How would you use propensity score matching here

You need to estimate the causal impact of a new recommender feature on 7-day retention.

The feature was not randomly assigned; users choose to opt in after seeing a prompt, and more engaged users are more likely to opt in. You have observational data with these columns:

• user_id
• opt_in (0/1)
• pre-period covariates (for example, prior watch time, sessions, country, device)
• outcome: retained_7d (0/1)

Describe how you would use propensity score matching (PSM) to estimate the treatment effect. Cover the following:

1. Identification assumptions, and what could violate them.
2. How to estimate the propensity scores and select covariates.
3. Matching algorithm and common support.
4. Balance diagnostics.
5. How to estimate ATE versus ATT and quantify uncertainty.
6. Sensitivity analyses and alternatives (such as weighting, doubly robust methods, IV) when PSM is weak.

Overview: This question tests skill with propensity score matching and related causal inference ideas for estimating treatment effects from observational data, covering identification assumptions, propensity score estimation and covariate choice, matching algorithms and common support, balance diagnostics, the choice of estimand (ATE vs ATT), uncertainty quantification, plus sensitivity checks and alternative approaches. It is common in analytics and experimentation interviews for data scientist roles because it examines understanding of confounding and identification in nonrandomized settings and calls for intermediate-to-advanced applied statistics reasoning about methodological trade-offs.