Understanding Causal Impact Analysis

Causal impact analysis is a powerful statistical technique for measuring the effect of an intervention when randomized controlled trials are not feasible. It's particularly useful in scenarios like:

• Measuring the impact of a marketing campaign
• Evaluating policy changes
• Assessing the effect of a website redesign

The Challenge

When you implement an intervention (like launching a new feature), you observe what happens afterward. But the key question is: What would have happened without the intervention?

This counterfactual scenario is impossible to observe directly - you can't both launch and not launch the feature in the same time period.

The Solution: Synthetic Controls

Causal impact analysis uses a technique called synthetic controls to estimate what would have happened without the intervention:

1. Pre-intervention period: Build a model that predicts your metric of interest using related variables
2. Post-intervention period: Use the model to generate a counterfactual prediction
3. Compare: The difference between actual and predicted values is the causal effect

Key Requirements

For causal impact analysis to work effectively, you need:

• Sufficient pre-intervention data to build a reliable model
• Control time series that are correlated with your outcome but unaffected by the intervention
• No confounding interventions during the analysis period

Mathematical Framework

The approach uses Bayesian structural time series (BSTS) models to:

• Capture trends and seasonality
• Model relationships with control variables
• Quantify uncertainty in the estimates

The result is not just a point estimate of the effect, but a full posterior distribution showing the range of plausible effects.

Example Application

Imagine you launch a new feature on your website:

• Pre-period: 90 days before launch
• Post-period: 30 days after launch
• Outcome: Daily active users
• Controls: Page views on other products, industry metrics

The analysis would show:

• Expected DAU without the feature (counterfactual)
• Actual DAU with the feature
• The causal effect and its credible interval

Benefits

Causal impact analysis provides:

1. Rigorous causal inference without randomization
2. Uncertainty quantification through Bayesian inference
3. Clear visualization of the effect over time
4. Statistical significance testing built into the framework

In upcoming tutorials, we'll walk through implementing causal impact analysis using Python and R!