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

Factor analysis, path analysis, structural equation modeling, and related multivariate statistical methods are based on maximum likelihood or generalized least squares estimation developed for covariance structure models. Large-sample theory provides a chi-square goodness-of-fit test for comparing a model against a general alternative model based on correlated variables. This model comparison is insufficient for model evaluation: In large samples virtually any model tends to be rejected as inadequate, and in small samples various competing models, if evaluated, might be equally acceptable. A general null model based on modified independence among variables is proposed to provide an additional reference point for the statistical and scientific evaluation of covariance structure models. Use of the null model in the context of a procedure that sequentially evaluates the statistical necessity of various sets of parameters places statistical methods in covariance structure analysis into a more complete framework. The concepts of ideal models and pseudo chi-square tests are introduced, and their roles in hypothesis testing are developed. The importance of supplementing statistical evaluation with incremental fit indices associated with the comparison of hierarchical models is also emphasized. Normed and nonnormed fit indices are developed and illustrated.

Significance tests and goodness of fit in the analysis of covariance structures

For comments on an earlier draft of this chapter and for detailed advice I am indebted to Robert M. Hauser, Halliman H. Winsborough, and Toni Richards, several anonymous reviewers, and the editor of this volume. I also wish to thank John Raisian, Nancy Rytina, and Barbara Mann for their comments and Mark Wilson for able research assistance. The opinions expressed here are the sole responsibility of the author.

Asymptotic Confidence Intervals for Indirect Effects in Structural Equation Models

Measurement invariance is usually tested using Multigroup Confirmatory Factor Analysis, which examines the change in the goodness-of-fit index (GFI) when cross-group constraints are imposed on a measurement model. Although many studies have examined the properties of GFI as indicators of overall model fit for single-group data, there have been none to date that examine how GFIs change when between-group constraints are added to a measurement model. The lack of a consensus about what constitutes significant GFI differences places limits on measurement invariance testing. We examine 20 GFIs based on the minimum fit function. A simulation under the two-group situation was used to examine changes in the GFIs (ΔGFIs) when invariance constraints were added. Based on the results, we recommend using Δcomparative fit index, ΔGamma hat, and ΔMcDonald's Noncentrality Index to evaluate measurement invariance. These three ΔGFIs are independent of both model complexity and sample size, and are not correlated with the o...

Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance

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.

https://www.jstor.org/stable/pdfplus/270754.pdf

Assessing Reliability and Stability in Panel Models

This paper is about the logic of interpreting recursive causal theories in sociology. We review the distinction between associations and effects and discuss the decomposition of effects into direct and indirect components. We then describe a general method for decomposing effects into their components by the systematic application of ordinary least squares regression. The method involves successive computation of reduced-form equations, beginning with an equation containing only exogenous variables, then computing equations which add intervening variables in sequence from cause to effect. This generates all the information required to decompose effects into their various direct and indirect parts. This method is a substitute for the often more cumbersome computation of indirect effects from the structural coefficients (direct effects) of the causal model Finally, we present a way of summarizing this information in tabular form and illustrate the procedures using an empirical example.

https://faculty.washington.edu/matsueda/courses/529/Readings/Alwin%20and%20Hauser%201975.pdf

The Decomposition of Effects in Path Analysis

This paper details the authors selection design and use of a life history calendar (LHC) to collect retrospective life course data. A sample of nine hundred [U.S.] 23-year-olds originally interviewed in 1980 were asked about the incidence and timing of various life events in the nine years since their 15th birthday....The following aspects of the LHC are described: (a) the concept uses and advantages of the LHC (b) the time units and domains used (c) the mode of recording the responses and the decisions and problems involved (d) interviewer training and (e) coding. The following results attest to the accuracy of the LHC retrospective data: (a) only four of the calendars had missing data in any month; (b) the data obtained in 1980 about current work school attendance marriage and children showed a remarkable correspondence to the retrospective 1985 LHC reports of these events; (c) the interviewers were positive about the LHCs ability to increase respondent recall. (EXCERPT)

https://socialinquiry.files.wordpress.com/2011/10/d-freedman-et-al_1988_the-life-history-calendar_-a-technique-for-collecting-retrospective-data.pdf

The life history calendar: a technique for collecting retrospective data.

An evaluation of a cognitive theory of response-order effects in survey measurement

Tonnies, Ferdinand 1957 Community and Society. New York: Harper Torchbooks. Vidmar, Neil and Linda Crinklaw 1974 "Assignment of responsibility for an accident: a methodological and conceptual critique." Canadian Journal of Behavioral Science 6:112-30. Weber, Max 1947 The Theory of Social and Economic Organization. Talcott Parsons (ed.) New York: Free Press. Yngvesson, Barbara and Patricia Hennessey 1975 "Small claims, complex disputes: a review of the small claims literature." Law and Society Review 9:219-74.

Duane F. Alwin

Papers

Assessing Reliability and Stability in Panel Models

The Decomposition of Effects in Path Analysis

The life history calendar: a technique for collecting retrospective data.

An evaluation of a cognitive theory of response-order effects in survey measurement

Causes and Consequences of Sex-Role Attitudes and Attitude Change.