The DOI matches its Crossref record; 148 of the 186 references it cites were found in a registry or an index; 5 of the 68 sources its claims cite were checked for support.
An Introduction to Causal Inference
Open accessAbstract
This paper summarizes recent advances in causal inference and underscores 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 underlie all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: those about (1) the effects of potential interventions, (2) probabilities of counterfactuals, and (3) direct and indirect effects (also known as "mediation"). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both. The tools are demonstrated in the analyses of mediation, causes of effects, and probabilities of causation.
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Claims the paper makes
101 Own interpretation · 55 No basis given · 29 Sources not found · 9 No full text of the sources · 9 Not checked yet · 2 Partly supported · 1 Supported · 1 Supported so far · 1 Couldn’t confirm · accuracy not yet measured
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“Note also that the truncated factorization formula is not restricted to interventions on a single variable; it is applicable to simultaneous or sequential interventions such as those invoked in the analysis of time varying treatment with time varying confounders (Robins, 1986, Arjas andParner, 2004).”
§ An Introduction to Causal Inference > 14
What the sources say
- Supportedcites Robins, 1986 source
The paper’s “Definition of a treatment” allows a possibly joint covariate intervention at a given time. “Causal inference in alternative designed randomized trials” describes treatments assigned at successive times based on past covariate history, and the “G-Computation Algorithm” calculates outcomes under those treatment strategies. Together, these passages support the cited example of simultaneous or sequential interventions, although the paper calls its calculation the G-computation algorithm rather than the truncated factorization formula. (LLM, conf=0.87)
- Not matchedcites Arjas andParner, 2004
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Supported
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“A more recent analysis (Tian and Pearl, 2002) shows that the key to identifiability lies not in blocking paths between X and Y but, rather, in blocking paths between X and its immediate successors on the pathways to Y.”
§ An Introduction to Causal Inference > 3.3.3 General control of confounding
What the sources say
- Partly supportedcites Tian and Pearl, 2002 sourceExperimental — accuracy not yet measured
The Conclusion says the key is blocking back-door paths between X and its immediate successors on pathways to the outcomes, rather than back-door paths between X and the outcomes. The citing sentence captures that contrast but omits “back-door,” making its claim about paths generally broader than the source supports. (LLM, conf=0.86)
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Partly supported
Every source the paper cites for this claim was checked and supports it.
In the paper
“Theorem 3 (Tian and Pearl, 2002) A sufficient condition for identifying the causal effect P(y|do(x)) is that every path between X and any of its children traces at least one arrow emanating from a measured variable.”
§ An Introduction to Causal Inference > 3.3.3 General control of confounding
What the sources say
- Supportedcites Tian and Pearl, 2002 source
The Introduction states that the effect of a singleton X is identifiable when there is no consecutive sequence of confounding arcs between X and its children. Theorem 3’s proof (section labeled “Induction step”) expresses this as no bidirected path connecting X to any child; a path containing an arrow from a measured variable is not an all-bidirected path. Theorem 3 concerns the effect on all other measured variables, from which the effect on Y can be obtained by marginalization. (LLM, conf=0.86)
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Supported
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“As expected, the distribution of Z is not affected by the intervention, since P(z|do(x 0 )) = ∑ y P(z,y|do(x 0 )) = ∑ y P(z)P(y|x 0 ) = P(z)”
§ An Introduction to Causal Inference > 3.2.3 Causal effects from data and graphs
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Naturally, if we were to apply this derivation to the linear models of Fig. 1(a) or 1(b), we would get the expected dependence between Y and the intervention do(x 0 ): E(Y|do(x 0 )) = E(f Y (x 0 ,u Y )) = E(β x 0 + u Y ) = β x 0”
§ An Introduction to Causal Inference > 3.2.2 Estimating the effect of interventions
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“and the causal effect of X on Y can be obtained immediately by marginalizing over the Z variables, giving P(y|do(x 0 )) = ∑ z 1 ,z 2 ,z 3 P(z 1 )P(z 2 )P(z 3 |z 1 ,z 2 )P(y|z 2 ,z 3 ,x 0 )”
§ An Introduction to Causal Inference > 14
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“For example, the variable Z 3 in Fig. 4, though it is a member of every sufficient set and hence a confounder, can be unassociated with both Y and X (Pearl, 2000a, p. 195).”
§ An Introduction to Causal Inference > Definition 3 (Admissible sets -the back-door criterion)
What the sources say
- Not matchedcites Pearl, 2000a, p. 195
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In our example of Fig. 2(b), the distribution P(z,y|do(x 0 )) associated with the modified model is given by P(z,y|do(x 0 )) = P(z)P(y|x 0 )”
§ An Introduction to Causal Inference > 3.2.3 Causal effects from data and graphs
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“the absence of any dashed arc between Z and {Y,X} translates into the independence restriction”
§ An Introduction to Causal Inference > 5.3 Combining graphs and potential outcomes
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The readers can easily verify that, in linear systems, the controlled direct effect reduces to the path coefficient of the link X → Y (see footnote 12) regardless of whether confounders are present (as in Fig. 6(b)) and regardless of whether the error terms are correlated or not.”
§ An Introduction to Causal Inference > 38
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- It may state two separate claims as one. 52
- Probably not a substantial claim. 61
- The quote only partly states this claim. 3
The sources with a verdict support this claim; the rest weren’t checked yet, have no full text we could read, or their verdicts aren’t rated yet.
In the paper
“the algebraic machinery offered by the counterfactual notation, Y x (u), once a problem is properly formalized, can be extremely powerful in refining assumptions (Angrist et al., 1996, Heckman andVytlacil, 2005), deriving consistent estimands (Robins, 1986), bounding probabilities of necessary and sufficient causation (Tian and Pearl, 2000), and combining data from experimental and nonexperimental”
§ An Introduction to Causal Inference > 34
What the sources say
- Not checked — no full text of the sourcecites Angrist et al., 1996 source
- Supportedcites Robins, 1986 source
The paper’s “Graphical approach to causal inference in observational survival studies” section explicitly sets out to determine which causal parameters can be consistently estimated from observed data and to develop an algorithm to estimate them. This supports the portion of the citing sentence attached to Robins (1986): deriving consistent estimands. Page numbers are unavailable in our copy. (LLM, conf=0.93)
- Not checked — no full text of the sourcecites Tian and Pearl, 2000 source
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“They are assumed to be connected to observed variables via consistency constraints (Robins, 1986) such as X = x =⇒ Y x = Y,(32)”
§ An Introduction to Causal Inference > 5.1 The "black-box" missing-data paradigm
What the sources say
- Could not verifycites Robins, 1986 sourceExperimental — accuracy not yet measured
The 'Definition of a treatment' section discusses hypothetical survival histories under treatment, and Section 2C.3 relates planned and observed exposure histories. Neither passage states that a hypothetical outcome equals the observed outcome when the hypothetical treatment matches the treatment received. Searches for consistency and that outcome-equality condition did not find it in our copy. (LLM, conf=0.68)
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- Could not verify
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Using a similar derivation, though somewhat more involved, we can show that P(y|do(x)) is identifiable and given by the conditional probability P(y|x).”
§ An Introduction to Causal Inference > 3.2.2 Estimating the effect of interventions
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“while that of Y is sensitive to x 0 , and is given by P(y|do(x 0 )) = ∑ z P(z,y|do(x 0 )) = ∑ z P(z)P(y|x 0 ) = P(y|x 0 )”
§ An Introduction to Causal Inference > 3.2.3 Causal effects from data and graphs
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“We will see that, despite our ignorance of f X , f Y , f Z and P(u), E(Y|do(x 0 )) is nevertheless identifiable and is given by the conditional expectation E(Y|X = x 0 ).”
§ An Introduction to Causal Inference > 3.2.2 Estimating the effect of interventions
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“it is hardly straightforward to show that the assumptions of Eqs. ( 40)-( 41) imply the conditional independence (Y x ⊥⊥ Z|{X z ,X}) but do not imply the conditional independence (Y x ⊥⊥ Z|X).”
§ An Introduction to Causal Inference > 5.3 Combining graphs and potential outcomes
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Second, the total effect is not the sum of the direct and indirect effects.Instead, we have:”
§ An Introduction to Causal Inference > 42
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one. The quote only partly states this claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Comparing (59) and ( 54) reveals that the approximate method always underestimates the indirect effect and the distortion is minimal for high values of P(x = 1) and (1p x ).”
§ An Introduction to Causal Inference > Additional information
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The error terms e_x, e_z, and e_xz are three independent Bernoulli variables with probabilities p_x, p_z, and p_xz, respectively.
- The authors state this as an assumption: The assumption of nonconfoundedness permits use of the Mediation Formula for estimating the Z-mediated effect of X on Y.
In the paper
“In particular, it can be shown (Pearl, 2001) that expression (43) is both valid and identifiable in Markovian models (i.e., no unobserved confounders) where each term on the right can be reduced to a”
§ An Introduction to Causal Inference > 6.1.3 Natural direct effects
What the sources say
- Not matchedcites Pearl, 2001
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: Certain assumptions of no confounding are valid, or the model is Markovian with no unobserved confounders.
- Not matched
In the paper
“We thus obtained the standard expressions for indirect effects in linear systems, which can be estimated either as a difference in two regression coefficients (Eq. 53) or a product of two regression coefficients (Eq.52), with Y regressed on both X and Z.”
§ An Introduction to Causal Inference > Additional information
What the sources say
- Not matchedcites MacKinnon et al., 2007b
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The assumption of nonconfoundedness permits use of the Mediation Formula for estimating the Z-mediated effect of X on Y.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“If however we were to apply the approximation in (57) to data generated by the nonlinear model of Fig. 7, a distorted solution would ensue;”
§ An Introduction to Causal Inference > 42
hedgeddirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one. The quote only partly states this claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“If the correct data-generating process was the linear model of (50), we would obtain the expected estimates a 2 = c z ,E(z|x )-E(z|x ) = b x (xx) and”
§ An Introduction to Causal Inference > 42
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“We see that DE x,x (Y), the natural direct effect of the transition from x to x , involves probabilities of nested counterfactuals and cannot be written in terms of the do(x) operator.”
§ An Introduction to Causal Inference > 6.1.3 Natural direct effects
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“When the outcome Y is binary (e.g., recovery, or hiring) the ratio (1 -IE/TE) represents the fraction of responding individuals who owe their response to direct paths, while (1 -DE/TE) represents the fraction who owe their response to Z-mediated paths.”
§ An Introduction to Causal Inference > 42
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In linear systems, the direct effect is fully specified by the path coefficient attached to the link from X to Y; therefore, the direct effect is independent of the values at which we hold Z.”
§ An Introduction to Causal Inference > 6.1.3 Natural direct effects
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Demystifying enigmatic notions such as”
§ An Introduction to Causal Inference > 3 Structural Models, Diagrams, Causal Effects, and Counterfactuals
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
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Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Note also that both assumptions are causal, not associational, since none can be determined from the joint density of the observed variables, X and Y; the association between the unobserved terms, U Y and U X , can only be uncovered in an experimental setting; or (in more intricate models, as in Fig. 5) from other causal assumptions.”
§ An Introduction to Causal Inference > 3.1 A brief introduction to structural equation models
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Solidifying the mathematical foundations of the potential-outcome model, and formulating the counterfactual foundations of structural equation models.”
§ An Introduction to Causal Inference > 3 Structural Models, Diagrams, Causal Effects, and Counterfactuals
plaindirect- Asserted: passes — The authors put it forward as true.
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- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Reducing the evaluation of”
§ An Introduction to Causal Inference > 3 Structural Models, Diagrams, Causal Effects, and Counterfactuals
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Had any of these two links been added to the diagram, we would not have been able to identify the direct effect β .”
§ An Introduction to Causal Inference > 3.1 A brief introduction to structural equation models
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The definition, axiomatization and algorithmization of counterfactuals and joint probabilities of counterfactuals”
§ An Introduction to Causal Inference > 3 Structural Models, Diagrams, Causal Effects, and Counterfactuals
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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Probably not a substantial claim.
None of the sources cited for this claim have been checked yet.
In the paper
“Although the basic elements of SCM were introduced in the mid 1990's (Pearl, 1995), and have been adapted widely by epidemiologists (Greenland, Pearl, andRobins, 1999, Glymour andGreenland, 2008), statisticians (Cox andWermuth, 2004, Lauritzen, 2001), and social scientists (Morgan and Winship, 2007), its potentials as a comprehensive theory of causation are yet to be fully utilized.”
§ An Introduction to Causal Inference > 3 Structural Models, Diagrams, Causal Effects, and Counterfactuals
What the sources say
- Not matchedcites Pearl, 1995
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites Greenland, Pearl, andRobins, 1999
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not checked — no full text of the sourcecites Morgan and Winship, 2007
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Not matched
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“Weeding out myths and misconceptions from outdated traditions (Meek and Glymour, 1994, Greenland et al., 1999, Cole and Hernan, 2002, Arah, 2008, Shrier, 2009, Pearl, 2009c).”
§ An Introduction to Causal Inference > 3 Structural Models, Diagrams, Causal Effects, and Counterfactuals
What the sources say
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Although each causal assumption in isolation cannot be tested, the sum total of all causal assumptions in a model often has testable implications.”
§ An Introduction to Causal Inference > 3.1 A brief introduction to structural equation models
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The structural theory that we use in this survey satisfies the criteria above.”
§ An Introduction to Causal Inference > 3 Structural Models, Diagrams, Causal Effects, and Counterfactuals
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“a missing arrow represents a claim of zero influence, while a missing double arrow represents a claim of zero covariance.”
§ An Introduction to Causal Inference > 3.1 A brief introduction to structural equation models
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In other words, S must be associated with X and, simultaneously, associated with Y, given X.”
§ An Introduction to Causal Inference > Definition 3 (Admissible sets -the back-door criterion)
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Tests for c-equivalence (27) are fairly easy to perform, and they can also be assisted by propensity scores methods.”
§ An Introduction to Causal Inference > 3.3.2 Confounding equivalence -a graphical test
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
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Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“Theorem 2 (Pearl and Paz, 2009) Let Z and T be two sets of variables in G, containing no descendant of X.A necessary and sufficient conditions for Z and T to be c-equivalent is that at least one of the following conditions holds: 1. Z m = T m , (i.e., the Markov boundary of Z coincides with that of T) 2. Z and T are admissible (i.e., satisfy the back-door condition)”
§ An Introduction to Causal Inference > 3.3.2 Confounding equivalence -a graphical test
What the sources say
- Not matchedcites Pearl and Paz, 2009
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Correlations may only impede our ability to estimate β from nonexperimental data, but will not change its definition as given in ( 14).”
§ An Introduction to Causal Inference > 3.2.2 Estimating the effect of interventions
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
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Probably not a substantial claim. It may state two separate claims as one.
In the paper
“This special handling of collision nodes (or colliders, e.g., Z → X←U X ) reflects a general phenomenon known as Berkson's paradox (Berkson, 1946), whereby observations on a common consequence of two independent causes render those causes dependent.”
§ An Introduction to Causal Inference > Definition 1 (d-separation)
What the sources say
- Not checked — no full text of the sourcecites Berkson, 1946 source
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Non-Markovian models, such as those involving correlated errors (resulting from unmeasured confounders), permit identification only under certain conditions, and these conditions too can be determined from the graph structure (Section 3.3).”
§ An Introduction to Causal Inference > 3.2.3 Causal effects from data and graphs
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“From this distribution, one is able to assess treatment efficacy by comparing aspects of this distribution at different levels of x 0 .”
§ An Introduction to Causal Inference > 3.2.1 Representing interventions
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The conditional independencies entailed by d-separation constitute the main opening through which the assumptions embodied in structural equation models can confront the scrutiny of nonexperimental data.”
§ An Introduction to Causal Inference > Definition 1 (d-separation)
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“We see that the derivation of (13) was enabled by two assumptions; first, Y is a function of X and U Y only, and, second, U Y is independent of {U Z ,U X }, hence of X.”
§ An Introduction to Causal Inference > 3.2.2 Estimating the effect of interventions
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The back-door criterion allows us to write Eq. ( 25) directly, by selecting a sufficient set S directly from the diagram, without manipulating the truncated factorization formula.”
§ An Introduction to Causal Inference > Definition 3 (Admissible sets -the back-door criterion)
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that this formula corresponds precisely to what is commonly called”
§ An Introduction to Causal Inference > 14
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Such an extension, based on simulating hypothetical interventions in the model, was proposed in (Haavelmo, 1943, Strotz and Wold, 1960, Spirtes, Glymour, and Scheines, 1993, Pearl, 1993a, 2000a, Lindley, 2002) and has led to new ways of defining and estimating causal effects in nonlinear and nonparametric models (that is, models in which the functional form of the equations is unknown).”
§ An Introduction to Causal Inference > 3.2 From linear to nonparametric models and graphs
What the sources say
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The chain model of Fig. 2(a), for example, encodes seven causal assumptions, each corresponding to a missing arrow or a missing double-arrow between a pair of variables.None of those assumptions is testable in isolation, yet the totality of all those assumptions implies that Z is unassociated with Y in every stratum of X.”
§ An Introduction to Causal Inference > 3.1 A brief introduction to structural equation models
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
In the paper
“As noted by Robins, the formula dictates an adjustment for covariates (e.g., Z 3 ) that might be affected by previous treatments (e.g., Z 2 ).”
§ An Introduction to Causal Inference > 14
What the sources say
- Not matchedcites Robins
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
hedgeddirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“The graphical tools presented in this section unveil the character of these covariates and show precisely what covariates should, and should not be included in the conditioning set for propensity-score matching (see also (Pearl andPaz, 2009, Pearl, 2009e)).”
§ An Introduction to Causal Inference > 3.3.4 From identification to estimation
What the sources say
- Not matchedcites Pearl andPaz, 2009
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites Pearl, 2009e
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
boostedconditional- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Queries about causal effects (written P(y|do(x)) in the structural analysis) are phrased as queries about the marginal distribution of the counterfactual variable of interest, written P * (Y x = y).”
§ An Introduction to Causal Inference > 5.1 The "black-box" missing-data paradigm
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Such assumptions are cast in a language so far removed from ordinary understanding of scientific theories that, for all practical purposes, they cannot be comprehended or ascertained by ordinary mortals.”
§ An Introduction to Causal Inference > 5.2 Problem formulation and the demystification of "ignorability"
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Identification of counterfactual queries, on the other hand, often require a symbiosis of both algebraic and graphical techniques.”
§ An Introduction to Causal Inference > 4.3 Identification, estimation, and approximation
plaincorrelational- Asserted: passes — The authors put it forward as true.
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- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Equation ( 34) generalizes (32) to cases where Z is held fixed, at z.”
§ An Introduction to Causal Inference > 5.1 The "black-box" missing-data paradigm
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“causal conclusions are only as valid as the causal assumptions upon which they rest.”
§ An Introduction to Causal Inference > 5.2 Problem formulation and the demystification of "ignorability"
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
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Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Even the most experienced potential-outcome expert would be unable to discern whether any subset Z of covariates in Fig. 4 would satisfy this conditional independence condition.”
§ An Introduction to Causal Inference > 5.2 Problem formulation and the demystification of "ignorability"
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
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Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This framework is not a contender for a comprehensive theory of causation for it is subsumed by the structural theory and excludes ordinary cause-effect relationships from its assumption vocabulary.”
§ An Introduction to Causal Inference > 5 The Potential Outcome Framework
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
In the paper
“Shpitser and Pearl (2006) have further extended this theorem by (1) presenting a necessary and sufficient condition for identification, and (2) extending the condition from causal effects to any counterfactual expression.”
§ An Introduction to Causal Inference > 3.3.3 General control of confounding
What the sources say
- Not matchedcites Shpitser and Pearl (2006)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“When e includes all factors u, we have a deterministic, unit-level causation on our hand; when e contains only a few known attributes (e.g., age, income, occupation etc.) while others are assigned probabilities, a population-level analysis ensues.”
§ An Introduction to Causal Inference > 3.4 Counterfactual analysis in structural models
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Structural equation models, in their counterfactual reading, have removed this lingering difficulty by providing the needed language for causal analysis.”
§ An Introduction to Causal Inference > 4.2 Explicating causal assumptions
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
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Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“More importantly, investigators must keep in mind that only a tiny fraction of any kernel lends itself to statistical tests, the bulk of it must remain untestable, at the mercy of scientific judgment.”
§ An Introduction to Causal Inference > 4.3 Identification, estimation, and approximation
plain- Asserted: passes — The authors put it forward as true.
- Checkable: unclear — It is unclear whether it could be checked against evidence.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“To communicate scientific knowledge, the potential-outcome analyst must express assumptions as constraints on P * , usually in the form of conditional independence assertions involving counterfactual variables.”
§ An Introduction to Causal Inference > 5.2 Problem formulation and the demystification of "ignorability"
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
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Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The main drawback of this black-box approach surfaces in problem formulation, namely, the phase where a researcher begins to articulate the”
§ An Introduction to Causal Inference > 5.2 Problem formulation and the demystification of "ignorability"
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Instead of bringing the theory to the problem, the problem must be reformulated to fit the theory; all background knowledge pertaining to a given problem must first be translated into the language of counterfactuals (e.g., ignorability conditions) before analysis can commence.”
§ An Introduction to Causal Inference > 5.2 Problem formulation and the demystification of "ignorability"
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“When counterfactual variables are not viewed as byproducts of a deeper, process-based model, it is hard to ascertain whether all relevant judgments have been articulated, whether the judgments articulated are redundant, or whether those judgments are self-consistent.”
§ An Introduction to Causal Inference > 5.2 Problem formulation and the demystification of "ignorability"
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Not all questions of causal character can be encoded in P(y|do(x)) type expressions, thus implying that not all causal questions can be answered from experimental studies.”
§ An Introduction to Causal Inference > 3.4 Counterfactual analysis in structural models
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The corresponding unbiased estimands for these causal quantities are readable directly from the diagram.”
§ An Introduction to Causal Inference > 3.3.3 General control of confounding
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Statistical test can be used for rejecting certain kernels, in the rare cases where such kernels have testable implications, but the lion's share of supporting causal claims falls on the shoulders of untested causal assumptions.”
§ An Introduction to Causal Inference > 4.3 Identification, estimation, and approximation
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A major impediment to progress in mediation analysis has been the lack of notational facility for expressing the key notion of”
§ An Introduction to Causal Inference > 6.1.2 Controlled direct-effects
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We see that the assumption of conditional ignorability (35) qualifies Z as an admissible covariate for adjustment; it mirrors therefore the”
§ An Introduction to Causal Inference > 5.2 Problem formulation and the demystification of "ignorability"
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
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It may state two separate claims as one.
- The authors state this as an assumption: In Fig. 4, a set Z of covariates satisfies the conditional independence Y_x ⊥⊥ X | Z (conditional ignorability).
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The potential-outcome analysis proceeds by treating the observed distribution P(x 1 ,...,x n ) as the marginal distribution of an augmented probability function P * defined over both observed and counterfactual variables.”
§ An Introduction to Causal Inference > 5.1 The "black-box" missing-data paradigm
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For example, the formal definition of the causal effect P(y|do(x)), as given in Eq. ( 7), is universally applicable to all models, parametric as well as nonparametric, through the formation of a submodel M x .”
§ An Introduction to Causal Inference > 4.1 Defining the target quantity
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
In the paper
“Pearl (2000a, Chapter 7) shows, using the structural interpretation of Y x (u), that it is indeed legitimate to treat counterfactuals as jointly distributed random variables in all respects, that consistency constraints like (32) are automatically satisfied in the structural interpretation and, moreover, that investigators need not be concerned about any additional constraints except the following”
§ An Introduction to Causal Inference > 5.1 The "black-box" missing-data paradigm
What the sources say
- Not matchedcites Pearl (2000a, Chapter 7)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The methodology dictates that every investigation involving causal relationships (and this entails the vast majority of empirical studies in the health, social, and behavioral sciences) should be structured along the following four-step process:”
§ An Introduction to Causal Inference > 4 Methodological Principles of Causal Inference
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Today we understand that the longevity and natural appeal of structural equations stem from the fact that they permit investigators to communicate causal assumptions formally and in the very same vocabulary in which scientific knowledge is stored.”
§ An Introduction to Causal Inference > 4.2 Explicating causal assumptions
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The main conceptual difference between the two approaches is that, whereas the structural approach views the intervention do(x) as an operation that changes a distribution but keeps the variables the same, the potential-outcome approach views the variable Y under do(x) to be a different variable, Y x , loosely connected to Y through relations such as (32), but remaining unobserved whenever X = x.”
§ An Introduction to Causal Inference > 5.1 The "black-box" missing-data paradigm
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A collection of constraints of this type might sometimes be sufficient to permit a unique solution to the query of interest.”
§ An Introduction to Causal Inference > 5.2 Problem formulation and the demystification of "ignorability"
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“It should be emphasized, however, that contrary to conventional wisdom (e.g., (Rubin, 2007(Rubin, , 2009))), propensity score methods are merely efficient estimators of the right hand side of (25); they entail the same asymptotic bias, and cannot be expected to reduce bias in case the set S does not satisfy the back-door criterion (Pearl, 2000a(Pearl, , 2009c,d),d).”
§ An Introduction to Causal Inference > 3.3.4 From identification to estimation
What the sources say
- Not matchedcites Pearl, 2000a
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites 2009c,d
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Clearly, the distribution P(u Y ,u X ,u Z ) induces a well defined probability on the counterfactual event Y x 0 = y, as well as on joint counterfactual events, such as 'Y x 0 = y AND Y x 1 = y ,' which are, in principle, unobservable if x 0 = x 1 .”
§ An Introduction to Causal Inference > 24
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Clearly, this notion must be interpreted as (hypothetically) setting the intermediate variables to constants by physical intervention, not by analytical means such as selection, regression, conditioning, matching or adjustment.”
§ An Introduction to Causal Inference > 6.1.2 Controlled direct-effects
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For example, questions of attribution (e.g., what fraction of death cases are due to specific exposure?)or of susceptibility (what fraction of the healthy unexposed population would have gotten the disease had they been exposed?)cannot be answered from experimental studies, and naturally, this kind of questions cannot be expressed in P(y|do(x)) notation.”
§ An Introduction to Causal Inference > 3.4 Counterfactual analysis in structural models
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The surgical definition of counterfactuals given by ( 29), provides the conceptual and formal basis for the Neyman-Rubin potential-outcome framework, an approach to causation that takes a controlled randomized trial (CRT) as its ruling paradigm, assuming that nothing is known to the experimenter about the science behind the data.”
§ An Introduction to Causal Inference > 24
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Replacing”
§ An Introduction to Causal Inference > 5.2 Problem formulation and the demystification of "ignorability"
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“researchers in the graph-less potential-outcome camp rarely use”
§ An Introduction to Causal Inference > 5.2 Problem formulation and the demystification of "ignorability"
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The reason for this fundamental limitation is that no death case can be tested twice, with and without treatment.”
§ An Introduction to Causal Inference > 7 Conclusions
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Clearly, P(Y = y|do(X = x)) is equivalent to P(Y x = y).”
§ An Introduction to Causal Inference > 7 Conclusions
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The Mediation Formula represents the average increase in the outcome Y that the transition from X = x to X = x is expected to produce absent any direct effect of X on Y.”
§ An Introduction to Causal Inference > 42
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The quote only partly states this claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“When unified and synthesized, the two components offer statistical investigators a powerful and comprehensive methodology for empirical research.”
§ An Introduction to Causal Inference > 7 Conclusions
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence.
In the paper
“It can also be evaluated from observational studies whenever a sufficient set of covariates can be measured that satisfies the back-door criterion and, more generally, in a wide class of graphs that permit the identification of conditional interventions.”
§ An Introduction to Causal Inference > 48
What the sources say
- Not matchedcites Shpitser and Pearl (2009)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The Mediation Formula of Eq. ( 49) explicates this target quantity formally, and casts it in terms of estimable quantities.”
§ An Introduction to Causal Inference > Additional information
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The algebraic component of the structural language coincides with the potential-outcome framework”
§ An Introduction to Causal Inference > 7 Conclusions
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This paper surveys recent advances in causal analysis from the unifying perspective of the structural theory of causation”
§ An Introduction to Causal Inference > 7 Conclusions
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“and its graphical component embraces Wright's method of path diagrams.”
§ An Introduction to Causal Inference > 7 Conclusions
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Causal inference requires two additional ingredients: a science-friendly language for articulating causal knowledge, and a mathematical machinery for processing that knowledge, combining it with data and drawing new causal conclusions about a phenomenon.”
§ An Introduction to Causal Inference > 7 Conclusions
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This is what we normally assess in a controlled experiment, with X randomized, in which the distribution of Y is estimated for each level x of X.”
§ An Introduction to Causal Inference > 7 Conclusions
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It is remarkable that counterfactual quantities like DE and IE that could not be expressed in terms of do(x) operators, and appear therefore void of empirical content, can, under certain conditions be estimated from empirical studies, and serve to guide policies.”
§ An Introduction to Causal Inference > 6.1.4 Natural indirect effects
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Most of all, they demonstrate the effectiveness and viability of the scientific approach to causation whereby the dominant paradigm is to model the activities of Nature, rather than those of the experimenter.”
§ An Introduction to Causal Inference > 48
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“These include: randomization, intervention, direct and indirect effects, confounding, counterfactuals, and attribution.”
§ An Introduction to Causal Inference > 7 Conclusions
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Moreover, the formula is readily estimable by regression.”
§ An Introduction to Causal Inference > 42
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The derivation of the Mediation Formula was facilitated by taking seriously the four steps of the structural methodology (Section 4) together with the graphicalcounterfactual-structural symbiosis spawned by the surgical interpretation of counterfactuals (Eq.( 29)).”
§ An Introduction to Causal Inference > Additional information
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In nonlinear systems, those values would, in general, modify the effect of X on Y and thus should be chosen carefully to represent the target policy under analysis.”
§ An Introduction to Causal Inference > 6.1.3 Natural direct effects
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The theory invokes non-parametric structural equations models as a formal and meaningful language for defining causal quantities, formulating causal assumptions, testing identifiability, and explicating many concepts used in causal discourse.”
§ An Introduction to Causal Inference > 7 Conclusions
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It calls therefore for a two-step regression which, in principle, can be performed non-parametrically.”
§ An Introduction to Causal Inference > 42
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Nonparametric estimation is not always practical.When Z consists of a vector of several mediators, the dimensionality of the problem would prohibit the estimation of E(Y|x,z) for every (x,z) cell, and the need arises to use parametric approximation.”
§ An Introduction to Causal Inference > 42
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“Pearl (2001) has suggested therefore that signal sensing is more fundamental to the notion of causation than manipulation; the latter being but a crude way of stimulating the former in experimental setup.”
§ An Introduction to Causal Inference > 6.1.4 Natural indirect effects
What the sources say
- Not matchedcites Pearl (2001)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The second term represents the correction needed to account for confounding bias, that is, P(y|do(x )) = P(y|x ).”
§ An Introduction to Causal Inference > Additional information
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- The authors state this as an assumption: Y is monotonic relative to X, i.e., Y1(u) ≥ Y0(u).
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This precludes from the analysis all typical families, in which a father and a grandfather have simultaneous, complementary influences on children's upbringing.”
§ An Introduction to Causal Inference > Additional information
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In linear systems, to take an even sharper example, the direct effect would be undefined whenever indirect paths exist from the cause to its effect.”
§ An Introduction to Causal Inference > Additional information
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This means that a grandfather would be deemed to have no direct effect on his grandson's behavior in families where he has had some effect on the father.”
§ An Introduction to Causal Inference > Additional information
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“The first term on the r.h.s. of ( 61) is the familiar excess risk ratio (ERR) that epidemiologists have been using as a surrogate for PN in court cases (Cole, 1997, Robins andGreenland, 1989b).”
§ An Introduction to Causal Inference > Additional information
What the sources say
- Not matchedcites Cole, 1997
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites Robins and Greenland, 1989b
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- The authors state this as an assumption: Y is monotonic relative to X, i.e., Y1(u) ≥ Y0(u).
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For example, the direct effect is definable only in units absent of indirect effects.”
§ An Introduction to Causal Inference > Additional information
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper relies on this without support.
Most studies in the health, social and behavioral sciences aim to answer causal rather than associative questions.
“Most studies in the health, social and behavioral sciences aim to answer causal rather than associative -questions.”
The paper relies on this without support.
Causal questions require knowledge of the data-generating process and cannot be computed from the data alone or from the distributions that govern the data.
“Such questions require some knowledge of the data-generating process, and cannot be computed from the data alone, nor from the distributions that govern the data.”
The paper relies on this without support.
Much of the conceptual framework and algorithmic tools needed for causal problems are well established but not known to many researchers who could use them.
“Remarkably, although much of the conceptual framework and algorithmic tools needed for tackling such problems are now well established, they are not known to many of the researchers who could put them into practical use.”
The paper relies on this without support.
Solving causal problems systematically requires extensions in the standard mathematical language of statistics, and these extensions are not typically emphasized in mainstream literature.
“Solving causal problems systematically requires certain extensions in the standard mathematical language of statistics, and these extensions are not typically emphasized in the mainstream literature.”
The paper relies on this without support.
Many statistical researchers have not yet benefited from causal inference results in counterfactual analysis, nonparametric structural equations, graphical models, and the symbiosis between counterfactual and graphical methods.
“As a result, many statistical researchers have not yet benefited from causal inference results in (i) counterfactual analysis, (ii) nonparametric structural equations, (iii) graphical models, and (iv) the symbiosis between counterfactual and graphical methods.”
The paper relies on this without support.
SCM's potentials as a comprehensive theory of causation are yet to be fully utilized.
“its potentials as a comprehensive theory of causation are yet to be fully utilized.”
The paper relies on this without support.
The bulk of SEM methodology was developed for linear analysis and, until recently, no comparable methodology existed for models with dichotomous variables or nonlinear dependencies.
“However, the bulk of SEM methodology was developed for linear analysis and, until recently, no comparable methodology has been devised to extend its capabilities to models involving dichotomous variables or nonlinear dependencies.”
The paper relies on this without support.
In the bulk of statistical literature before 2000, causal claims rarely appear in the mathematics.
“Moreover, in the bulk of the statistical literature before 2000, causal claims rarely appear in the mathematics.”
The paper relies on this without support.
Few have taken seriously the textbook requirement that any introduction of new notation must entail a systematic definition of syntax and semantics.
“However, few have taken seriously the textbook requirement that any introduction of new notation must entail a systematic definition of the syntax and semantics that governs the notation.”
The authors state this as an assumption.
The structure of the underlying DAG is only partially known.
“Second, assuming that the structure of the underlying DAG is only partially known, one may wish to test, using adjustment, which of two hypothesized structures is compatible with the data.”
The authors state this as an assumption.
The assumptions of Gaussian, zero-mean disturbances and additive interactions are deemed reasonable.
“For example, if the assumptions of Gaussian, zero-mean disturbances and additive interactions are deemed reasonable, then the estimand given in (28) can be converted to the product E(Y|do(x)) = r W 3 X r YW 3 •X x, where r YZ•X is the (standardized) coefficient of Z in the regression of Y on Z and X.”
The authors state this as an assumption.
The equations in the example are linear, as in Fig. 1.
“For example, assuming linear equations (as in Fig. 1), x = u X y = β x + u X ,”
The paper relies on this without support.
The laws of nature, as reflected in the functions fX, fY, etc., remain invariant from one unit to another; only the attributes U=u vary.
“As we go from one unit to another, the laws of nature, as they are reflected in the functions f X , f Y , etc. remain invariant; only the attributes U = u vary from individual to individual.”
The authors state this as an assumption.
The hypothetical entities Yx are assumed to obey the axioms of probability calculus, the laws of conditioning, and the axioms of conditional independence.
“The new hypothetical entities Y x are treated as ordinary random variables; for example, they are assumed to obey the axioms of probability calculus, the laws of conditioning, and the axioms of conditional independence.”
The authors state this as an assumption.
In Fig. 4, a set Z of covariates satisfies the conditional independence Y_x ⊥⊥ X | Z (conditional ignorability).
“if one can plausibly assume that, in Fig. 4, a set Z of covariates satisfies the conditional independence”
The authors state this as an assumption.
Z does not affect Y directly except through X, expressed by the exclusion restriction Y_xz = Y_x.
“To further formulate the understanding that Z does not affect Y directly, except through X, the analyst would write a, so called,”
The authors state this as an assumption.
In the mediation model of Fig. 6(a), all error terms are mutually independent.
“We will use the simple mediation model of Fig. 6(a), where all error terms (not shown explicitly) are assumed to be mutually independent”
The authors state this as an assumption.
Certain assumptions of no confounding are valid, or the model is Markovian with no unobserved confounders.
“if certain assumptions of”
The authors state this as an assumption.
Z_x ⊥⊥ Y_x,z | W holds for some set W of measured covariates.
“One condition for the validity of ( 43) is that Z x ⊥⊥ Y x ,z |W holds for some set W of measured covariates.”
The authors state this as an assumption.
The generic mediation structure of Fig. 6(a) holds.
“it embodies no causal assumption other than the generic mediation structure of Fig. 6(a).”
The authors state this as an assumption.
The error terms e_x, e_z, and e_xz are three independent Bernoulli variables with probabilities p_x, p_z, and p_xz, respectively.
“Let us further assume that e x ,e z and e xz are three independent Bernoulli variables with probabilities p x , p z , and p xz , respectively.”
The authors state this as an assumption.
The assumption of nonconfoundedness permits use of the Mediation Formula for estimating the Z-mediated effect of X on Y.
“and that the assumption of nonconfoundedness permits us to use the Mediation Formula (49) for estimating the Z-mediated effect of X on Y.”
The authors state this as an assumption.
Y is monotonic relative to X, i.e., Y1(u) ≥ Y0(u).
“If Y is monotonic relative to X, i.e., Y 1 (u)≥Y 0 (u)”
The authors state this as an assumption.
The causal effect P(y|do(x)) is identifiable.
“whenever the causal effect P(y|do(x)) is identifiable”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Thus, our results generate and underline experimentally testable hypotheses that can inform future dietary interventions in terms of design and biomarker assessment (46).”
From Amino acids, lipid metabolites, and ferritin as potential mediators linking red meat consumption to type 2 diabetes (2015) · cites this paper as [46]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ An Introduction to Causal Inference > Additional information
“TE(Y) = p z p xz + p x + p x p z p xz (56”
§ An Introduction to Causal Inference > 42
“TE = DE + IE -DE • IE”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ An Introduction to Causal Inference > 24
“x = u X y = β x + u X ,”
§ An Introduction to Causal Inference > 24
“the conditioning events Y = y 0 and X = x 0 yield U X = x 0 and U Y = y 0 -β x 0”
Citations
Cites
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Metadata
- Authors
- Pearl, J.
- Affiliations
- University of California, Los Angeles (US)
- Corresponding author
- Pearl, Judea
- Venue
- The International Journal of Biostatistics
- Publisher
- Walter de Gruyter GmbH
- Published
- 2010-02-26
- Volume
- 6
- Issue
- 2
- Pages
- Article 7-Article 7
- ISSN
- 1557-4679 (ISSN-L)
- PMC
- PMC2836213
- OpenAlex
- W2145429839
- Cited by
- 755
- References
- 186
- Citations by year
- 2026: 66 · 2025: 84 · 2024: 69 · 2023: 56 · 2022: 75 · 2021: 76 · 2020: 55 · 2019: 52 · 2018: 40 · 2017: 35 · 2016: 29 · 2015: 29 · 2014: 19 · 2013: 24 · 2012: 21
- FWCI
- 3.03
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The International Journal of Biostatistics (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Science Foundation (0914211)
- National Institutes of Health (1r01lm009961-01)
- Office of Naval Research
- U.S. National Library of Medicine (R01-LM009961, 1R01 LM009961-01)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy of Biology and Scientific Explanation
- Keywords
- causal inference, structural causal models, counterfactual reasoning, direct and indirect effects, mediation analysis, causal assumptions
- MeSH terms
- Algorithms, Humans, Research Design, Models, Statistical, Causality, Confounding Factors, Epidemiologic
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-11, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-11 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Cited sources are checked with a language model’s help (gpt-6-sol).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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