Collider (statistics)

{{Short description|Variable that is causally influenced by two or more variables}}

{{for|collider bias in statistics|Berkson's paradox}}

In statistics and causal graphs, a variable is a collider when it is causally influenced by two or more variables. The name "collider" reflects the fact that in graphical models, the arrow heads from variables that lead into the collider appear to "collide" on the node that is the collider.{{citation |last1=Hernan |first1=Miguel A. |year=2010 |title=Causal inference |last2=Robins |first2=James M. |publisher=CRC |series=Chapman & Hall/CRC monographs on statistics & applied probability |isbn=978-1-4200-7616-5 |page=70}} They are sometimes also referred to as inverted forks.{{cite journal |url=https://psyarxiv.com/t3qub |author=Julia M. Rohrer |title=Thinking Clearly About Correlations and Causation: Graphical Causal Models for Observational Data |website=PsyArXiv |date=2018-07-02 |doi=10.31234/osf.io/t3qub|hdl=21.11116/0000-0006-5734-E |hdl-access=free }}

File:Collider(statistics).png model of a collider]]

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.{{cite journal |last1=Ali |first1=R. Ayesha |last2=Richardson |first2=Thomas S. |last3=Spirtes |first3=Peter |last4=Zhange |first4=Jiji |title=Towards characterizing Markov equivalence classes for directed acyclic graphs with latent variables |journal=Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2006) |date=2012 |pages=10–17 |arxiv=1207.1365 }}

The result of having a collider in the path is that the collider blocks the association between the variables that influence it.{{citation

|last1 = Greenland

|first1 = Sander

|title = Causal Diagrams for Epidemiologic Research

|last2 = Pearl

|first2 = Judea

|last3 = Robins

|first3 = James M.

|journal = Epidemiology

|pages = 37–48

|volume = 10 | issue = 1

|date = January 1999

|issn = 1044-3983

|oclc = 484244020

|url=http://www.epidemiology.ch/history/PDF%20bg/Greenland,%20Pearl%20and%20Robins%201999%20causal%20diagrams%20for%20epidemiologic%20research.pdf

|doi=10.1097/00001648-199901000-00008

|pmid = 9888278

}}{{cite journal |last1=Pearl |first1=Judea |title=Fusion, Propagation and Structuring in Belief Networks |journal=Artificial Intelligence |date=1986 |volume=29 |issue=3 |pages=241–288 |doi=10.1016/0004-3702(86)90072-x |citeseerx=10.1.1.84.8016}}{{cite book |last1=Pearl |first1=Judea |authorlink=Judea Pearl |title=Probabilistic reasoning in intelligent systems: networks of plausible inference |url=https://archive.org/details/probabilisticrea00pear |url-access=registration |date=1988 |publisher=Morgan Kaufmann}} Thus, the collider does not generate an unconditional association between the variables that determine it.

Conditioning on the collider via regression analysis, stratification, experimental design, or sample selection based on values of the collider creates a non-causal association between X and Y (Berkson's paradox). 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.{{cn|date=May 2023}}

Colliders are sometimes confused with confounder variables. Unlike colliders, confounder variables should be controlled for when estimating causal associations.{{cn|date=May 2023}}

To detect and manage collider bias, scholars have made use of directed acyclic graphs.{{Cite journal |last=Schneider |first=Eric B. |date=2020 |title=Collider bias in economic history research |url=https://doi.org/10.1016/j.eeh.2020.101356 |journal=Explorations in Economic History |volume=78 |pages=101356 |doi=10.1016/j.eeh.2020.101356 |issn=0014-4983 |archive-url=https://eprints.lse.ac.uk/106578/1/Schneider_Collider_Bias_in_Economic_History_Research_2020_v4.pdf |archive-date=April 11, 2024|url-access=subscription }}

Randomization and quasi-experimental research designs are not useful in overcoming collider bias.