrepreneur's intention to withdraw from entrepreneurship. Those who seem most susceptible to the impact of economic stress are those with relatively limited contact with business-related social ties. We discuss implications and directions for future research.
Journal Article