An estimand is the population quantity or probabilistic target that an analysis seeks to determine. Separate three steps: pose a question, write the mathematical quantity that answers it, and use an estimator to infer that quantity from data. section 1.5.1
Use an estimand to make an analysis target explicit:
- Translate a question into a quantity: the mean height of Bostonians answers a population question, while P(D=4|I) answers an image-classification question. section 1.5.1
- In causal inference, identify a lower-level estimand equivalent to a higher-level intervention query before choosing an estimation method. section 10.3
- Choose among identified estimands by comparing the assumptions required for each, then select an estimator using statistical and computational trade-offs. section 11.3.4 section 11.4
Backdoor adjustment for game engagement
To estimate the causal effect of high versus low engagement on in-game purchases, adjust for the common cause G: ∑g P(I=i|E=high,G=g)P(G=g). This level-1 quantity is the backdoor adjustment estimand for the intervention-level query. A confounder omitted from the causal model would violate its identifying assumption. section 10.3 section 11.3.4
Listing 10.5 Deriving the estimand to get P(IE=“high”) from P(E, I, G)
from y0.graph import NxMixedGraph as Y0Graph
from y0.dsl import P, Variable
from y0.algorithm.identify import Identification, identify
query = P(I @ e)
base_distribution = P(I, E, G)
identification_task = Identification.from_expression(
graph=dag,
query=query,
estimand=base_distribution)
identify(identification_task)
Inspect a Python-oriented y0 workflow that derives an estimand from a causal query, graph, and base distribution. section 10.3
