Frame the analytical approach

Step 1: Consider what Astrid is asking

Astrid made a distinction: "whether PM2.5 changed" and "whether the regulation caused the change" are different questions. Direct AI to articulate what different analytical framings would look like for her data.

A descriptive framing would show trends -- PM2.5 over time, by city, by season. Informative, but it would not answer whether the regulation had an effect. A prediction framing would forecast future PM2.5 levels -- technically interesting but not what the agency needs. An inferential framing would test whether there is a statistically significant change in PM2.5 after the regulation, controlling for the factors that also affect air quality.

The agency needs to know whether the regulation worked. That is an inferential question: is there a significant shift in PM2.5 after the regulation, once you account for seasonal patterns, weather effects, and long-term trends?

The specific approach is an interrupted time series analysis. The "interruption" is the regulation. The analysis models the pre-regulation trend and seasonal pattern, then tests whether the post-regulation levels are significantly different from what the pre-regulation model would have predicted.

Step 2: Plan the analytical decomposition

Before starting the analysis, plan the pieces and their order. What depends on what?

1. Profile and clean the data (already started in Unit 1)
2. Model the seasonal and weather effects -- these are the confounders that must be separated from the regulation's effect
3. Test for a significant change in PM2.5 levels after the regulation, controlling for those confounders
4. Validate the model's assumptions and sensitivity
5. Interpret and communicate honestly

Each step depends on the one before it. The seasonal model must be adequate before you can test for the regulation's effect. The assumption checks must pass before you trust the results.

Step 3: Document the framing

Open materials/methodology-memo-template.md. Fill in the "Analytical Question and Framing" section.

Document the question type (inferential -- interrupted time series). List the alternative framings you considered and why they were set aside. Write the rationale for the chosen framing: the agency needs to know whether the regulation caused the change, controlling for weather, season, and trend. Descriptive analysis would not answer that. Prediction would answer a different question. The interrupted time series framing directly addresses the agency's decision.

Step 4: Write the decomposition plan

Still in the methodology memo, write the decomposition plan. What pieces, what order, what depends on what. This is the analytical roadmap for the rest of the project.

The plan should be specific enough that you could hand it to someone else and they would know what to do -- but not so detailed that it pre-commits to decisions you have not made yet. The model specification, the exact controls, the validation approach -- those come later.