I knew the answer but fumbled the explanation a bit.
Start by defining standardized mean difference (SMD) and its role in assessing covariate balance after propensity score matching. Explain the conventional 0.1 threshold as a rule of thumb that balances bias reduction and sample retention, referencing its roots in the causal inference literature. Then, discuss why this threshold is widely adopted, including its simplicity, interpretability, and empirical validation across many studies.
Pro tip: Emphasize that the 0.1 threshold is not a strict statistical cutoff but a practical guideline; in high-stakes settings like Netflix, you might tighten it to 0.05 or use alternative balance metrics like variance ratios, especially when the matched sample is large enough.
Explain that SMD measures the difference in means between treated and control groups in units of pooled standard deviation, used to assess covariate balance after matching.
State that an SMD of 0.1 or below is commonly considered indicative of negligible imbalance, a convention popularized by Rosenbaum and Rubin (1985) and widely adopted in observational studies.
Discuss that 0.1 balances bias reduction and sample size: it is stringent enough to remove substantial confounding but lenient enough to retain enough matched units for precise effect estimation.
Note that the threshold is a rule of thumb, not a statistical test; in some contexts, stricter thresholds (e.g., 0.05) or additional balance metrics (e.g., variance ratios, KS statistics) are used.
Connect to Netflix's experimentation culture: with large datasets, you can afford stricter balance criteria, and you should also consider the impact of imbalance on the specific metric of interest.
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Start by clarifying why logistic regression might not fit (e.g., non-linearity, high-dimensionality, or complex interactions), then propose alternatives like tree-based models, regularized regression, or doubly robust methods. Emphasize that the choice depends on the bias-variance trade-off, interpretability needs, and the ultimate goal of balancing covariates in causal inference.
Pro tip: Mention that propensity scores are a means to an end—the goal is covariate balance—so you can use any model that achieves that, and always validate balance with metrics like standardized mean differences. Also, highlight that Netflix often deals with large-scale, high-dimensional data, so scalable methods like gradient boosting are practical.
Identify specific limitations such as non-linear relationships, high-dimensional features, or complex interactions that logistic regression cannot capture well.
Suggest tree-based methods (random forests, gradient boosting), regularized regression (LASSO, ridge), or generalized additive models (GAMs) as flexible alternatives.
Mention combining propensity score weighting with outcome regression (e.g., TMLE, AIPW) to protect against model misspecification.
Assess covariate balance using standardized mean differences and cross-validation; compare model performance via metrics like AUC or calibration.
Relate the choice to Netflix's needs: scalability, interpretability for stakeholders, and integration with A/B testing frameworks.
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Start by acknowledging that matching reduces but doesn't eliminate confounding, then outline a systematic diagnostic approach using balance checks, sensitivity analysis, and falsification tests. Emphasize that residual confounding is assessed through both statistical and design-based methods, and that the goal is to quantify robustness rather than prove absence.
Pro tip: Frame residual confounding as a continuum of bias, not a binary issue, and propose a sensitivity analysis (e.g., E-value) to quantify how strong an unmeasured confounder would need to be to overturn your results. This shows you think like a scientist who communicates uncertainty, which is highly valued at Netflix.
Compute standardized mean differences (SMDs) for all measured covariates and check if they are below the conventional threshold (e.g., 0.1). Also inspect distributional overlap using plots like love plots or empirical CDFs.
Use methods like Rosenbaum bounds, E-values, or the impact threshold for a confounding variable (ITCV) to quantify how much an unmeasured confounder would need to change the effect estimate to alter conclusions.
Identify an outcome that should not be affected by the treatment (e.g., a pre-treatment variable) and test whether the matched groups differ on it. If they do, residual confounding is likely present.
Check if the treatment effect varies implausibly across subgroups defined by covariates. Large, unexplained heterogeneity may signal residual confounding or model misspecification.
Contrast findings with those from regression adjustment, propensity score weighting, or instrumental variables. If estimates diverge substantially, residual confounding may be a concern.
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Went with bootstrap variance estimation since it's the most defensible in practice and doesn't require strong distributional assumptions.
Start by clarifying the causal estimand (e.g., ATT) and the matching procedure (e.g., 1:1 nearest neighbor with replacement). Then describe a variance estimator that accounts for the matching process, such as the Abadie-Imbens conditional variance estimator or a bootstrap that redoes the matching. Finally, discuss practical considerations like bias-variance tradeoff and when to use which method.
Pro tip: Mention that ignoring the matching step in variance estimation leads to underestimation, and that the Abadie-Imbens estimator is a standard choice in causal inference packages like MatchIt. Also, note that Netflix often deals with large datasets, so computational efficiency matters—bootstrapping may be feasible but can be slow, so consider analytical approximations.
State the target estimand (e.g., ATT) and the specific matching algorithm (e.g., 1:1 nearest neighbor with replacement, caliper). This sets the context for variance estimation.
Select a method that accounts for the matching: either an analytical estimator (e.g., Abadie-Imbens) or a resampling method (e.g., bootstrap that redoes matching).
For Abadie-Imbens, explain that it conditions on the matched sample and uses a weighted variance formula that incorporates matching weights and the number of times each control is used. For bootstrap, describe resampling units and re-matching.
Mention assumptions like unconfoundedness and overlap, and note that variance estimators may be biased if matching is not exact or if there is hidden bias.
Mention software (e.g., MatchIt in R, or custom code) and how to handle large data (e.g., using analytical estimators for speed).
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