statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

and

causal graphs In statistics, econometrics, epidemiology, genetics and related disciplines, causal graphs (also known as path diagrams, causal Bayesian networks or DAGs) are probabilistic graphical models used to encode assumptions about the data-generating pro ...

, a variable is a collider when it is causally influenced by two or more variables. The name "collider" reflects the fact that in

graphical model A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a Graph (discrete mathematics), graph expresses the conditional dependence structure between random variables. They are ...

s, the arrow heads from variables that lead into the collider appear to "collide" on the

node In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer to: In mathematics *Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two or more curves, lines, ...

that is the collider. They are sometimes also referred to as inverted forks. Collider(statistics)

The causal variables influencing the collider are themselves not necessarily associated. If they are not adjacent, the collider is ''unshielded''. Otherwise, the collider is shielded and part of a triangle. The result of having a collider in the

path A path is a route for physical travel – see Trail. Path or PATH may also refer to: Physical paths of different types * Bicycle path * Bridle path, used by people on horseback * Course (navigation), the intended path of a vehicle * Desire p ...

is that the collider blocks the association between the variables that influence it. Thus, the collider does not generate an unconditional association between the variables that determine it. Conditioning on the collider via

regression analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...

, stratification, experimental design, or sample selection based on values of the collider create a non-causal association between X and Y (

Berkson's paradox Berkson's paradox, also known as Berkson's bias, collider bias, or Berkson's fallacy, is a result in conditional probability and statistics which is often found to be counterintuitive, and hence a veridical paradox. It is a complicating factor ari ...

). In the terminology of causal graphs, conditioning on the collider opens the path between X and Y. This will introduce bias when estimating the causal association between X and Y, potentially introducing associations where there are none. Colliders can therefore undermine attempts to test causal theories. Colliders are sometimes confused with

confounder In statistics, a confounder (also confounding variable, confounding factor, extraneous determinant or lurking variable) is a variable that influences both the dependent variable and independent variable, causing a spurious association. Con ...

variables. Unlike colliders, confounder variables ''should'' be controlled for when estimating causal associations.

References

{{reflist Epidemiology Independence (probability theory) Graphical models Causal inference

See also

References