Test regional response-rate differences rigorously
Overview
This question evaluates applied statistical modeling and causal-inference competencies, including adjustment for confounding, analysis of proportion/count outcomes, variance estimation under clustering, multiple-comparison control, diagnostic detection of Simpson’s paradox, and clear effect-size reporting; it is categorized under Statistics & Math and emphasizes practical application with necessary conceptual understanding. Such problems are commonly asked to assess the ability to justify and interpret comparative analyses that account for covariate mix, temporal structure, and multiple-testing concerns, and this summary is in English.
Goal
Assess whether provider response rates differ by region after adjusting for job category mix and time.
Data
You have job-level observations with the following fields:
- job_category (categorical)
- region (categorical)
- invitations_sent (integer ≥ 0)
- provider_responses (integer ≥ 0, ≤ invitations_sent)
- created_at (timestamp)
Interpretation: For each job, invitations_sent providers were invited and provider_responses of them responded.
Task
Propose and justify a statistical approach to estimate regional differences in response rates while controlling for job_category and time. Include:
- Model specification: family/link, explicit formula, fixed effects for job_category and time (e.g., month), and any interactions you recommend.
- How you will compute or regularize standard errors (e.g., clustering/robust variance).
- A multiple-comparison strategy across many regions (e.g., Holm–Bonferroni or Benjamini–Hochberg on region effects).
- A diagnostic for Simpson’s paradox driven by job_category mix.
- How you will report effect sizes and practical significance, not just p-values.
State any minimal assumptions you need (e.g., how you define time buckets from created_at).
Solution
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