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Causal Diagrams For Empirical Research
"... The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subjectmatter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if ..."
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Cited by 176 (35 self)
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The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subjectmatter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data. If so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions; otherwise, the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained. Key words: Causal inference, graph models, interventions treatment effect 1 Introduction The tools introduced in this paper are aimed at helping researchers communicate qualitative assumptions about causeeffect relationships, elucidate the ramifications of such assumptions, and derive causal inferences from a combination...
Direct and Indirect Effects
, 2005
"... The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and practical difficulties (in nonlinear models), because they cannot be isolated by holding certain variables constant. This pape ..."
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Cited by 82 (23 self)
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The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and practical difficulties (in nonlinear models), because they cannot be isolated by holding certain variables constant. This paper presents a new way of defining the effect transmitted through a restricted set of paths, without controlling variables on the remaining paths. This permits the assessment of a more natural type of direct and indirect effects, one that is applicable in both linear and nonlinear models and that has broader policyrelated interpretations. The paper establishes conditions under which such assessments can be estimated consistently from experimental and nonexperimental data, and thus extends pathanalytic techniques to nonlinear and nonparametric models.
Axioms of Causal Relevance
 Artificial Intelligence
, 1996
"... This paper develops axioms and formal semantics for statements of the form "X is causally irrelevant to Y in context Z," which we interpret to mean "Changing X will not affect Y if we hold Z constant." The axiomization of causal irrelevance is contrasted with the axiomization ..."
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Cited by 52 (13 self)
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This paper develops axioms and formal semantics for statements of the form "X is causally irrelevant to Y in context Z," which we interpret to mean "Changing X will not affect Y if we hold Z constant." The axiomization of causal irrelevance is contrasted with the axiomization of informational irrelevance, as in "Learning X will not alter our belief in Y , once we know Z." Two versions of causal irrelevance are analyzed, probabilistic and deterministic. We show that, unless stability is assumed, the probabilistic definition yields a very loose structure, that is governed by just two trivial axioms. Under the stability assumption, probabilistic causal irrelevance is isomorphic to path interception in cyclic graphs. Under the deterministic definition, causal irrelevance complies with all of the axioms of path interception in cyclic graphs, with the exception of transitivity. We compare our formalism to that of [Lewis, 1973], and offer a graphical method of proving theorems abou...
Graphs, Causality, And Structural Equation Models
, 1998
"... Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers. ..."
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Cited by 48 (14 self)
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Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers.
Confidence limits for the indirect effect: Distribution of the product and resampling methods
 Multivariate Behavioral Research
, 2004
"... The most commonly used method to test an indirect effect is to divide the estimate of the indirect effect by its standard error and compare the resulting z statistic with a critical value from the standard normal distribution. Confidence limits for the indirect effect are also typically based on cri ..."
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Cited by 46 (3 self)
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The most commonly used method to test an indirect effect is to divide the estimate of the indirect effect by its standard error and compare the resulting z statistic with a critical value from the standard normal distribution. Confidence limits for the indirect effect are also typically based on critical values from the standard normal distribution. This article uses a simulation study to demonstrate that confidence limits are imbalanced because the distribution of the indirect effect is normal only in special cases. Two alternatives for improving the performance of confidence limits for the indirect effect are evaluated: (a) a method based on the distribution of the product of two normal random variables, and (b) resampling methods. In Study 1, confidence limits based on the distribution of the product are more accurate than methods based on an assumed normal distribution but confidence limits are still imbalanced. Study 2 demonstrates that more accurate confidence limits are obtained using resampling methods, with the biascorrected bootstrap the best method overall. An indirect effect implies a causal hypothesis whereby an independent variable causes a mediating variable which, in turn, causes a dependent
An Axiomatic Characterization of Causal Counterfactuals
, 1998
"... This paper studies the causal interpretation of counterfactual sentences using a modifiable structural equation model. It is shown that two properties of counterfactuals, namely, composition and effectiveness, are sound and complete relative to this interpretation, when recursive (i.e., feedback ..."
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Cited by 45 (17 self)
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This paper studies the causal interpretation of counterfactual sentences using a modifiable structural equation model. It is shown that two properties of counterfactuals, namely, composition and effectiveness, are sound and complete relative to this interpretation, when recursive (i.e., feedbackless) models are considered. Composition and effectiveness also hold in Lewis's closestworld semantics, which implies that for recursive models the causal interpretation imposes no restrictions beyond those embodied in Lewis's framework. A third property, called reversibility, holds in nonrecursive causal models but not in Lewis's closestworld semantics, which implies that Lewis's axioms do not capture some properties of systems with feedback. Causal inferences based on counterfactual analysis are exemplified and compared to those based on graphical models.
Equivalence of the mediation, confounding, and suppression effect
 Prevention Science
, 2000
"... This paper describes the statistical similarities among mediation, confounding, and suppression. Each is quantified by measuring the change in the relationship between an independent and a dependent variable after adding a third variable to the analysis. Mediation and confounding are identical stati ..."
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Cited by 40 (1 self)
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This paper describes the statistical similarities among mediation, confounding, and suppression. Each is quantified by measuring the change in the relationship between an independent and a dependent variable after adding a third variable to the analysis. Mediation and confounding are identical statistically and can be distinguished only on conceptual grounds. Methods to determine the confidence intervals for confounding and suppression effects are proposed based on methods developed for mediated effects. Although the statistical estimation of effects and standard errors is the same, there are important conceptual differences among the three types of effects. KEY WORDS: mediation; confounding; suppression; confidence intervals. Once a relationship between two variables has been established, it is common for researchers to consider the role of a third variable in this relationship (Lazarsfeld, 1955). This paper will examine three types of third variable effectsâ€”mediation, confounding, and suppressionâ€”in which an additional variable may clarify the nature of the relationship between an independent and a dependent variable. These three concepts have largely been developed within different areas of inquiry, and although the three types of effects are conceptually distinct, they share considerable statistical similarities. Some aspects of the similarity of these concepts have been mentioned in several different articles (Olkin & Finn, 1995; Robins, 1989; Spirtes, Glymour, & Scheines, 1993; Tzelgov & Henik, 1991). In this paper, we demonstrate that mediation, confounding, and suppression effects can each be considered in terms of a general third variable model, and that point and interval estimates of mediation effects can be adapted for use in confounding and suppression frameworks. The paper focuses
Reasoning With Cause And Effect
, 1999
"... This paper summarizes basic concepts and principles that I have found to be useful in dealing with causal reasoning. The paper is written as a companion to a lecture under the same title, to be presented at IJCAI99, and is intended to supplement the lecture with technical details and pointers to mo ..."
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Cited by 37 (0 self)
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This paper summarizes basic concepts and principles that I have found to be useful in dealing with causal reasoning. The paper is written as a companion to a lecture under the same title, to be presented at IJCAI99, and is intended to supplement the lecture with technical details and pointers to more elaborate discussions in the literature. The ruling conception will be to treat causation as a computational schema devised to identify the invariant relationships in the environment, so as to facilitate reliable prediction of the effect of actions. This conception, as well as several of its satellite principles and tools, has been guiding paradigm for several research communities in AI, most notably those connected with causal discovery, troubleshooting, planning under uncertainty and modeling the behavior of physical systems. My hopes are to encourage a broader and more effective usage of causal modeling by explicating these common principles in simple and familiar mathematical form. Af...