I went with logistic regression first and framed it as the default when you want interpretability and your covariates are well-behaved.
Start by framing the causal inference problem: self-selection creates confounding, so you need to balance observed covariates between treated and control groups. Walk through the full PSM pipeline—propensity model choice, estimation, matching, balance diagnostics, and ATT calculation—while emphasizing assumptions and sensitivity checks. Tie each decision back to the business context of 7-day retention at TikTok.
Pro tip: Don't just say 'logistic regression'—explain why it's often preferred for propensity scores (calibration, interpretability, stable odds) and mention that you'd validate with balance metrics like standardized mean differences, not AUC. Also, proactively note that PSM only addresses observed confounding, and suggest a sensitivity analysis (e.g., Rosenbaum bounds) to show maturity.
Clarify that you're estimating ATT: the effect of the feature on 7-day retention for those who used it. State key assumptions: conditional independence (no unobserved confounding), positivity, and SUTVA.
Select a model to estimate P(T=1|X). Justify logistic regression for its calibration and interpretability, but mention alternatives like gradient boosting if nonlinearities are suspected. Include relevant covariates (demographics, past behavior, engagement metrics) and avoid post-treatment variables.
Use a matching algorithm (e.g., nearest neighbor with caliper, optimal matching) on the propensity score or logit of it. Specify caliper width (e.g., 0.2 SD of logit) and whether matching is with or without replacement. Consider trimming to ensure common support.
Check covariate balance using standardized mean differences (<0.1) and variance ratios. Inspect propensity score distributions to ensure overlap. If balance is poor, revise the model or matching method.
Compute ATT as the difference in mean 7-day retention between matched treated and control groups. Use bootstrapping or Abadie-Imbens standard errors. Conduct sensitivity analysis (e.g., Rosenbaum bounds) to assess robustness to unobserved confounding.
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Caliper in standard deviation units of the logit of the propensity score is the right framing and I got that out.
Start by clarifying the goal of matching (e.g., causal inference, bias reduction) and the data context. Then explain the trade-offs between 1-to-1 with and without replacement, how to set the caliper based on propensity score distribution, and how to tune these choices using diagnostics like balance checks and sensitivity analysis. Emphasize that the optimal strategy depends on the specific problem and data.
Pro tip: Always check covariate balance after matching and consider the impact of replacement on variance and bias. In practice, using a caliper of 0.2 standard deviations of the logit of propensity score is a good starting point, but validate with your specific data.
Determine whether matching is for causal inference, reducing confounding, or creating comparable groups. This guides whether to prioritize bias reduction or variance.
Discuss that matching with replacement can reduce bias by allowing control units to be reused, but may increase variance and correlation. Without replacement ensures independence but may sacrifice match quality.
Explain that the caliper defines the maximum allowed distance between matched units. A common rule is 0.2 * SD of the logit of propensity score, but it should be tuned based on balance and sample size.
Use balance metrics (e.g., standardized mean differences) and sensitivity analysis to evaluate different calipers and replacement strategies. Consider cross-validation or simulation to optimize.
Account for sample size, computational cost, and interpretability. For large datasets, with replacement may be feasible; for small, without replacement might be necessary.
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Standardized mean differences below 0.1 per covariate, variance ratios close to 1, KS tests for distributional differences.
Start by outlining the standard balance diagnostics you would run after matching, such as standardized mean differences (SMD) and variance ratios, and then explain your iterative process for addressing insufficient balance, including model refinement and sensitivity analysis. Emphasize that balance is not just a statistical check but a critical step to ensure valid causal inference in A/B tests and product analytics.
Pro tip: Mention that you prioritize balance on key covariates that are most predictive of the outcome, and that you use the 'balance as a continuous target' mindset rather than a binary threshold. This shows you understand the trade-offs and practical constraints in real-world experimentation.
Compute standardized mean differences (SMD) for all covariates and inspect variance ratios between treated and control groups. Also check for interactions and higher-order moments if relevant.
Use Love plots or other visualizations to identify covariates with poor balance. Assess whether imbalances are practically significant, not just statistically significant.
If balance is insufficient, adjust the matching algorithm: change the distance metric (e.g., propensity score, Mahalanobis), caliper width, or add exact matching constraints. Consider using genetic matching or coarsened exact matching.
If matching still fails, explore weighting methods (e.g., inverse probability weighting, entropy balancing) or regression adjustment. Document the trade-offs and potential biases.
Assess how sensitive results are to unobserved confounding using methods like Rosenbaum bounds. Report the robustness of findings and acknowledge limitations.
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Plot the distributions and look for regions where one group has near-zero density.
Start by defining lack of overlap (positivity violation) and its impact on causal inference. Then outline a systematic process: detect via diagnostics, assess severity, and apply appropriate handling methods. Emphasize trade-offs and practical considerations for large-scale experimentation at TikTok.
Pro tip: Mention that in large-scale A/B tests, lack of overlap often signals a broken randomization or targeting issue, so fixing the experiment design is preferable to post-hoc adjustments. Also, highlight that trimming can introduce bias if not done carefully, and sensitivity analysis is crucial.
Use propensity score distributions (e.g., histograms, density plots) and summary statistics (min/max, percentiles) to visually and numerically assess overlap. Calculate common support region and identify extreme scores.
Measure the proportion of units outside the common support and check covariate balance within the overlap region. Determine if the lack of overlap is due to a few outliers or systematic differences.
Consider trimming (discarding units outside common support), weighting (e.g., inverse probability weighting with stabilization), or matching with calipers. For severe cases, revisit experiment design or use alternative methods like doubly robust estimation.
Compare results with and without handling to assess robustness. Conduct sensitivity analysis to unmeasured confounding and report limitations. If possible, validate with a holdout set or simulation.
Clearly explain the issue and chosen approach to stakeholders, emphasizing trade-offs. If overlap is poor, recommend improvements for future experiments (e.g., better targeting, stratification).
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This tripped me up more than it should have.
Start by clarifying that both methods address the fact that propensity scores are estimated, not known, which affects the variance of treatment effect estimates. Then compare Abadie-Imbens standard errors, which provide a closed-form correction for estimated propensity scores, with bootstrapping, which is more flexible but computationally intensive. Conclude with practical guidance based on sample size, computational constraints, and the need for valid inference.
Pro tip: Mention that Abadie-Imbens standard errors are specifically designed for matching estimators and are robust to misspecification of the propensity score model, whereas bootstrapping may fail to capture the full uncertainty when matching is not smooth. Also note that in large-scale A/B tests at TikTok, computational efficiency often favors Abadie-Imbens unless the matching procedure is complex.
Explain that after propensity score matching (PSM), treatment effect estimates are uncertain due to both sampling variability and the estimation of propensity scores. Standard errors must account for this extra uncertainty.
Abadie-Imbens standard errors provide a closed-form variance estimator that adjusts for the fact that propensity scores are estimated. They are derived under the assumption that matching is done without replacement and are valid for various matching estimators.
Bootstrapping involves resampling the data with replacement and re-running the entire matching and estimation procedure to obtain an empirical distribution of the treatment effect. It is a general-purpose method but can be computationally expensive and may not be valid for certain matching algorithms.
Use Abadie-Imbens when you need a fast, theoretically justified variance estimate for common matching estimators (e.g., nearest neighbor, caliper) and when the sample is large. Use bootstrapping when the matching procedure is complex, when you need to account for additional sources of uncertainty (e.g., from a first-stage model), or when the sample is small and computational resources are available.
In practice, for large-scale experiments like those at TikTok, Abadie-Imbens is often preferred for its computational efficiency and theoretical guarantees. However, if the matching is not standard or if there is concern about model misspecification, bootstrapping can serve as a robustness check.
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Gamma is the odds ratio of treatment assignment that an unobserved confounder could introduce while still leaving your conclusions intact.
Start by defining Rosenbaum sensitivity analysis in simple terms: it assesses how robust a causal conclusion is to unmeasured confounding. Then explain the gamma parameter as the odds ratio of differential treatment assignment due to unmeasured confounding, and describe how to find the tipping point by incrementally increasing gamma until the p-value crosses the significance threshold. Finally, tailor the communication to a product manager by using a concrete example and focusing on the practical implication: how much unmeasured bias would be needed to overturn the result.
Pro tip: Emphasize that sensitivity analysis is not about proving causality but about quantifying the strength of unmeasured confounding needed to explain away the effect—this shows you understand its role in responsible decision-making. Also, when communicating to a PM, avoid statistical jargon and instead say something like: 'Our result is strong enough that an unmeasured factor would need to be X times more common in the treatment group to make the effect disappear.'
Explain that it's a method to assess how sensitive a causal inference is to hidden bias from unmeasured confounding. Mention that it's commonly used in observational studies when randomization isn't possible.
Describe gamma (Γ) as the odds ratio of receiving treatment for two individuals with identical observed covariates but different unobserved factors. A gamma of 1 means no hidden bias; larger values indicate stronger potential bias.
Explain that you incrementally increase gamma and recompute the p-value or confidence interval for the treatment effect. The tipping point is the gamma value at which the conclusion flips (e.g., p-value exceeds 0.05 or CI includes zero).
Translate the tipping point into a practical statement: 'Our result would only be overturned if an unmeasured factor made treatment X times more likely.' Use analogies and focus on the decision at hand, not the math.
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