Glossary and DAG Hand-outs

A reference page covering causal inference terminology and links to hand-out PDFs on directed acyclic graphs (DAGs), confounding, selection bias, and measurement error.

Causal inference glossary

Causal inference rests on mathematical foundations that enjoy broad agreement, but the terminology varies across disciplines. The same word sometimes carries different (even opposite) meanings in different literatures. Terms to watch include "selection", "fixed effects", "standardisation", "moderator", "structural equation model", and "identification".

Core concepts

Term	Definition
Average Treatment Effect (ATE)	The expected difference in potential outcomes across the entire population: $ATE = E [Y (1) - Y (0)]$ . Also called the marginal effect.
Conditional Average Treatment Effect (CATE)	The ATE within a subgroup defined by covariates $X = x$ : $CATE (x) = E [Y (1) - Y (0) ∣ X = x]$ .
Potential outcomes	The outcomes that would be observed under each possible treatment level. For individual $i$ : $Y_{i} (1)$ under treatment, $Y_{i} (0)$ under control. Also called counterfactual outcomes.
Counterfactual	The potential outcome corresponding to the treatment level not actually received. Unobservable for any given individual.
Causal consistency	$Y_{i} (a) = Y_{i}$ when $A_{i} = a$ . The observed outcome equals the potential outcome under the treatment actually received. Requires well-defined treatment and no interference.
Exchangeability	Potential outcomes are independent of treatment assignment: $Y (a) ⊥ ⊥ A$ . In observational studies, we require conditional exchangeability: $Y (a) ⊥ ⊥ A ∣ L$ .
Positivity	Every subgroup has a non-zero probability of receiving each treatment level: $P (A = a ∣ L = l) > 0$ .

Graphical concepts

Term	Definition
DAG (directed acyclic graph)	A graph with directed edges (arrows) and no cycles. Used to encode causal assumptions about which variables influence which.
Confounder	A common cause of both the exposure and the outcome. Creates a non-causal (backdoor) path that must be blocked for valid causal inference.
Collider	A variable caused by two or more other variables on a path. Conditioning on a collider opens a spurious association.
Mediator	A variable on the causal pathway between exposure and outcome ( $A \to M \to Y$ ). Conditioning on a mediator blocks the indirect effect.
Backdoor path	A non-causal path from exposure to outcome that passes through a common cause. Blocking all backdoor paths satisfies the backdoor criterion.
d-separation	A graphical criterion for determining conditional independence. Two variables are d-separated given a set $Z$ if every path between them is blocked by $Z$ .

Estimation and sensitivity

Term	Definition
Propensity score	The probability of receiving treatment given covariates: $e (L) = P (A = 1 ∣ L)$ . Used for weighting, matching, or stratification.
E-value	The minimum strength of association an unmeasured confounder would need with both treatment and outcome (on the risk ratio scale) to explain away an observed effect.
RATE (Rank Average Treatment Effect)	A metric for assessing treatment effect heterogeneity. Measures how well a prioritisation rule identifies individuals with larger effects.
QINI curve	A cumulative gain curve showing the benefit of treating individuals in order of predicted treatment effect. Area under the QINI curve summarises heterogeneity.
Policy tree	A decision tree that assigns treatment based on covariates to maximise a welfare criterion. Used for identifying high-response subgroups.
Doubly robust estimation	An estimation strategy that yields consistent causal estimates if either the outcome model or the propensity score model (but not necessarily both) is correctly specified.

DAG hand-outs

The following hand-outs cover DAG conventions, common structures, and specific forms of bias. All PDFs are available for download from the hand-outs folder (Dropbox).

Foundations

Hand-out	Topic
1a. Local conventions	Conventions for causal diagram construction and interpretation
1b. Directed graph terminology	Core terminology for directed acyclic graphs
S1. Graphical key	Visual reference guide for DAG symbols and notation
S2. Glossary	Comprehensive glossary of causal inference terminology

Common applications

Hand-out	Topic
2. Common causal questions	Frequently encountered causal questions and how to set them up
6. Effect modification	When and how treatment effects vary across subgroups
9. External validity	Generalising causal findings across populations and contexts

Time series and confounding

Hand-out	Topic
3. Time series approaches	How longitudinal data help address confounding bias
4. Three-wave panel methods	Using three-wave panel data for causal inference
5. Time series limitations	When time series approaches may not resolve confounding
S3. Time-resolved confounding	Advanced approaches to time-varying confounding

Advanced topics

Hand-out	Topic
7. Selection bias	Selection bias in longitudinal studies
8. Measurement error	Structural approaches to representing and addressing measurement error
10. Experimental design	How experiments address confounding and selection bias

Supplementary materials

Hand-out	Topic
S5. Timing examples	Practical examples of confounding and timing issues
S6. Detailed panel examples	What can go wrong in a three-wave panel
S7. Cross-sectional approaches	When to report multiple DAGs in cross-sectional studies
S8. Bias correction	Quantitative approaches to bias correction
S9. Mediator bias	Confounding bias in mediation analysis
S10. Misclassification bias	Examples of misclassification bias and bias towards the null

Accessing hand-outs

All PDFs are in the hand-outs folder on Dropbox. File names match the numbering in the tables above (e.g., 1a-terminologylocalconventions.pdf, S2-glossary.pdf).

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