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The Mediation Formula: A guide to the assessment of causal pathways in nonlinear models
 STATISTICAL CAUSALITY. FORTHCOMING.
, 2011
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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
The causal mediation formula – a guide to the assessment of pathways and mechanisms
 Prevention Science DOI: 10.1007/s1112101102701, Online
, 2012
"... Recent advances in causal inference have given rise to a general and easytouse formula for assessing the extent to which the effect of one variable on another is mediated by a third. This socalled Mediation Formula is applicable to nonlinear models with both discrete and continuous variables, and ..."
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Cited by 10 (3 self)
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Recent advances in causal inference have given rise to a general and easytouse formula for assessing the extent to which the effect of one variable on another is mediated by a third. This socalled Mediation Formula is applicable to nonlinear models with both discrete and continuous variables, and permits the evaluation of pathspecific effects with minimal assumptions regarding the datagenerating 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 “mediatedeffect ” and show how to estimate the two components in nonlinear systems with continuous and categorical variables.
Some Thoughts Concerning Transfer Learning, with Applications to Metaanalysis and Datasharing Estimation
, 2012
"... A deeply entrenched axiom in the theory of learning states that the more one learns the easier it is to learn. In other words, the more proficient one becomes in performing familiar tasks, the easier it is to learn new tasks. This phenomenon, long recognized by psychologists and educators, has also ..."
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Cited by 6 (4 self)
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A deeply entrenched axiom in the theory of learning states that the more one learns the easier it is to learn. In other words, the more proficient one becomes in performing familiar tasks, the easier it is to learn new tasks. This phenomenon, long recognized by psychologists and educators, has also been demonstrated in machine learning, especially in selftaught
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.
External Validity and Transportability: A Formal Approach
, 2011
"... We provide a formal definition of the notion of “transportability, ” or “external validity, ” as a license to transfer causal information from experimental studies to a different population in which only observational studies can be conducted. We introduce a formal representation called “selection d ..."
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Cited by 1 (0 self)
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We provide a formal definition of the notion of “transportability, ” or “external validity, ” as a license to transfer causal information from experimental studies to a different population in which only observational studies can be conducted. We introduce a formal representation called “selection diagrams ” for expressing differences and commonalities between populations of interest and, using this representation, we derive procedures for deciding whether causal effects in the target population can be inferred from experimental findings in a different population. When the answer is affirmative, the procedures identify the set of experimental and observational studies that need be conducted to license the transport. We further discuss how transportability analysis can guide the transfer of knowledge in nonexperimental learning to minimize remeasurement cost and improve prediction power.
CLINICAL TRIALS ARTICLE Clinical Trials 2013; 10: 363–377
"... Accommodating missingness when assessing surrogacy via principal stratification ..."
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Accommodating missingness when assessing surrogacy via principal stratification
Comment on “Causal inference, probability theory,
, 2013
"... Modern causal inference owes much of its progress to a strict and crisp distinction between probabilistic and causal information. This distinction recognizes that probability theory is insufficient for posing causal questions, let alone answering them, and dictates that every exercise in causal infe ..."
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Modern causal inference owes much of its progress to a strict and crisp distinction between probabilistic and causal information. This distinction recognizes that probability theory is insufficient for posing causal questions, let alone answering them, and dictates that every exercise in causal inference must commence with some extra knowledge that cannot be expressed in probability alone. 1 The paper by Baker attempts to overturn this distinction and argues that “probability theory is a desirable and sufficient basis for many topics in causal inference. ” My comments will disprove Baker’s claim, in the hope of convincing readers of the importance of keeping the boundaries between probabilistic and causal concepts crisp and visible. Baker’s argument begins with: “...besides explaining such causal graph topics as Mbias (adjusting for a collider) and bias amplification and attenuation (when adjusting for instrumental variable), probability theory is also the foundation of the paired availability design for historical control ” (abstract). While I am not versed in the intricacies of “paired availability design ” (Google Scholar lists only a handful of entries in this category), I doubt it can be based solely on probabilities. Indeed, Baker himself resorts to counterfactuals and other nonprobabilistic notions2 in explaining the research questions a “paired availability design ” attempts to answer. I am quite familiar however with the concepts of “Mbias, ” “bias, ” “Simpson’s paradox, ” and “instrumental variable ” which I will show to have no interpretation in probability theory alone. I will start with the concept of “instrumental variable ” which should be familiar to most readers, and which is often mistaken to have probabilistic definition (see [2, pp. 387–389]). Assume we have a joint distribution P (x, y, z) defined on three variables X, Y, and Z. We ask: What condition should P satisfy in order for Z to qualify as an instrumental variable relative to the pair (X, Y). It is well known that, if X is 1 Cartwright [1] summarized this limitation in a wellknown slogan: “no causes in, no causes out.”
1 1 Instrumental Variable Estimation When Compliance is not Deterministic: The Stochastic Monotonicity Assumption
, 2014
"... Abstract: The instrumental variables (IV) method is a method for making causal inferences about the effect of a treatment based on an observational study in which there are unmeasured confounding variables. The method requires a valid IV, a variable that is independent of the unmeasured confounding ..."
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Abstract: The instrumental variables (IV) method is a method for making causal inferences about the effect of a treatment based on an observational study in which there are unmeasured confounding variables. The method requires a valid IV, a variable that is independent of the unmeasured confounding variables and is associated with the treatment but which has no effect on the outcome beyond its effect on the treatment. An additional assumption that is often made for the IV method is deterministic monotonicity, which is an assumption that for each subject, the level of the treatment that a subject would take if given a level of the IV is a monotonic increasing function of the level of the IV. Under deterministic monotonicity, the IV method identifies the average treatment effect for the compliers (those subject who would take the treatment if encouraged to do so by the IV and not take the treatment if not encouraged). However, deterministic monotonicity is sometimes not realistic. We introduce a stochastic monotonicity condition which relaxes deterministic monotonicity in that it does not require that a monotonic increasing relationship hold within subjects between the levels of the IV and the level of the treatment that the subject would take if given a level of the IV, but only that a monotonic increasing relationship hold