Read this definition of a propensity score in ordinary language.
Propensity Score: For a unit with covariates X=x, the probability of being assigned treatment:
PS(x) = prob(T = 1|X=x)
Basic Concepts of Statistical Inference for Causal Effects in Experiments and Observational Studies Donald B. Rubin. P 18
ICS212 Fall 2022
The propensity score of a unit with characteristics x is the probability of being assigned to the treatment group given that its covariates are x.
ICS212 Fall 2022
Translate these assertions about the assignment mechanisms for randomized experiments
= "is independent of"
= "given that" or "conditional on"
The probability that any given individual is assigned to treatment or control is independent of potential outcomes.
The probability that any given individual is assigned to treatment or control is independent of potential outcomes and is a known function of covariates (for example, we might decide to have more women than men in our treatment group).
ICS212 Fall 2022
Translate these assertions about the assignment mechanisms for randomized experiments
= "is independent of"
= "given that" or "conditional on"
ICS212 Fall 2022
pr(X|a,b,c) = pr(X|a)
- What do each of the underlined parts of this mathematical description of an assignment mechanism mean?
- What does it mean altogether?
probability of being in treatment group
given unit i's characteristics
and what would happen under treatment and no treatment
is the same as
pr(T) given i's characteristics and the observed outcome
- What do each of the underlined parts of this mathematical description of an assignment mechanism mean?
- What does it mean altogether?
ICS212 Fall 2022
pr(X|a,b,c) = pr(X|a)
ICS212 Fall 2022
means the probability of X given a, b, and c is the same as the probability of X given a.
pr(X|a,b,c) = pr(X|a)
And that means the X does not depend on b, and c.
- What do each of the underlined parts of this mathematical description of an assignment mechanism mean?
- What does it mean altogether?
probability of being in treatment group
given unit i's characteristics
and what would happen under treatment and no treatment
is the same as
pr(T) given i's characteristics
- What do each of the underlined parts of this mathematical description of an assignment mechanism mean?
ICS212 Fall 2022
means the probability of X given a, b, and c is the same as the probability of X given a.
pr(X|a,b,c) = pr(X|a)
And that means the X does not depend on b, and c.
- What do each of the underlined parts of this mathematical description of an assignment mechanism mean?
- What does it mean altogether?
LP14:PropensityScores
By Dan Ryan
