Estimate weather’s effect on mental health

## Scenario You are studying whether **weather** (e.g., temperature, precipitation, sunlight, air pressure) affects **mental health outcomes** (e.g., depression score, anxiety index, crisis hotline calls, therapy app usage). You have observational data at either the **person-day** level or **region-day** level. ## Task Describe how you would estimate the **causal effect** of weather on mental health while addressing confounding. Your answer should include: 1. **Define the outcome and treatment** - What is the outcome variable (continuous score vs binary event)? - What is the “treatment” (e.g., +5°C temperature shock, rainy day indicator, hours of sunlight)? - Consider possible **lagged effects** (weather today impacts mental health over the next few days). 2. **Confounders & biases** - List plausible confounders (seasonality, holidays, location, socioeconomic status, pollution, day-of-week, long-term trends). - Discuss selection bias (who appears in the dataset) and measurement error. 3. **Identification strategy** - Propose an approach to identify a causal effect (e.g., fixed effects, difference-in-differences/event study, instrumental variables, propensity scores), and state assumptions. 4. **Model specification and checks** - Provide a concrete regression / model form. - How would you test key assumptions (parallel trends, no unobserved time-varying confounders, SUTVA)? 5. **Interpretation** - How would you interpret the effect size? - What sensitivity analyses would you run to assess robustness? ## Output Provide a structured plan and at least one model equation (LaTeX is OK).