A propensity score is the probability of a unit (e.g., person, classroom, school) being assigned to a particular treatment given a set of observed covariates. Propensity scores are used to reduce selection bias by equating groups based on these covariates.
Suppose that we have a binary treatment T, an outcome Y, and background variables X. The propensity score is defined as the conditional probability of treatment given background variables:
Let Y(0) and Y(1) denote the potential outcomes under control and treatment, respectively. Then treatment assignment is (conditionally) unconfounded if treatment is independent of potential outcomes conditional on X. This can be written compactly as
where denotes statistical independence.
If unconfoundedness holds, then
Pearl (2000) has shown that a simple graphical criterion called backdoor provides an equivalent definition of unconfoundedness.
Read more about Propensity Score: Advantages and Disadvantages
Famous quotes containing the words propensity and/or score:
“The source of our actions resides in an unconscious propensity to regard ourselves as the center, the cause, and the conclusion of time. Our reflexes and our pride transform into a planet the parcel of flesh and consciousness we are.”
—E.M. Cioran (b. 1911)
“And there’s a score of duchesses, surpassing womankind,
Or who have found a painter to make them so for pay
And smooth out stain and blemish with the elegance of his mind:
I knew a phoenix in my youth, so let them have their day.”
—William Butler Yeats (1865–1939)