Estimate ATE, ITT, and TOT from experiment

You are given a single dataset (CSV) from an A/B experiment on a streaming product. The goal is to estimate the causal effect of a personalization feature on minutes streamed.

Data

Assume one row per user with the following columns:

• user_id (string/int): unique user identifier
• assigned (0/1): randomized assignment (instrument) to personalization (1) vs control (0)
• personalized (0/1): whether the user actually received personalization (there may be non-compliance)
• minutes_streamed (float): outcome measured over a fixed window after assignment
• x1, x2, ... (optional covariates): additional user features (some may be irrelevant)

Tasks

1. ATE (Average Treatment Effect) : Estimate the causal effect of receiving personalization on minutes_streamed .
   • State clearly what assumptions you are using (e.g., full compliance vs. unconfoundedness vs. random assignment).
   • Provide an estimator and how you would compute it in Python/R.
2. ITT and TOT (with non-compliance):
   • Estimate ITT : the effect of being assigned to personalization ( assigned ) on minutes_streamed .
   • Estimate TOT (a.k.a. LATE for compliers): the effect of actually receiving personalization ( personalized ) using assigned as an instrument.
   • Report the formulas and how to compute them.
3. IV/LATE conceptual checks :
   • Under what conditions is the IV/TOT estimate a valid causal effect?
   • What population does it apply to (e.g., compliers/always-takers/never-takers)?
   • What breaks if the exclusion restriction or monotonicity fails?