## Mediation Workshop: 4/7/16, UC Berkeley

In this workshop, we'll discuss the assessment of mediation.

Click here for a pdf of the slides.

Click here for a word document containing R code that runs some mediation simulations.

Recommended Readings

*=of high interest

**=of highest interest

**Biesanz JC, Falk CF, Savalei V (2010). Assessing Mediational Models: Testing and Interval Estimation of Indirect Effects. Multivariate Behavioral Research, 45, 661-701.

This is an excellent Monte Carlo study of the performance of several methods for interval estimation and significance testing in mediational models. They test all methods under standard conditions, as well as under a particular type of departure from normality and missingness, examining both type I error rates and power. Their consistent finding is that the bias-corrected and accelerated bootstrap confidence interval—an often-recommended procedure—gives too many type I errors. The Sobel test has low power. Most of the other methods perform roughly uniformly.

**Bullock JG, Green DP, Ha SE (2010). Yes, But What’s the Mechanism? (Don’t Expect an Easy Answer). Journal of Personality and Social Psychology, 98: 550-558.

An excellent an accessible explanation of the many reasons why establishing and estimating the effects of a causal process is extremely hard, certainly much harder than running a mediation analysis. Frequently proposed improvements—bootstrapping, randomizing the IV, randomizing both the IV and the DV, moderated mediation, mixed-effects approaches, longitudinal data, etc.—either don’t address the fundamental problem or bring major difficulties or assumptions of their own.

*Fiedler K, Schott M, Meiser T (2011). What mediation analyses can (not) do. Journal of Experimental Social Psychology, 47: 1231-1236.

A nice complement to Bullock, Green, & Ha, making many of the same points in different ways and including a Monte Carlo study.

Freedman D (1987). As Others See Us: A Case Study in Path Analysis. Journal of Educational Statistics, 12: 101-128.

A classic account of the limitations of path analysis for explicating causal processes. Somewhat more technical than Bullock, Green, and Ha, but still accessible.

**Freedman D (1991). Statistical Models and Shoe Leather. Sociological Methodology, 21:291-313.

This is a fantastic article. It doesn’t discuss mediation models specifically, but it generally argues that fancy statistics cannot provide causal information. Instead, causal information comes from hard work in study design and execution, Freedman’s “shoe leather.”

*Glynn AN (2012). The Product and Difference Fallacies for Indirect Effects. American Journal of Political Science, 56:257-269.

Explores the consequences of heterogeneity in the effects of the independent variable and mediator. If there is heterogeneity and the effects of the IV and mediator covary, then the estimated indirect effect obtained by multiplying coefficients from two regressions (or estimates from two experiments) will not reflect the average indirect effect in the population.

Hayes AF & Preacher KJ (2014). Statistical mediation analysis with a multicategorical independent variable. British Journal of Mathematical and Statistical Psychology, 67: 451-470.

I’m including this because one of the student questions asked about how to do this.

**Imai K, Keele L, & Tingley D (2010). A General Approach to Causal Mediation Analysis. Psychological Methods, 15:309-334.

A great paper on what is called “causal” mediation analysis, which casts mediational questions in a “potential outcomes” or “counterfactual” framework, which is a way of thinking about causation used often in statistics and computer science. If all the associations between variables are linear, the variables are normal, and there are no treatment-mediator interactions, then the causal mediation approach reduces to standard Baron-Kenny style approaches. The main advantages of the causal mediation framework are: 1) It extends to nonlinear relationships between variables, 2) it clarifies the assumptions necessary for using mediation analyses to ground causal claims, 3) It provides a method of “sensitivity analysis,” which is a way of characterizing how robust causal claims are to violations of assumptions. The paper is a little technical, but if you are serious about mediation analysis, it’s well worth the effort. Their methods are implemented in R and Stata packages.

Imai K, Yamamoto T (2013). Identification and Sensitivity Analysis for Multiple Causal Mechanisms: Revisiting Evidence from Framing Experiments. Political Analysis, 21:141-171.

Extends the causal mediation framework described in Imai, Keele, & Yamamoto (2010) to the case of multiple mediators working in parallel. Identification of multiple mediation effects depends on the assumption that the candidate mediators are causally independent. For example, if the candidate mediators can cause each other, then the estimated effects are likely to be badly biased.

MacKinnon DP, Krull JL, & Lockwood CM (2000). Equivalence of the Mediation, Confounding, and Suppression Effect. Prevention Science, 1:173.

This paper points out that mediation is not statistically distinguishable from confounding or suppression. Thus, the claim that the candidate mediator is actually a mediator cannot rest on the results of the mediation analysis itself.

Cole DA & Maxwell SE (2003). Testing Mediation Models with Longitudinal Data: Questions and Tips in the Use of Structural Equation Modeling. Journal of Abnormal Psychology, 112: 558-577.

One frequent complaint about mediational models is that the data used often aren’t longitudinal, but there are surprisingly few guides to running mediational analyses with longitudinal data. This paper describes one of the major approaches to longitudinal data, requiring three waves of measurement. Most of the benefits of longitudinal data only accrue if the mediator is measured at least at timepoints 1 and 2 and the outcome is measured at least at timepoints 2 and 3.

Maxwell SE & Cole DE (2007). Bias in Cross-Sectional Analyses of Longitudinal Mediation. Psychological Methods, 12:23-44.

Maxwell and Cole propose two theoretical models of mediated change over time. Under their models, attempts to measure mediation using cross-sectional data are doomed. The message is that if you think mediated change is a longitudinal process, then you need to collect longitudinal data on the IV, mediator, and outcome.

*Pirlott AG & MacKinnon DP (in press). Design approaches to experimental mediation. Journal of Experimental Social Psychology.

An excellent and accessible review of manipulation-of-mediator designs, as well as a restatement of the challenges of both measurement-of-mediator and manipulation-of-mediator designs.

**Two blog posts by Matthew Salganik, a sociologist at Princeton:

These blog posts are a great informal introduction to the difficulties of studying mediators, along with pointers to some other literature.

Zhang (2014). Monte Carlo based statistical power analysis for mediation models: methods and software. Behavior Research Methods.

This paper gives a clear example of a Monte Carlo (that is, simulation-based) power analysis, along with an R package, bmem, that you can use to conduct your own power analysis of a mediation study.