I knew convex hull and no interference but fumbled explaining why pre-period fit matters as a proxy for unobserved confounders.
Start by briefly defining synthetic control and its purpose, then systematically list each core assumption (no interference, parallel trends, convex hull, no anticipation, and donor pool validity). For each, explain the assumption, how it can be tested or assessed, and the specific direction of bias if violated. Conclude by discussing practical implications and robustness checks.
Pro tip: Emphasize that synthetic control is most credible when you can show pre-treatment fit and placebo tests; if an assumption is violated, quantify the potential bias rather than just stating it.
Briefly explain that synthetic control constructs a weighted combination of control units to mimic the treated unit's pre-treatment outcomes, then estimates the treatment effect as the post-treatment difference.
Enumerate the key assumptions: no interference (SUTVA), parallel trends (or that the synthetic control would have followed the treated unit's counterfactual), convex hull condition, no anticipation, and valid donor pool.
For each assumption, describe what it means, how it might be violated, and the specific distortion to the treatment effect estimate (e.g., bias direction, attenuation, exaggeration).
Mention how to assess assumptions: pre-treatment fit, placebo tests, leave-one-out, and sensitivity analyses. Explain what to do if assumptions are violated.
Summarize how violations affect decision-making and what alternative methods or adjustments could be used.
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Emphasize that synthetic control is a pre-treatment design: all predictor and lag choices must be justified using only pre-intervention data and domain knowledge. Describe a principled process that separates design decisions from outcome evaluation, and highlight how you would validate the absence of leakage through placebo tests and temporal cross-validation.
Pro tip: Frame the problem as 'designing a pre-treatment-only pipeline' and explicitly state that you never look at post-treatment outcomes when selecting predictors or lags—this signals deep understanding of causal inference and avoids the most common pitfall.
Clearly specify the intervention date and restrict all data used for model selection to the period before that date. Identify the outcome variable and ensure it is not used in any form during predictor/lag selection.
Choose predictors that are theoretically related to the outcome and measured pre-treatment. Use pre-treatment fit metrics (e.g., RMSE on pre-period) to compare candidate sets, but avoid using post-treatment outcomes to guide selection.
Test lag lengths using only pre-treatment data with time-series cross-validation (e.g., rolling-origin). Select lags that minimize pre-treatment prediction error without peeking at post-treatment performance.
Run placebo interventions in the pre-period to check that the method does not produce false positives. Assess sensitivity of results to predictor and lag choices to ensure robustness.
Record all decisions (predictors, lags, validation metrics) before examining post-treatment outcomes. This prevents unconscious leakage and increases credibility of the analysis.
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Talked through pointwise vs cumulative effects and the placebo distribution logic using donor units.
Structure your answer around the three core components: treatment effect estimation, p-value generation, and uncertainty quantification. Emphasize the synthetic control method's reliance on a donor pool and placebo tests, and connect it to Reddit's experimentation context by highlighting how it handles non-randomized settings. Be concrete about algorithms (e.g., constrained regression, permutation tests) and validation steps.
Pro tip: Mention that you validate the synthetic control by checking pre-treatment fit and running in-time placebo tests; this shows you understand the method's assumptions and pitfalls. Also, note that p-values from permutation tests are exact but limited by the number of donors, so you might use additional robustness checks like leave-one-out.
Explain how you build a weighted combination of donor units that mimics the treated unit's pre-treatment outcomes. Use constrained optimization (e.g., nested optimization or quadratic programming) to minimize pre-treatment RMSE, possibly including covariates.
Compute the difference between the treated unit's post-treatment outcomes and the synthetic control's post-treatment outcomes. This difference is the estimated treatment effect over time.
Perform in-space placebo tests: iteratively assign treatment to each donor unit, compute the effect, and compare the treated unit's effect to the distribution of placebo effects. The p-value is the proportion of placebo effects as extreme as the treated effect.
Use the placebo distribution to construct confidence intervals or uncertainty bands around the treatment effect. Alternatively, use bootstrap or Bayesian methods if assumptions allow, but emphasize permutation-based intervals for robustness.
Check pre-treatment fit and placebo tests in time to ensure validity. Discuss limitations (e.g., donor pool size, spillovers) and how you would communicate uncertainty to stakeholders.
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Probably my strongest answer of the session.
Start by explaining that poor pre-period fit indicates a violation of the parallel trends assumption, which is critical for valid causal inference. Then outline a systematic diagnostic process: check for outliers, seasonality, and structural breaks; try transformations or alternative control groups; and if all else fails, consider switching to a method like synthetic control or matched cohorts. Emphasize that the choice depends on the trade-offs between bias and variance, and the specific context of the experiment.
Pro tip: Always quantify the impact of poor pre-period fit on your effect estimate—e.g., by simulating a placebo test—to decide whether the violation is fatal or manageable. This shows you're pragmatic and focused on decision-making, not just diagnostics.
Plot pre-period trends for treatment and control groups, and compute metrics like RMSE or placebo tests. Identify whether the issue is due to outliers, seasonality, level shifts, or divergent trends.
Investigate data collection issues, missing data, or external events (e.g., holidays, product changes) that could cause divergence. Ensure the pre-period is long enough and stable.
Consider transformations (e.g., log, differencing), adding covariates, using propensity score matching, or trimming outliers. If seasonality is present, adjust with seasonal decomposition or include time fixed effects.
If fit remains poor, switch to methods that are more robust to parallel trends violations, such as synthetic control, difference-in-differences with staggered adoption, or causal impact using Bayesian structural time series.
Weigh the bias-variance trade-off, interpretability, and business constraints. Run sensitivity analyses to see how results change under different assumptions, and communicate uncertainty clearly.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.