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Applications of causally defined direct and indirect effects in mediation analysis using SEM
 University of California
"... Judea Pearl for helpful advice This paper summarizes some of the literature on causal effects in mediation analysis. It presents causallydefined direct and indirect effects for continuous, binary, ordinal, nominal, and count variables. The expansion to noncontinuous mediators and outcomes offers a ..."
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Judea Pearl for helpful advice This paper summarizes some of the literature on causal effects in mediation analysis. It presents causallydefined direct and indirect effects for continuous, binary, ordinal, nominal, and count variables. The expansion to noncontinuous mediators and outcomes offers a broader array of causal mediation analyses than previously considered in structural equation modeling practice. A new result is the ability to handle mediation by a nominal variable. Examples with a binary outcome and a binary, ordinal or nominal mediator are given using Mplus to compute the effects. The causal effects require strong assumptions even in randomized designs, especially sequential ignorability, which is presumably often violated to some extent due to mediatoroutcome confounding. To study the effects of violating this assumption, it is shown how a sensitivity analysis can be carried out. This can be used both in planning a new study and in evaluating the results of an existing study.
Trygve Haavelmo and the Emergence of Causal Calculus
, 2012
"... Haavelmo was the first to recognize the capacity of economic models to guide policies. This paper describes some of the barriers that Haavelmo’s ideas have had (and still have) to overcome, and lays out a logical framework for capturing the relationships between theory, data and policy questions. Th ..."
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Cited by 15 (5 self)
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Haavelmo was the first to recognize the capacity of economic models to guide policies. This paper describes some of the barriers that Haavelmo’s ideas have had (and still have) to overcome, and lays out a logical framework for capturing the relationships between theory, data and policy questions. The mathematical tools that emerge from this framework now enable investigators to answer complex policy and counterfactual questions using embarrassingly simple routines, some by mere inspection of the model’s structure. Several such problems are illustrated by examples, including misspecification tests, identification, mediation and introspection. Finally, we observe that modern economists are largely unaware of the benefits that Haavelmo’s ideas bestow upon them and, as a result, econometric research has not fully utilized modern advances in causal analysis. 1
Crowdsourcing Narrative Intelligence
"... Narrative intelligence is an important part of human cognition, especially in sensemaking and communicating with people. Humans draw on a lifetime of relevant experiences to explain stories, to tell stories, and to help choose the most appropriate actions in reallife settings. Manual authoring the ..."
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Cited by 10 (3 self)
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Narrative intelligence is an important part of human cognition, especially in sensemaking and communicating with people. Humans draw on a lifetime of relevant experiences to explain stories, to tell stories, and to help choose the most appropriate actions in reallife settings. Manual authoring the required knowledge presents a significant bottleneck in the creation of systems demonstrating narrative intelligence. In this paper, we describe a novel technique for automatically learning scriptlike narrative knowledge from crowdsourcing. By leveraging human workers’ collective understanding of social and procedural constructs, we can learn a potentially unlimited range of scripts regarding how realworld situations unfold. We present quantitative evaluations of the learned primitive events and the temporal ordering of events, which suggest we can identify orderings between events with high accuracy. 1.
Advantages of Monte Carlo Confidence Intervals for Indirect Effects
"... Monte Carlo simulation is a useful but underutilized method of constructing confidence intervals for indirect effects in mediation analysis. The Monte Carlo confidence interval method has several distinct advantages over rival methods. Its performance is comparable to other widely accepted methods ..."
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Cited by 9 (1 self)
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Monte Carlo simulation is a useful but underutilized method of constructing confidence intervals for indirect effects in mediation analysis. The Monte Carlo confidence interval method has several distinct advantages over rival methods. Its performance is comparable to other widely accepted methods of interval construction, it can be used when only summary data are available, it can be used in situations where rival methods (e.g., bootstrapping and distribution of the product methods) are difficult or impossible, and it is not as computerintensive as some other methods. In this study we discuss Monte Carlo confidence intervals for indirect effects, report the results of a simulation study comparing their performance to that of competing methods, demonstrate the method in applied examples, and discuss several software options for implementation in applied settings. In its simplest form, mediation occurs when the effect of an independent variable (X) on a dependent variable (Y) is transmitted via a mediator variable (M) (see Figure 1).1 This mediation effect is also commonly referred to as the indirect effect of X on Y through M. Mediation models permit researchers to test simple hypotheses about how causal processes may occur and form the building blocks of more complicated structural models. Mediation models often involve parsing the total effect (c) of X on Y into a direct effect (c′) and an indirect effect (a × b, or simply ab). These
Graphical Causal Models
, 2013
"... This chapter discusses the use of directed acyclic graphs (DAGs) for causal inference in the observational social sciences. It focuses on DAGs’ main uses, discusses central principles, and gives applied examples. DAGs are visual representations of qualitative causal assumptions: They encode resear ..."
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Cited by 8 (3 self)
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This chapter discusses the use of directed acyclic graphs (DAGs) for causal inference in the observational social sciences. It focuses on DAGs’ main uses, discusses central principles, and gives applied examples. DAGs are visual representations of qualitative causal assumptions: They encode researchers ’ beliefs about how the world works. Straightforward rules map these causal assumptions onto the associations and independencies in observable data. The two primary uses of DAGs are (1) determining the identifiability of causal effects from observed data and (2) deriving the testable implications of a causal model. Concepts covered in this chapter include identification, dseparation, confounding, endogenous selection, and over control. Illustrative applications then demonstrate that conditioning on variables at any stage in a causal process can induce as well as remove bias, that confounding is a fundamentally causal rather than an associational concept, that conventional approaches to causal mediation analysis are often biased, and that causal inference in social networks inherently faces endogenous selection bias. The chapter discusses several graphical criteria for the identification of causal effects of single, timepoint treatments (including the famous backdoor criterion), as well identification criteria for multiple, timevarying treatments.
Interpretation and Identification of Causal Mediation
, 2013
"... This paper reviews the foundations of causal mediation analysis and offers a general and transparent account of the conditions necessary for the identification of natural direct and indirect effects, thus facilitating a more informed judgment of the plausibility of these conditions in specific appli ..."
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Cited by 4 (1 self)
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This paper reviews the foundations of causal mediation analysis and offers a general and transparent account of the conditions necessary for the identification of natural direct and indirect effects, thus facilitating a more informed judgment of the plausibility of these conditions in specific applications. We show that the conditions usually cited in the literature are overly restrictive, and can be relaxed substantially, without compromising identification. In particular, we show that natural effects can be identified by methods that go beyond standard adjustment for confounders, applicable to observational studies in which treatment assignment remains confounded with the mediator or with the outcome. These identification conditions can be validated algorithmically from the diagramatic description of one’s model, and are guaranteed to produce unbiased results whenever the description is correct. The identification conditions can be further relaxed in parametric models, possibly including interactions, and permit us to compare the relative importance of several pathways, mediated by interdependent variables.
The Mathematics of Causal Relations
, 2008
"... This paper introduces empirical researchers to recent advances in causal inference and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all caus ..."
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Cited by 2 (1 self)
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This paper introduces empirical researchers to recent advances in causal inference and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, and the conditional nature of causal claims inferred from nonexperimental studies. In particular, the paper advocates a formalism based on nonparametric structural equations [Pearl, 2000a] which provides both a mathematical foundation for the analysis of counterfactuals and a conceptually transparent language for expressing causal knowledge. This framework gives rise to a friendly calculus of causation that uni es the graphical, potential outcome (NeymanRubin) and structural equation approaches and resolves longstanding problems in several of the sciences. These include questions of confounding, causal e ect estimation, policy analysis, legal responsibility, direct and indirect e ects, instrumental variables, surrogate designs, and the integration of data from experimental and observational studies.
A state space modeling approach to mediation analysis
 Journal of Educational and Behavioral Statistics
"... Mediation is a causal process that evolves over time. Thus, a study of mediation requires data collected throughout the process. However, most applications of mediation analysis use crosssectional rather than longitudinal data. Another implicit assumption commonly made in longitudinal designs for ..."
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Mediation is a causal process that evolves over time. Thus, a study of mediation requires data collected throughout the process. However, most applications of mediation analysis use crosssectional rather than longitudinal data. Another implicit assumption commonly made in longitudinal designs for mediation analysis is that the same mediation process universally applies to all members of the population under investigation. This assumption ignores the important issue of ergodicity before aggregating the data across subjects. We first argue that there exists a discrepancy between the concept of mediation and the research designs that are typically used to investigate it. Second, based on the concept of ergodicity, we argue that a given mediation process probably is not equally valid for all individuals in a population. Therefore, the purpose of this article is to propose a twofaceted solution. The first facet of the solution is that we advocate a singlesubject timeseries design that aligns data collection with researchers ’ conceptual understanding of mediation. The second facet is to introduce a flexible statistical method—the state space
Correlation and Causation – the logic of cohabitation
, 2012
"... Recent advances in graphical models and the logic of causation have given rise to new ways in which scientists analyze causeeffect relationships. Today, we understand precisely the conditions under which causal relationships can be inferred from data, the assumptions and measurements needed for pre ..."
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Recent advances in graphical models and the logic of causation have given rise to new ways in which scientists analyze causeeffect relationships. Today, we understand precisely the conditions under which causal relationships can be inferred from data, the assumptions and measurements needed for predicting the effect of interventions (e.g., treatments on recovery) and how retrospective counterfactuals (e.g., “I should have done it differently”) can be reasoned about algorithmically or derived from data. The paper provides a brief account of these developments.