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

Criteria for evaluating structural equation models with latent variables are defined, critiqued, and illustrated. An overall program for model evaluation is proposed based upon an interpretation of converging and diverging evidence. Model assessment is considered to be a complex process mixing statistical criteria with philosophical, historical, and theoretical elements. Inevitably the process entails some attempt at a reconcilation between so-called objective and subjective norms.

On the evaluation of structural equation models

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

/pdf/experimental-design-and-data-analysis-for-biologists-8ybva8d53x.pdf

Experimental Design and Data Analysis for Biologists

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.

/pdf/addressing-moderated-mediation-hypotheses-theory-methods-and-463wvvjm24.pdf

Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions.

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...

/pdf/beyond-baron-and-kenny-statistical-mediation-analysis-in-the-263fzzzo4o.pdf

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

R. M. Baron and D. A. Kenny (1986; see record 1987-13085-001) provided clarion conceptual and methodological guidelines for testing mediational models with cross-sectional data. Graduating from cross-sectional to longitudinal designs enables researchers to make more rigorous inferences about the causal relations implied by such models. In this transition, misconceptions and erroneous assumptions are the norm. First, we describe some of the questions that arise (and misconceptions that sometimes emerge) in longitudinal tests of mediational models. We also provide a collection of tips for structural equation modeling (SEM) of mediational processes. Finally, we suggest a series of 5 steps when using SEM to test mediational processes in longitudinal designs: testing the measurement model, testing for added components, testing for omitted paths, testing the stationarity assumption, and estimating the mediational effects.

Testing mediational models with longitudinal data: questions and tips in the use of structural equation modeling.

Most empirical tests of mediation utilize cross-sectional data despite the fact that mediation consists of causal processes that unfold over time. The authors considered the possibility that longitudinal mediation might occur under either of two different models of change: (a) an autoregressive model or (b) a random effects model. For both models, the authors demonstrated that cross-sectional approaches to mediation typically generate substantially biased estimates of longitudinal parameters even under the ideal conditions when mediation is complete. In longitudinal models where variable M completely mediates the effect of X on Y, cross-sectional estimates of the direct effect of X on Y, the indirect effect of X on Y through M, and the proportion of the total effect mediated by M are often highly misleading.

Bias in cross-sectional analyses of longitudinal mediation.

Utility of confirmatory factor analysis in test validation research

Maxwell and Cole (2007) showed that cross-sectional approaches to mediation typically generate substantially biased estimates of longitudinal parameters in the special case of complete mediation. However, their results did not apply to the more typical case of partial mediation. We extend their previous work by showing that substantial bias can also occur with partial mediation. In particular, cross-sectional analyses can imply the existence of a substantial indirect effect even when the true longitudinal indirect effect is zero. Thus, a variable that is found to be a strong mediator in a cross-sectional analysis may not be a mediator at all in a longitudinal analysis. In addition, we show that very different combinations of longitudinal parameter values can lead to essentially identical cross-sectional correlations, raising serious questions about the interpretability of cross-sectional mediation data. More generally, researchers are encouraged to consider a wide variety of possible mediation models beyond simple cross-sectional models, including but not restricted to autoregressive models of change.

Bias in Cross-Sectional Analyses of Longitudinal Mediation: Partial and Complete Mediation Under an Autoregressive Model

Elementary school students (n = 330) and their parents (n = 228) participated in a 3-year longitudinal study of the temporal relation between anxiety and depressive symptoms in children. Every 6 months, children and parents completed depression and anxiety questionnaires for a total of 6 waves. Structural equation modeling revealed that individual differences on all measures were remarkably stable over time. Nevertheless, high levels of anxiety symptoms at 1 point in time predicted high levels of depressive symptoms at subsequent points in time even after controlling for prior levels of depression symptoms. These findings were consistent across self- and parent reports. Results support the temporal hypothesis that anxiety leads to depression in children and adolescents.

David A. Cole

Papers

Testing mediational models with longitudinal data: questions and tips in the use of structural equation modeling.

Bias in cross-sectional analyses of longitudinal mediation.

Utility of confirmatory factor analysis in test validation research

Bias in Cross-Sectional Analyses of Longitudinal Mediation: Partial and Complete Mediation Under an Autoregressive Model

A longitudinal look at the relation between depression and anxiety in children and adolescents.