Week 1
, Thinking Clearly About Correlations and Causation: Graphical Causal Models for
Observational Data
https://journals.sagepub.com/doi/10.1177/2515245917745629
Chains have the structure A → B → C, for example, intelligence → educational attainment →
income. Chains can transmit an association between the node at the beginning and the node at the
end: If intelligence causally affects educational attainment, and educational attainment causally
affects income, then intelligence and income can be correlated. Such an association reflects a
genuine causal effect. In this chain, intelligence causally influences income via educational
attainment.
Forks have the structure A ← B → C, for example, educational attainment ← intelligence → income.
A fork can transmit an association, but it is not causal. In isolation, this fork indicates that
educational attainment and income may be correlated because they share a common cause,
intelligence. Forks are the causal structure most relevant for the phenomenon of confounding.
Inverted forks have the structure A → B ← C, for example, educational attainment → income ←
intelligence. An inverted fork does not transmit an association: If educational attainment and
intelligence both affect income, this does not imply that they are in any way correlated. Inverted
forks are relevant to the problem of collider bias, which I discuss later in this article.
Along such a chain, variables that are directly or indirectly causally affected by a certain variable are
called its descendants; conversely, variables that directly or indirectly affect a certain variable are
considered its ancestors. For example, in this path, intelligence is an ancestor of grades, educational
attainment, and income, and income is a descendant of grades.
DAGs are acyclic because they do not allow for cyclic paths in which variables become their own
ancestors.
The main challenge in using observational data is confounding — when a third variable influences
both the cause (independent variable) and the outcome (dependent variable), creating a spurious
correlation. DAGs help identify and address this problem by ensuring that all relevant common
causes of included variables are represented. Only variables that causally affect at least two others in
the graph need to be included, while unrelated or idiosyncratic factors can be ignored. Once the
DAG is constructed, researchers can identify back-door paths — indirect routes linking cause and
outcome through confounders — that transmit spurious associations. To isolate the true causal
effect, these back-door paths must be blocked through appropriate statistical control.
The goal of third-variable control is to block open back-door paths so the true causal effect can be
identified from observational data, following Pearl’s back-door criterion. This requires assuming the
DAG correctly represents the causal structure and includes all relevant variables — a strong and
case-dependent assumption. Back-door paths can be blocked by controlling for certain nodes (e.g.,
controlling for intelligence blocks multiple spurious paths between education and income). Different
statistical techniques can serve this purpose, but the variables must be measured. Even when the
DAG is correct and the right controls are chosen, problems can still arise at the stage of estimating
the effect, since identification and estimation are separate challenges.
How to control for a variable
1. Stratified analysis.
, o Works for simple categorical confounders (e.g., sex) by splitting the sample into
homogeneous groups.
o Transparent but impractical with continuous or multiple confounders.
2. Regression models.
o Commonly used to statistically control for covariates by including them in the model.
o Requires correct specification of relationships (e.g., nonlinear or interactive effects),
otherwise residual confounding remains.
3. Matching.
o Matches individuals with similar covariate profiles (e.g., via propensity scores) to
create balanced comparison groups.
o Useful when many confounders exist but still subject to the same limitations as
other statistical adjustments (e.g., omitted variables, model misspecification).
4. Measurement error.
o Imperfect measurement of confounders (like intelligence) weakens statistical
control, often leading to inflated false positive rates, especially in large samples.
o Latent-variable modeling (e.g., SEM) can help but requires very large samples.
5. Genetic confounding & control by design.
o Genetic factors can create spurious associations (e.g., maternal depression → cold
parenting + inherited vulnerability → child depression).
o Solutions: measure genetic predispositions, use adoption studies, twin studies, or
natural experiments.
o Such design-based approaches (e.g., instrumental variables, regression
discontinuity) can sometimes substitute for post hoc statistical control and are
widely used in economics.
Learning to Let Go: When Statistical Control Hurts
Misconception: Adding more covariates does not always improve causal inference.
Controlling for the wrong variables can create bias.
1. Colliders
A collider is a variable influenced by both the independent and dependent variable (A → C
← B).
Normally, colliders block associations, but controlling for them introduces spurious
correlations between their causes.
Example: publication status is influenced by both methodological rigor and innovativeness.
Conditioning on publication creates a false negative correlation between rigor and
innovativeness (collider bias).
Similar biases can arise from:
o Nonresponse bias (only analyzing completed questionnaires).
o Attrition bias (dropouts in longitudinal studies).
o Nonrepresentative samples (e.g., only college students).
2. Mediators
A mediator lies on the causal pathway between cause and outcome.
Controlling for mediators blocks the very mechanism of interest, underestimating the causal
effect (overcontrol bias).
Example: adult intelligence mediates the effect of education on income. Controlling for it
removes part of education’s real effect.
Mediators (or their descendants, like chess performance as a proxy for intelligence) should
not be controlled for unless the goal is explicitly to estimate direct effects.
Even in experiments, controlling for mediators can create new back-door paths and bias
estimates unless the mediator itself is randomized.
, Causal Knowledge as a Prerequisite for Confounding Evaluation: An Application to Birth
Defects Epidemiology
https://academic-oup-com.eur.idm.oclc.org/aje/article/155/2/176/108106?
login=true&token=eyJhbGciOiJub25lIn0.eyJleHAiOjE3NTkyMjk4MzQsImp0aSI6IjJmODM2O
Tc0LTA3ZjgtNDM0ZC1hMTQxLWJmZWQ3N2ViNzNiMiJ9
Strategies for Confounder Identification.
Strategy 1: automatic variable selection (e.g., stepwise selection) assumes important
confounders will be chosen, but may include nonconfounders.
Strategy 2: comparing adjusted vs. unadjusted estimates (e.g., ≥10% change) selects
variables that significantly alter estimates.
Strategy 3: combines statistical associations with subject-matter knowledge, checking that a
confounder is associated with both exposure and outcome but not on the causal pathway.
All three strategies can still produce bias from omitting true confounders or adjusting for
nonconfounders.
Definition: A collider is a variable that is caused by two or more other variables.
Key point: If you condition on (adjust for or stratify by) a collider, you can create a spurious
association between its causes—even if those causes are otherwise independent.
, Thinking Clearly About Correlations and Causation: Graphical Causal Models for
Observational Data
https://journals.sagepub.com/doi/10.1177/2515245917745629
Chains have the structure A → B → C, for example, intelligence → educational attainment →
income. Chains can transmit an association between the node at the beginning and the node at the
end: If intelligence causally affects educational attainment, and educational attainment causally
affects income, then intelligence and income can be correlated. Such an association reflects a
genuine causal effect. In this chain, intelligence causally influences income via educational
attainment.
Forks have the structure A ← B → C, for example, educational attainment ← intelligence → income.
A fork can transmit an association, but it is not causal. In isolation, this fork indicates that
educational attainment and income may be correlated because they share a common cause,
intelligence. Forks are the causal structure most relevant for the phenomenon of confounding.
Inverted forks have the structure A → B ← C, for example, educational attainment → income ←
intelligence. An inverted fork does not transmit an association: If educational attainment and
intelligence both affect income, this does not imply that they are in any way correlated. Inverted
forks are relevant to the problem of collider bias, which I discuss later in this article.
Along such a chain, variables that are directly or indirectly causally affected by a certain variable are
called its descendants; conversely, variables that directly or indirectly affect a certain variable are
considered its ancestors. For example, in this path, intelligence is an ancestor of grades, educational
attainment, and income, and income is a descendant of grades.
DAGs are acyclic because they do not allow for cyclic paths in which variables become their own
ancestors.
The main challenge in using observational data is confounding — when a third variable influences
both the cause (independent variable) and the outcome (dependent variable), creating a spurious
correlation. DAGs help identify and address this problem by ensuring that all relevant common
causes of included variables are represented. Only variables that causally affect at least two others in
the graph need to be included, while unrelated or idiosyncratic factors can be ignored. Once the
DAG is constructed, researchers can identify back-door paths — indirect routes linking cause and
outcome through confounders — that transmit spurious associations. To isolate the true causal
effect, these back-door paths must be blocked through appropriate statistical control.
The goal of third-variable control is to block open back-door paths so the true causal effect can be
identified from observational data, following Pearl’s back-door criterion. This requires assuming the
DAG correctly represents the causal structure and includes all relevant variables — a strong and
case-dependent assumption. Back-door paths can be blocked by controlling for certain nodes (e.g.,
controlling for intelligence blocks multiple spurious paths between education and income). Different
statistical techniques can serve this purpose, but the variables must be measured. Even when the
DAG is correct and the right controls are chosen, problems can still arise at the stage of estimating
the effect, since identification and estimation are separate challenges.
How to control for a variable
1. Stratified analysis.
, o Works for simple categorical confounders (e.g., sex) by splitting the sample into
homogeneous groups.
o Transparent but impractical with continuous or multiple confounders.
2. Regression models.
o Commonly used to statistically control for covariates by including them in the model.
o Requires correct specification of relationships (e.g., nonlinear or interactive effects),
otherwise residual confounding remains.
3. Matching.
o Matches individuals with similar covariate profiles (e.g., via propensity scores) to
create balanced comparison groups.
o Useful when many confounders exist but still subject to the same limitations as
other statistical adjustments (e.g., omitted variables, model misspecification).
4. Measurement error.
o Imperfect measurement of confounders (like intelligence) weakens statistical
control, often leading to inflated false positive rates, especially in large samples.
o Latent-variable modeling (e.g., SEM) can help but requires very large samples.
5. Genetic confounding & control by design.
o Genetic factors can create spurious associations (e.g., maternal depression → cold
parenting + inherited vulnerability → child depression).
o Solutions: measure genetic predispositions, use adoption studies, twin studies, or
natural experiments.
o Such design-based approaches (e.g., instrumental variables, regression
discontinuity) can sometimes substitute for post hoc statistical control and are
widely used in economics.
Learning to Let Go: When Statistical Control Hurts
Misconception: Adding more covariates does not always improve causal inference.
Controlling for the wrong variables can create bias.
1. Colliders
A collider is a variable influenced by both the independent and dependent variable (A → C
← B).
Normally, colliders block associations, but controlling for them introduces spurious
correlations between their causes.
Example: publication status is influenced by both methodological rigor and innovativeness.
Conditioning on publication creates a false negative correlation between rigor and
innovativeness (collider bias).
Similar biases can arise from:
o Nonresponse bias (only analyzing completed questionnaires).
o Attrition bias (dropouts in longitudinal studies).
o Nonrepresentative samples (e.g., only college students).
2. Mediators
A mediator lies on the causal pathway between cause and outcome.
Controlling for mediators blocks the very mechanism of interest, underestimating the causal
effect (overcontrol bias).
Example: adult intelligence mediates the effect of education on income. Controlling for it
removes part of education’s real effect.
Mediators (or their descendants, like chess performance as a proxy for intelligence) should
not be controlled for unless the goal is explicitly to estimate direct effects.
Even in experiments, controlling for mediators can create new back-door paths and bias
estimates unless the mediator itself is randomized.
, Causal Knowledge as a Prerequisite for Confounding Evaluation: An Application to Birth
Defects Epidemiology
https://academic-oup-com.eur.idm.oclc.org/aje/article/155/2/176/108106?
login=true&token=eyJhbGciOiJub25lIn0.eyJleHAiOjE3NTkyMjk4MzQsImp0aSI6IjJmODM2O
Tc0LTA3ZjgtNDM0ZC1hMTQxLWJmZWQ3N2ViNzNiMiJ9
Strategies for Confounder Identification.
Strategy 1: automatic variable selection (e.g., stepwise selection) assumes important
confounders will be chosen, but may include nonconfounders.
Strategy 2: comparing adjusted vs. unadjusted estimates (e.g., ≥10% change) selects
variables that significantly alter estimates.
Strategy 3: combines statistical associations with subject-matter knowledge, checking that a
confounder is associated with both exposure and outcome but not on the causal pathway.
All three strategies can still produce bias from omitting true confounders or adjusting for
nonconfounders.
Definition: A collider is a variable that is caused by two or more other variables.
Key point: If you condition on (adjust for or stratify by) a collider, you can create a spurious
association between its causes—even if those causes are otherwise independent.
