Business Problem Structuring and Case Frameworks Questions

Day 0 — kickoff & context (30–60m)

• Quick sync with PM/ops to confirm affected KPIs (revenue, orders, AOV, conversion), timing of decline, recent product/price/marketing changes, and region list.
• Assign roles: Analyst A = data engineering & exploratory diagnostics; Analyst B = cohort/regional deep dives & dashboarding. I coordinate, do hypothesis testing and escalation.

Day 1–2 — rapid diagnostics (time-boxed, results by end of day 2)

• Global diagnostic checks (Analyst A)
  • Time series of revenue by region, product line, channel (daily/weekly granularity). Look for inflection points.
  • Check data pipeline integrity: missing data, schema changes, attribution shifts, currency conversions.
  • Seasonality and external events overlay (holidays, macro indicators).
• Funnel and unit-level metrics (Analyst B)
  • Revenue = traffic × conversion × AOV. Inspect each component by region/channel.
  • Orders per user, sessions, cart add rate, checkout completion, refund rate.
• Quick anomaly detection & significance
  • Apply simple change-point detection and week-over-week % change; run basic t-tests or proportion tests for conversion drops.

Prioritized regional splits & cohorts (day 2–5)

• Regions by severity and revenue contribution: prioritize top-3 regions with largest absolute or % decline.
• Channel splits: paid search, organic, app vs web, partners.
• Customer cohorts: new vs returning, high-value vs low-value customers, device, currency.
• Product/category-level: top 20 SKUs, categories with highest drop.
• Geo-demographic overlays where available (city, urban/rural) and payment method shifts.

Quick experiments & dashboards to produce (day 3–9)

• Real-time triage dashboard (Analyst B): daily revenue, sessions, conversion, AOV by region/channel with anomaly flags and sparkline; enable drill-down to product and cohort.
• Funnel diagnostic dashboard (Analyst B): conversion at each funnel step by region and device.
• Hypothesis-driven quick analyses (Analyst A + me):
  • Attribution lag check: compare last-click vs assisted conversions.
  • Price/currency impact: simulate revenue if exchange rates changed.
  • Promo/marketing exposure: correlate spend impressions with conversion.
• Rapid experiments (if causal levers suspected and feasible)
  • Small geo A/B (e.g., restore previous UI or promo) for top-affected region if product change suspected — run for minimum detectable effect window.
  • Re-targeted email/promo to returning customers in worst regions and measure immediate lift.

What I escalate to leadership immediately

• Data integrity failures that invalidate comparisons (e.g., missing transactions, broken tracking, attribution model change).
• Major product/price/marketing change rollout coinciding with decline and high likelihood of causality.
• Regulatory/payment failure or partner outage affecting checkout.
• If early analyses show >X% revenue drop in top-revenue regions driven by conversion (not traffic) and experiments are needed — recommend pause/rollback of change and request resources for emergency A/B.

Expected outputs by end of two weeks

• Triage dashboard live, prioritized root-cause hypotheses with supporting stats, results of any quick experiments, recommended remediation actions (rollback, targeted campaigns, engineering fixes), and a short executive summary with next 30/90-day plan.

Key principles

• Time-boxed, hypothesis-driven work; surface data integrity first; focus on regions with highest business impact; communicate early and often with clear asks (rollback, engineering priority, marketing spend).

Approach overview: I’d triangulate causal estimates using three methods — difference-in-differences (DiD), propensity score matching (PSM), and instrumental variables (IV) — compare results and run robustness checks. Each method has different assumptions, so convergence increases confidence.

1. Difference-in-differences

• Setup: Identify treated group (exposed to product change) and control group (not exposed). Use pre- and post-period conversion rates and estimate DiD: (Δtreated − Δcontrol).
• Key assumptions: Parallel trends (absent treatment, groups would evolve similarly) and no spillovers.
• Tests: Visualize pre-treatment trends; run placebo DiD on earlier periods; include time-varying controls; event-study regressions (time dummies interacted with treatment) to check for pre-trend violations.

2. Propensity score matching

• Setup: Model probability of exposure using covariates (user demographics, prior conversion, channel, seasonality indicators). Match treated to similar controls and estimate average treatment effect on treated (ATT).
• Key assumptions: Conditional independence/unconfoundedness (all confounders observed) and overlap/common support.
• Tests: Assess covariate balance before/after matching (standardized mean differences), check common support, sensitivity analysis (Rosenbaum bounds) to unobserved confounding, try multiple matching algorithms (nearest, caliper, weighting).

3. Instrumental variables

• Setup: Find instrument Z that affects exposure but not conversion directly (e.g., rollout timing by region, A/B assignment eligibility, random server-side flag rollout). Two-stage least squares: first-stage exposure ~ Z + controls; second-stage conversion ~ predicted exposure + controls.
• Key assumptions: Relevance (Z strongly predicts exposure) and exclusion restriction (Z affects outcome only through exposure), plus monotonicity.
• Tests: First-stage F-statistic (>10); overidentification tests if multiple instruments (Sargan/Hansen); falsification: show Z has no direct effect on pre-period outcomes; test alternative channels.

Robustness and synthesis

• Control for time-varying confounders and concurrent marketing by including campaign indicators and interacting with time.
• Use event-study and heterogeneous effects (by segment) to understand dynamics.
• If methods disagree, investigate violations (e.g., unobserved confounding) and present bounds (partial identification) and sensitivity analyses. Conclude with best-supported estimate and caveats.

Goal clarification: estimate conversion funnel rates and drivers despite missing event types/timestamps, with transparent uncertainty and prioritized steps that enable immediate insights and longer-term accuracy.

Plan (prioritized):

1. Quick discovery (1–2 days)

• Inventory available tables, columns, ingestion delays; identify canonical user/session IDs.
• Map which funnel steps are missing and which related signals exist (pageviews, purchases, session_start, network logs).

2. Short-term pragmatic fixes (1–2 weeks) — enable analysis now

• Engineering/SQL requests:
  • Add derived session_id and user_id joins where missing (sessionization SQL).
  • Ensure all events surface ingest_time and event_time; backfill event_time where possible from logs.
  • Expose event_source, page_url, referrer, and HTTP status in analytic tables.
• Acceptable approximations / proxies:
  • Use page_view with URL patterns + referrer as proxy for "checkout_start".
  • Use server-side order_created as proxy for "purchase_complete" if client event missing.
  • If timestamps missing, use ingestion_time minus median delay as proxy for event_time.
• Example SQL (sessionization by 30-min gap):

WITH ordered AS (
  SELECT user_id, ts, event, 
    SUM(CASE WHEN ts - LAG(ts) OVER (PARTITION BY user_id ORDER BY ts) > INTERVAL '30 minutes' THEN 1 ELSE 0 END)
      OVER (PARTITION BY user_id ORDER BY ts) as session_group
  FROM events
)
SELECT user_id, session_group, MIN(ts) as session_start, MAX(ts) as session_end
FROM ordered GROUP BY user_id, session_group;

3. Medium-term engineering (4–8 weeks)

• Instrument missing events at source, include precise event_time, dedup keys, idempotency.
• Add schema versioning and lineage to track when instrumentation changes.

Sensitivity checks and validation:

• Construct multiple scenarios using different proxy definitions (tight vs loose URL patterns, ingestion_time vs backfilled event_time).
• Use holdout segments with reliable instrumentation (recent cohorts or a subset of users) to estimate bias between proxy and true events; derive correction factors.
• Perform bootstrapping and Monte Carlo: sample plausible timestamp offsets (based on measured delays) and recompute funnel metrics to get confidence intervals.
• Check robustness across dimensions (device, country, user tenure) to detect systematic bias.

Quantify & communicate uncertainty:

• Report point estimates with 90% empirical confidence intervals from Monte Carlo and bootstrap.
• Provide bias-adjusted estimates: e.g., "proxy conversion = 4.2% (±0.6%), estimated true = 3.8% after adjustment [range 2.9–4.7%]".
• Use visualizations: funnel bars with error bands, sensitivity tornado charts showing which assumptions drive results.
• Executive summary: explain main assumptions, expected direction of bias, actions planned to reduce uncertainty, and recommended decisions conditional on uncertainty (e.g., run an A/B test before wide rollout).

Key trade-offs:

• Faster proxies enable immediate decisions but increase uncertainty; invest in instrumentation to remove ambiguity for strategic metrics.
• Prioritize instrumenting events that change business decisions (checkout, payment, signup).

1. Audience mismatch — ads reached users unlikely to convert (wrong intent/demographics).
   Data/experiment: Compare campaign audience segments (age, gender, device, interests, past purchase propensity) vs. converters from historical baseline; run A/B test targeting high-propensity segment (lookalike or past purchasers) vs. original.
   Success criteria: Targeted variant shows statistically significant lift in conversion rate (CR) — e.g., >20% relative increase and p<0.05, with minimum sample size powering 80% power.

2. Creative messaging not driving intent — impressions/clicks but poor persuasion.
   Data/experiment: Multivariate creative test (headline, CTA, value prop); measure post-click micro conversions (add-to-cart, time on page) and final CR.
   Success criteria: At least one creative yields ≥15% higher add-to-cart rate and a statistically significant CR lift vs. control.

3. Landing page disconnect (UX or mismatch between ad promise and page).
   Data/experiment: Session-level funnel analysis (UTM-tagged ad click → landing page metrics: bounce, time, form completion) and A/B test of a landing page that mirrors ad messaging and reduces friction.
   Success criteria: Reduced bounce rate by ≥25% and increased CR by ≥20% on modified landing page with p<0.05.

4. Technical tracking/attribution issues (sales not attributed).
   Data/experiment: Reconcile ad platform conversions with backend sales/logs; run test purchases with unique promo codes per channel; audit pixels and tag firing with Tag Manager / server-side logs.
   Success criteria: Detection and fix of missed events (e.g., pixel not firing); attributed conversions align within ±5% of backend truth or promo-code-attributed sales >0.

5. Low product-market fit or price sensitivity (offer not compelling).
   Data/experiment: Run an experiment offering a limited discount/promo or free trial to ad cohort vs. control; survey a sample of clicks for purchase barriers.
   Success criteria: Promo group shows significantly higher CR (≥30% uplift) or survey indicates price as primary barrier in >40% of responses.

6. External factors (seasonality, supply issues, competitor activity).
   Data/experiment: Time-series analysis comparing sales vs. historical seasonal trends, inventory logs, competitor ad volume/price monitoring; run geo A/B test in unaffected regions.
   Success criteria: Identification of external driver (e.g., inventory stockout coincident with campaign) and geo where campaign yields normal lift; in unaffected geo, CR significantly higher than affected one (p<0.05).

For each test, predefine sample sizes, tracking, and evaluation window (e.g., campaign + 7 days) and use incremental/holdout analysis to measure true lift.

Situation: We need an attribution system that blends first-touch, last-touch, and data-driven methods when tracking is limited — i.e., partial user-level signals, sampling, and channel-level aggregates. The goal: produce channel contribution estimates, quantify uncertainty, deduplicate across channels, compare models, and give a budgeting recommendation.

Approach overview

• Build three parallel estimators: (A) deterministic rule-based (first-touch & last-touch), (B) algorithmic “data-driven” (probabilistic sequence model / Shapley-style), and (C) a hybrid / hierarchical ensemble that shrinks the data-driven estimate toward rule-based estimates when information is weak.
• Use Bayesian/regularized models and resampling to quantify uncertainty.

1. Data ingestion & deduplication

• Deterministic deduplication: when user identifiers exist (hashed IDs, login), merge events into a timeline per user.
• Probabilistic deduplication: when only partial signals exist, use probabilistic linkage (IP+UA+time windows, propensity matching) and propagate match uncertainty into the model (e.g., multiple imputation of link graphs).
• Aggregate-level fallback: if no user-level linking, aggregate conversions by channel and time window; rely on ecological models (see below).

2. Constructing the models

• First-touch / Last-touch: simple aggregated counting per channel (first- or last-appearance receives full credit). Produce point estimates and bootstrap CIs by resampling users/sessions.
• Data-driven model 1 — Markov transition model:
  • Build channel sequences per (deduplicated) user.
  • Estimate transition probabilities between channels and absorbing conversion state.
  • Compute removal effect: contribution = difference in conversion probability when channel removed (standard Markov attribution).
  • Pros: interpretable sequence-level effect. Cons: needs enough sequences.
• Data-driven model 2 — Shapley / cooperative game-theory approximation:
  • Treat channels as players; compute marginal contribution via sampling permutations (approximate Shapley) to estimate average incremental contribution.
  • Works at user or cohort level; more robust to order ambiguity.
• Data-driven model 3 — Causal / uplift / incremental model:
  • Use logged ad exposures and outcomes to build a causal model (e.g., double ML, causal forest, or Bayesian structural model) to estimate incremental conversions attributable to each channel controlling for confounders (time of day, campaign targeting).
  • If randomized experiments (holdouts / geo-tests) exist, use them to calibrate/validate uplift estimates.
• Hybrid ensemble:
  • Build a Bayesian hierarchical model where channel contribution parameter = alpha * data_driven + (1 - alpha) * rule_based, with alpha learned from data quality metrics (sample size, variance, match-rate).
  • Or use regularized stacking: meta-learner that learns weights for first-touch, last-touch, Markov, Shapley, uplift predictors using cross-validation minimizing out-of-sample prediction error for conversion or incremental conversions.

3. Handling limited data / small-sample regularization

• When match-rate or sample size is low, shrink complex model estimates toward simpler rule-based priors (empirical Bayes).
• Use strong priors informed by business knowledge (e.g., offline channels often have larger first-touch role).
• Use aggregation by cohort/time-window to increase effective sample size when necessary.

4. Quantifying uncertainty

• Bayesian credible intervals: run full posterior for hierarchical models (e.g., Stan/PyMC) to obtain posterior distributions of channel contributions.
• Bootstrap / permutation: resample users/sessions to get nonparametric CIs for Markov/Shapley estimates.
• Propagate deduplication uncertainty: perform multiple imputations of linkage and compute attribution across imputations to get between-imputation variance.
• Report: point estimate, 90% CI, and probability that channel contribution > 0 (or exceeds next-best channel).
• For budget decisions, convert uncertainty into ROI distributions (expected incremental conversions per $ spent and credible intervals) to support risk-aware decisions.

5. Model comparison & validation

• Holdout validation: partition users/time windows and compare predicted conversions to observed; prefer models that better predict holdout incremental conversions.
• Use experimental ground truth: prioritize models that align with A/B or geo experiments where available; calibrate model outputs to experiment-measured lift.
• Compare on metrics: bias (alignment to experiment), stability (variance across bootstraps), interpretability, and data requirements.
• Use Pareto ranking: tradeoff between bias/variance and operational complexity.

6. Recommendation for budgeting

• Primary policy: use the data-driven (causal/uplift or Shapley calibrated by experiments) estimate for budget allocation because it aims to capture incremental impact, but only if data quality and validation metrics exceed thresholds (e.g., user match-rate > X%, effective sample size > Y, model error below Z).
• If thresholds not met: use the hybrid Bayesian ensemble (shrunk) which blends data-driven signals with last/first-touch, with explicit uncertainty propagated.
• Always accompany budget changes with planned experiments (holdout groups or geo splits) covering the top channels — use model's uncertainty to size experiments and run iterative calibration.
• Operational rule: prioritize channels by expected incremental conversions per dollar and probability of positive ROI; invest more where expected ROI is high and uncertainty is manageable, and allocate a testing budget (~10–20%) for validation.

Example tools & implementation notes

• Sequence processing: Spark/Pandas to build session timelines.
• Markov/Shapley: Python (numpy/pandas), networkx for transitions, approximate Shapley with Monte Carlo sampling.
• Causal / uplift: EconML, causal forests, Double ML.
• Bayesian ensemble / uncertainty: PyMC3 / Stan for hierarchical models, or bootstrap pipelines for non-Bayesian methods.
• Reporting: produce a dashboard with point estimates, CIs, and alignment-to-experiment metrics.

Key trade-offs and reasoning

• First/last-touch are simple, low-variance but biased (over/under-credit).
• Markov/Shapley give sequence-aware, fairer allocation but need data and are higher variance.
• Causal uplift gives best incremental estimate when assumptions hold and confounders controlled.
• Shrinking to simpler models prevents overfitting under limited data and yields more stable budget signals.

This combined approach yields defensible channel contributions, explicit uncertainty, and a decision rule that uses data-driven estimates when supported by data, otherwise reverts to a regularized hybrid that balances bias and variance while mandating experimental validation for budget moves.