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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 247 (37 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...
On The Identification Of Nonparametric Structural Models
, 1997
"... In this paper we study the identifiability of nonparametric models, that is, models in which both the functional forms of the equations and the probability distributions of the disturbances remain unspecified. Identifiability in such models does not mean uniqueness of parameters but rather uniquenes ..."
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Cited by 2 (1 self)
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In this paper we study the identifiability of nonparametric models, that is, models in which both the functional forms of the equations and the probability distributions of the disturbances remain unspecified. Identifiability in such models does not mean uniqueness of parameters but rather uniqueness of the set of predictions of interest to the investigator. For example, predicting the effects of changes, interventions, and control. We provide sufficient and necessary conditions for identifying a set of causal predictions of the type: "Find the distribution of Y , assuming that X is controlled by external intervention", where Y and X are arbitrary variables of interest. Whenever identifiable, such predictions can be expressed in closed algebraic form, in terms of observed distributions. We also show how the identifying criteria can be verified qualitatively, by inspection, using the graphical representation of the structural model. When compared to standard identifiability tests of lin...
A Causal Calculus for Statistical Research
, 1996
"... A calculus is proposed that admits two conditioning operators: ordinary Bayes conditioning, P (yjX = x), and causal conditioning, P (yjset(X = x)), that is, conditioning P (y) on holding X constant (at x) by external intervention. This distinction, which will be supported by three rules of inferen ..."
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Cited by 1 (0 self)
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A calculus is proposed that admits two conditioning operators: ordinary Bayes conditioning, P (yjX = x), and causal conditioning, P (yjset(X = x)), that is, conditioning P (y) on holding X constant (at x) by external intervention. This distinction, which will be supported by three rules of inference, will permit us to derive probability expressions for the combined effect of observations and interventions. The resulting calculus yields simple solutions to a number of interesting problems in causal inference and should allow rankandfile researchers to tackle practical problems that are generally considered too hard, or impossible. Examples are: 1. Deciding whether the information available in a given observational study is sufficient for obtaining consistent estimates of causal effects. 2. Deriving algebraic expressions for causal effect estimands. 3. Selecting measurements that would render randomized experiments unnecessary. 4. Selecting a set of indirect (randomized) experiments ...
(Draft Copy) On the Statistical Interpretation of Structural Equations
"... F28.92> y 2 and x 1 were fixed" using the model described in (1), the result does not match the interpretation advanced by Goldberger. Specifically, assuming u 1 and u 2 are zeromean disturbances (independent on X 1 and X 2 ), Wermuth finds E(Y 1 j Y 2 = y 2 ; X 1 = x 1 ) 6= a 1 y 2 + a 2 ..."
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F28.92> y 2 and x 1 were fixed" using the model described in (1), the result does not match the interpretation advanced by Goldberger. Specifically, assuming u 1 and u 2 are zeromean disturbances (independent on X 1 and X 2 ), Wermuth finds E(Y 1 j Y 2 = y 2 ; X 1 = x 1 ) 6= a 1 y 2 + a 2 x 1 (unless further assumptions are made) and concludes that "the parameters in (1) cannot have the meaning Arthur Goldberger claims they have." 1 This exchange between a statistician and an economist exemplifies the long history of tension between regression analysis and structural equations modeling, which dates back to the inception of the latter by Wright [27],
(Draft Copy) On the Statistical Interpretation of Structural Equations
"... an economist might arrive at a model like this: ..."
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