The Causal Mediation Formula - A Guide to the Assessment of Pathways and Mechanisms

doi:10.1007/S11121-011-0270-1

Home
/
Papers
/
The Causal Mediation Formula - A Guide to the Assessment of Pathways and Mechanisms

Journal Article•DOI•

The Causal Mediation Formula - A Guide to the Assessment of Pathways and Mechanisms

Judea Pearl¹•Institutions (1)

University of California, Los Angeles¹

01 Oct 2011-Prevention Science (Springer US)-Vol. 13, Iss: 4, pp 426-436

TL;DR: This Mediation Formula is applicable to nonlinear models with both discrete and continuous variables, and permits the evaluation of path-specific effects with minimal assumptions regarding the data-generating process.

read less

Abstract: Recent advances in causal inference have given rise to a general and easy-to-use formula for assessing the extent to which the effect of one variable on another is mediated by a third. This Mediation Formula is applicable to nonlinear models with both discrete and continuous variables, and permits the evaluation of path-specific effects with minimal assumptions regarding the data-generating process. We demonstrate the use of the Mediation Formula in simple examples and illustrate why parametric methods of analysis yield distorted results, even when parameters are known precisely. We stress the importance of distinguishing between the necessary and sufficient interpretations of “mediated-effect” and show how to estimate the two components in nonlinear systems with continuous and categorical variables.

...read moreread less

Content maybe subject to copyright Report

Citations

PDF

Open Access

More filters

Journal Article•DOI•

Statistical mediation analysis with a multicategorical independent variable

[...]

Andrew F. Hayes¹, Kristopher J. Preacher²•Institutions (2)

Ohio State University¹, Vanderbilt University²

01 Nov 2014-British Journal of Mathematical and Statistical Psychology

TL;DR: A tutorial is provided illustrating an approach to estimation of and inference about direct, indirect, and total effects in statistical mediation analysis with a multicategorical independent variable that reproduces the observed and adjusted group means while also generating effects having simple interpretations.

...read moreread less

Abstract: 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.

...read moreread less

2,318 citations

Cites background or methods from "The Causal Mediation Formula - A Gu..."

...…certain alternative explanations, and more complex statistical approaches than we discuss here can be used in non-experimental studieswhen causal inference is less justified due to limitations of the design (such as non-random assignment; see, for example, Hong, 2012; Muth en, 2011; Pearl, 2012)....
[...]
...…in a mediation model are not confounded by omitted variables (Imai, Keele, & Tingley, 2010; Imai, Keele, &Yamamoto, 2010), and if no importantmoderation effects go unmodelled (Muller, Yzerbyt, & Judd, 2008; Pearl, 2012; VanderWeele & Vansteelandt, 2009, 2010; Yzerbyt, Muller, & Judd, 2004)....
[...]

Omnibus Tests of the Indirect Effect in Statistical Mediation Analysis with a Multicategorical Independent Variable

[...]

Andrew F. Hayes

27 Jan 2016

2,222 citations

Journal Article•DOI•

Unpacking the Black Box of Causality: Learning about Causal Mechanisms from Experimental and Observational Studies

[...]

Kosuke Imai¹, Luke Keele², Dustin Tingley³, Teppei Yamamoto⁴•Institutions (4)

Princeton University¹, Pennsylvania State University², Harvard University³, Massachusetts Institute of Technology⁴

01 Nov 2011-American Political Science Review

TL;DR: This work presents a minimum set of assumptions required under standard designs of experimental and observational studies and develops a general algorithm for estimating causal mediation effects and provides a method for assessing the sensitivity of conclusions to potential violations of a key assumption.

...read moreread less

Abstract: Identifying causal mechanisms is a fundamental goal of social science. Researchers seek to study not only whether one variable affects another but also how such a causal relationship arises. Yet commonly used statistical methods for identifying causal mechanisms rely upon untestable assumptions and are often inappropriate even under those assumptions. Randomizing treatment and intermediate variables is also insufficient. Despite these difficulties, the study of causal mechanisms is too important to abandon. We make three contributions to improve research on causal mechanisms. First, we present a minimum set of assumptions required under standard designs of experimental and observational studies and develop a general algorithm for estimating causal mediation effects. Second, we provide a method for assessing the sensitivity of conclusions to potential violations of a key assumption. Third, we offer alternative research designs for identifying causal mechanisms under weaker assumptions. The proposed approach is illustrated using media framing experiments and incumbency advantage studies.

...read moreread less

1,133 citations

Journal Article•DOI•

Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable

[...]

Felix Elwert¹, Christopher Winship²•Institutions (2)

University of Wisconsin-Madison¹, Harvard University²

30 Jul 2014-Review of Sociology

TL;DR: This article uses causal graphs (direct acyclic graphs, or DAGs) to highlight that endogenous selection bias stems from conditioning on a so-called collider variable, i.e., a variable that is itself caused by two other variables, one that is (or is associated with) the treatment and another that is not associated with the outcome.

...read moreread less

Abstract: Endogenous selection bias is a central problem for causal inference. Recognizing the problem, however, can be difficult in practice. This article introduces a purely graphical way of characterizing endogenous selection bias and of understanding its consequences (Hernan et al. 2004). We use causal graphs (direct acyclic graphs, or DAGs) to highlight that endogenous selection bias stems from conditioning (e.g., controlling, stratifying, or selecting) on a so-called collider variable, i.e., a variable that is itself caused by two other variables, one that is (or is associated with) the treatment and another that is (or is associated with) the outcome. Endogenous selection bias can result from direct conditioning on the outcome variable, a post-outcome variable, a post-treatment variable, and even a pre-treatment variable. We highlight the difference between endogenous selection bias, common-cause confounding, and overcontrol bias and discuss numerous examples from social stratification, cultural sociology, s...

...read moreread less

668 citations

Cites background or methods from "The Causal Mediation Formula - A Gu..."

...The new literature on causal mediation analysis discusses estimands and nonparametric identification conditions (Robins & Greenland 1992; Pearl 2001, 2012; Sobel 2008; Shpitser & VanderWeele 2011) as well as parametric and nonparametric estimation strategies (VanderWeele 2009c, 2011a; Imai, Keele,…...
[...]
...Bareinboim & Pearl (2012) discuss estimation under endogenous selection within the graphical framework adopted here....
[...]
...…mediation analysis discusses estimands and nonparametric identification conditions (Robins & Greenland 1992; Pearl 2001, 2012; Sobel 2008; Shpitser & VanderWeele 2011) as well as parametric and nonparametric estimation strategies (VanderWeele 2009c, 2011a; Imai, Keele, & Yamamoto 2010; Pearl 2012)....
[...]

Journal Article•DOI•

Mediation analysis in epidemiology: methods, interpretation and bias

[...]

Lorenzo Richiardi¹, Rino Bellocco¹, Daniela Zugna¹•Institutions (1)

University of Milano-Bicocca¹

01 Oct 2013-International Journal of Epidemiology

TL;DR: The impact of the three main sources of potential bias in the traditional approach to mediation analyses are reviewed and discussed: (i) mediator-outcome confounding; (ii) exposure-mediator interaction and (iii) mediATOR- outcome confounding affected by the exposure.

...read moreread less

Abstract: In epidemiological studies it is often necessary to disentangle the pathways that link an exposure to an outcome. Typically the aim is to identify the total effect of the exposure on the outcome, the effect of the exposure that acts through a given set of mediators of interest (indirect effect) and the effect of the exposure unexplained by those same mediators (direct effect). The traditional approach to mediation analysis is based on adjusting for the mediator in standard regression models to estimate the direct effect. However, several methodological papers have shown that under a number of circumstances this traditional approach may produce flawed conclusions. Through a better understanding of the causal structure of the variables involved in the analysis, with a formal definition of direct and indirect effects in a counterfactual framework, alternative analytical methods have been introduced to improve the validity and interpretation of mediation analysis. In this paper, we review and discuss the impact of the three main sources of potential bias in the traditional approach to mediation analyses: (i) mediator-outcome confounding;(ii) exposure-mediator interaction and (iii) mediator-outcome confounding affected by the exposure. We provide examples and discuss the impact these sources have in terms of bias.

...read moreread less

564 citations

1
2
3
4
…
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Collapse

References

PDF

Open Access

More filters

Journal Article•DOI•

The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations.

[...]

Reuben M. Baron, David A. Kenny

01 Dec 1986-Journal of Personality and Social Psychology

TL;DR: This article seeks to make theorists and researchers aware of the importance of not using the terms moderator and mediator interchangeably by carefully elaborating the many ways in which moderators and mediators differ, and delineates the conceptual and strategic implications of making use of such distinctions with regard to a wide range of phenomena.

...read moreread less

Abstract: In this article, we attempt to distinguish between the properties of moderator and mediator variables at a number of levels. First, we seek to make theorists and researchers aware of the importance of not using the terms moderator and mediator interchangeably by carefully elaborating, both conceptually and strategically, the many ways in which moderators and mediators differ. We then go beyond this largely pedagogical function and delineate the conceptual and strategic implications of making use of such distinctions with regard to a wide range of phenomena, including control and stress, attitudes, and personality traits. We also provide a specific compendium of analytic procedures appropriate for making the most effective use of the moderator and mediator distinction, both separately and in terms of a broader causal system that includes both moderators and mediators.

...read moreread less

80,095 citations

"The Causal Mediation Formula - A Gu..." refers background or methods in this paper

...…Judd and Kenny (1981) recognized the importance of controlling for mediator-output confounders, the point was not mentioned in the influential paper of Baron and Kenny (1986) and, as a result, it has been ignored by most researchers in the social and psychological sciences (Judd and Kenny 2010)....
[...]
...…as it is often called) will remain intact, and should be kept in mind throughout our discussion.4 Our focus in the sequel, however, will be on crossing the linear-to-nonlinear barrier, using the same causal assumptions that support the standard linear analysis of Baron and Kenny (1986)....
[...]
...Although the degree of moderation can be assessed separately from that of mediation, it is not necessary to base the assessment of one on the assumption that the other is absent, as suggested by some writers (Baron and Kenny 1986; Kraemer et al. 2008)....
[...]
...…from that of mediation, it is not necessary to base the assessment of one on the assumption that the other is absent, as suggested by some writers (Baron and Kenny 1986; Kraemer et al. 2008).9 If the policy evaluated aims to prevent the outcome Y by way of weakening the mediating pathways, the…...
[...]
...For the past few decades the analysis of mediation has been dominated by linear regression paradigms, most notably the one advanced by Baron and Kenny (1986), which can be stated as follows: To test the contribution of a given mediator Z to the effect of X on Y, first regress Y on X and estimate…...
[...]

Book•

Structural Equations with Latent Variables

[...]

Kenneth A. Bollen

28 Apr 1989

TL;DR: The General Model, Part I: Latent Variable and Measurement Models Combined, Part II: Extensions, Part III: Extensions and Part IV: Confirmatory Factor Analysis as discussed by the authors.

...read moreread less

Abstract: Model Notation, Covariances, and Path Analysis. Causality and Causal Models. Structural Equation Models with Observed Variables. The Consequences of Measurement Error. Measurement Models: The Relation Between Latent and Observed Variables. Confirmatory Factor Analysis. The General Model, Part I: Latent Variable and Measurement Models Combined. The General Model, Part II: Extensions. Appendices. Distribution Theory. References. Index.

...read moreread less

19,019 citations

Book•

Handbook of social psychology

[...]

Susan T. Fiske, Daniel T. Gilbert, Gardner Lindzey

01 Jan 1935

TL;DR: In this paper, Neuberg and Heine discuss the notion of belonging, acceptance, belonging, and belonging in the social world, and discuss the relationship between friendship, membership, status, power, and subordination.

...read moreread less

Abstract: VOLUME 2. Part III: The Social World. 21. EVOLUTIONARY SOCIAL PSYCHOLOGY (Steven L. Neuberg, Douglas T. Kenrick, and Mark Schaller). 22. MORALITY (Jonathan Haidt and Selin Kesebir). 23. AGGRESSION (Brad J. Bushman and L. Rowell Huesmann). 24. AFFILIATION, ACCEPTANCE, AND BELONGING: THE PURSUIT OF INTERPERSONAL CONNECTION (Mark R. Leary). 25. CLOSE RELATIONSHIPS (Margaret S. Clark and Edward P. Lemay, Jr.). 26. INTERPERSONAL STRATIFICATION: STATUS, POWER, AND SUBORDINATION (Susan T. Fiske). 27. SOCIAL CONFLICT: THE EMERGENCE AND CONSEQUENCES OF STRUGGLE AND NEGOTIATION (Carsten K. W. De Dreu). 28. INTERGROUP RELATIONS 1(Vincent Yzerbyt and Stephanie Demoulin). 29. INTERGROUP BIAS (John F. Dovidio and Samuel L. Gaertner). 30. SOCIAL JUSTICE: HISTORY, THEORY, AND RESEARCH (John T. Jost and Aaron C. Kay). 31. INFLUENCE AND LEADERSHIP (Michael A. Hogg). 32. GROUP BEHAVIOR AND PERFORMANCE (J. Richard Hackman and Nancy Katz). 33. ORGANIZATIONAL PREFERENCES AND THEIR CONSEQUENCES (Deborah H. Gruenfeld and Larissa Z. Tiedens). 34. THE PSYCHOLOGICAL UNDERPINNINGS OF POLITICAL BEHAVIOR (Jon A. Krosnick, Penny S. Visser, and Joshua Harder). 35. SOCIAL PSYCHOLOGY AND LAW (Margaret Bull Kovera and Eugene Borgida). 36. SOCIAL PSYCHOLOGY AND LANGUAGE: WORDS, UTTERANCES, AND CONVERSATIONS (Thomas Holtgraves). 37. CULTURAL PSYCHOLOGY (Steven J. Heine). AUTHOR INDEX. SUBJECT INDEX.

...read moreread less

13,453 citations

Monograph•DOI•

Causality: models, reasoning, and inference

[...]

Judea Pearl¹•Institutions (1)

University of California, Los Angeles¹

14 Sep 2009-Tijdschrift Voor Filosofie

TL;DR: The art and science of cause and effect have been studied in the social sciences for a long time as mentioned in this paper, see, e.g., the theory of inferred causation, causal diagrams and the identification of causal effects.

...read moreread less

Abstract: 1. Introduction to probabilities, graphs, and causal models 2. A theory of inferred causation 3. Causal diagrams and the identification of causal effects 4. Actions, plans, and direct effects 5. Causality and structural models in the social sciences 6. Simpson's paradox, confounding, and collapsibility 7. Structural and counterfactual models 8. Imperfect experiments: bounds and counterfactuals 9. Probability of causation: interpretation and identification Epilogue: the art and science of cause and effect.

...read moreread less

12,606 citations

"The Causal Mediation Formula - A Gu..." refers background or methods in this paper

...These techniques are directly applicable to the analysis of mediations (Pearl 2009, p. 128; Pearl 2011a, d; Shpitser and VanderWeele 2011), but are beyond the scope of this paper....
[...]
...To summarize, the Mediation Formula dictates that, in calculating IE, we should condition on both Z = 1 and Z = 0 and average while, in calculating DE, we should condition on only one value, X = 0, and no average need be taken....
[...]
...The Mediation Formula (8) represents the average increase in the outcome Y that the transition from X = x to X = x′ is expected to produce absent any direct effect of X on Y....
[...]
...The Mediation Formula of Eq....
[...]
...Both measures play a role in mediation analysis, and are given here a formal representation through the Mediation Formula....
[...]