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21
Transportability of causal and statistical relations: A formal approach
 In Proceedings of the TwentyFifth National Conference on Artificial Intelligence. AAAI Press, Menlo Park, CA
, 2011
"... We address the problem of transferring information learned from experiments to a different environment, in which only passive observations can be collected. We introduce a formal representation called “selection diagrams ” for expressing knowledge about differences and commonalities between environm ..."
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Cited by 25 (12 self)
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We address the problem of transferring information learned from experiments to a different environment, in which only passive observations can be collected. We introduce a formal representation called “selection diagrams ” for expressing knowledge about differences and commonalities between environments and, using this representation, we derive procedures for deciding whether effects in the target environment can be inferred from experiments conducted elsewhere. When the answer is affirmative, the procedures identify the set of experiments and observations 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.
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
Linear models: A useful “microscope” for causal analysis
 Department of Computer Science, University of California
"... This note reviews basic techniques of linear path analysis and demonstrates, using simple examples, how causal phenomena of nontrivial character can be understood, exemplified and analyzed using diagrams and a few algebraic steps. The techniques allow for swift assessment of how various features of ..."
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Cited by 15 (6 self)
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This note reviews basic techniques of linear path analysis and demonstrates, using simple examples, how causal phenomena of nontrivial character can be understood, exemplified and analyzed using diagrams and a few algebraic steps. The techniques allow for swift assessment of how various features of the model impact the phenomenon under investigation. This includes: Simpson’s paradox, casecontrol bias, selection bias, collider bias, reverse regression, bias amplification, near instruments, and measurement errors. 1
Causal inference by surrogate experiments: zidentifiability
, 2012
"... We address the problem of estimating the effect of intervening on a set of variables X from experiments on a different set, Z, that is more accessible to manipulation. This problem, which we call zidentifiability, reduces to ordinary identifiability when Z = ∅ and, like the latter, can be given sy ..."
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Cited by 14 (7 self)
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We address the problem of estimating the effect of intervening on a set of variables X from experiments on a different set, Z, that is more accessible to manipulation. This problem, which we call zidentifiability, reduces to ordinary identifiability when Z = ∅ and, like the latter, can be given syntactic characterization using the docalculus [Pearl, 1995; 2000]. We provide a graphical necessary and sufficient condition for zidentifiability for arbitrary sets X, Z, and Y (the outcomes). We further develop a complete algorithm for computing the causal effect of X on Y using information provided by experiments on Z. Finally, we use our results to prove completeness of docalculus relative to zidentifiability, a result that does not follow from completeness relative to ordinary identifiability.
Recovering from selection bias in causal and statistical inference
"... Selection bias is caused by preferential exclusion of units from the samples and represents a major obstacle to valid causal and statistical inferences; it cannot be removed by randomized experiments and can rarely be detected in either experimental or observational studies. In this paper, we provi ..."
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Cited by 13 (7 self)
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Selection bias is caused by preferential exclusion of units from the samples and represents a major obstacle to valid causal and statistical inferences; it cannot be removed by randomized experiments and can rarely be detected in either experimental or observational studies. In this paper, we provide complete graphical and algorithmic conditions for recovering conditional probabilities from selection biased data. We also provide graphical conditions for recoverability when unbiased data is available over a subset of the variables. Finally, we provide a graphical condition that generalizes the backdoor criterion and serves to recover causal effects when the data is collected under preferential selection.
Invited Commentary: Understanding Bias Amplification
, 2011
"... In choosing covariates for adjustment or inclusion in propensity score analysis, researchers must weigh the benefit of reducing confounding bias carried by those covariates against the risk of amplifying residual bias carried by unmeasured confounders. The latter is characteristic of covariates that ..."
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Cited by 12 (3 self)
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In choosing covariates for adjustment or inclusion in propensity score analysis, researchers must weigh the benefit of reducing confounding bias carried by those covariates against the risk of amplifying residual bias carried by unmeasured confounders. The latter is characteristic of covariates that act like instrumental variables (IV); that is, variables that are more strongly associated with the exposure than with the outcome (1). In this issue of the journal, Myers et al. (2) compare the bias amplification of a nearIV confounder with its biasreducing potential and suggest that, in practice, the latter outweighs the former. This commentary sheds broader light on this comparison by considering the cumulative effects of conditioning on multiple covariates, and showing that bias amplification may build up at a faster rate than bias reduction. We further derive a partial order on sets of covariates which reveals preference for conditioning on
Adjustments and their Consequences  Collapsibility Analysis using Graphical Models
, 2010
"... We consider probabilistic and graphical rules for detecting situations in which a dependence of one variable on another is altered by adjusting for a third variable (i.e., noncollapsibility), whether that dependence is causal or purely predictive. We focus on distinguishing situations in which adjus ..."
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Cited by 12 (3 self)
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We consider probabilistic and graphical rules for detecting situations in which a dependence of one variable on another is altered by adjusting for a third variable (i.e., noncollapsibility), whether that dependence is causal or purely predictive. We focus on distinguishing situations in which adjustment will reduce, increase, or leave unchanged the degree of bias in an association of two variables when that association is taken to represent a causal effect of one variable on the other. We then consider situations in which adjustment may partially remove or introduce a potential source of bias in estimating causal effects, and some additional special cases useful for casecontrol studies, cohort studies with loss, and trials with noncompliance (nonadherence).
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.
A General Algorithm for Deciding Transportability of Experimental Results
, 2013
"... Generalizing empirical findings to new environments, settings, or populations is essential in most scientific explorations. This article treats a particular problem of generalizability, called “transportability”, defined as a license to transfer information learned in experimental studies to a diff ..."
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Cited by 10 (5 self)
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Generalizing empirical findings to new environments, settings, or populations is essential in most scientific explorations. This article treats a particular problem of generalizability, called “transportability”, defined as a license to transfer information learned in experimental studies to a different population, on which only observational studies can be conducted. Given a set of assumptions concerning commonalities and differences between the two populations, Pearl and Bareinboim [1] derived sufficient conditions that permit such transfer to take place. This article summarizes their findings and supplements them with an effective procedure for deciding when and how transportability is feasible. It establishes a necessary and sufficient condition for deciding when causal effects in the target population are estimable from both the statistical information available and the causal information transferred from the experiments. The article further provides a complete algorithm for computing the transport formula, that is, a way of combining observational and experimental information to synthesize biasfree estimate of the desired causal relation. Finally, the article examines the differences between transportability and other variants of generalizability.
The Deductive Approach to Causal Inference
, 2014
"... This paper reviews concepts, principles and tools that have led to a coherent mathematical theory that unifies the graphical, structural, and potential outcome approaches to causal inference. The theory provides solutions to a number of pending problems in causal analysis, including questions of con ..."
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Cited by 2 (0 self)
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This paper reviews concepts, principles and tools that have led to a coherent mathematical theory that unifies the graphical, structural, and potential outcome approaches to causal inference. The theory provides solutions to a number of pending problems in causal analysis, including questions of confounding control, policy analysis, mediation, missing data and the integration of data from diverse studies.