Week 9 Notes - Course Introduction

Published

November 10, 2025

Key Takeaways: Space-Time Prediction (Bike Share Demand)

1. Motivation and Problem Context

  • Real-world task: forecast bike share demand to support rebalancing.
  • Demand varies across space (stations) and time (hours).
  • Operational need: predict which stations will be empty or full ahead of time.
  • Models must capture temporal patterns and spatial differences simultaneously.

2. Panel Data Framework

  • Definition: same units observed repeatedly over time.
  • Each row = station-hour combination.
  • Enables analysis of both:
    • Station-specific baselines (spatial effects).
    • Time-based dynamics (temporal effects).

Examples of temporal variation: - Morning/evening commute peaks. - Weather and weekday effects. - Weekend and holiday differences.

3. Data Preparation

Binning Trips

  • Aggregate trips into consistent time intervals (e.g., hourly).
  • Purpose: identify temporal patterns and create comparable time steps.

Creating Features

  • Extract from timestamps:
    • hour, day of week, week.
  • Label weekends and holidays.
  • Merge weather data (temperature, precipitation).

4. Temporal Lags

  • Past demand predicts future demand.
  • Common lag variables:
    • lag1Hour, lag3Hours, lag12Hours, lag1day.
  • Capture persistence and daily cycles.
  • Must compute within each station.

5. Building a Complete Panel

  • Missing station-hour combinations break lag calculations.
  • Use expand.grid() to create all station-hour pairs.
  • Fill missing trip counts with zeros.
  • Join:
    • Fixed attributes (station location, demographics).
    • Time-varying features (weather, hour, weekday).

6. Temporal Validation

  • Rule: never train on the future to predict the past.
  • Split by time, not randomly.
    • Train on early weeks → test on later weeks.
  • Mirrors operational forecasting: use past data to predict future behavior.
  • Prevents temporal leakage.

7. Model Development Progression

  1. Baseline: time + weather.
  2. + Temporal lags: add past demand variables.
  3. + Spatial features: add demographics.
  4. + Fixed effects: control for station-level baselines.
  5. + Holidays: capture disruptions in demand.

Performance metric: MAE (Mean Absolute Error)
→ Interpretable as “average trips off by X.”

8. Typical Results

Model Key Additions Improvement
1. Baseline Time + Weather Base level
2. + Lags Temporal persistence Major gain
3. + Demographics Neighborhood context Moderate
4. + Fixed Effects Station baselines Large gain
5. + Holidays Event adjustments Small gain

9. Space-Time Error Analysis

  • Examine residuals in both space and time.
  • Identify systematic under/over-prediction.
    • Rush hours or weekends?
    • Certain neighborhoods?
  • Map errors spatially to reveal missing features.
  • Check correlation between errors and demographics (equity concerns).

10. Policy Insights

  • High-volume stations: prediction accuracy most critical.
  • Temporal trends guide rebalancing schedules.
  • Persistent spatial errors may imply infrastructure or equity issues.
  • “Good enough” predictions depend on operational tolerance for error.

11. Broader Applications

  • Panel data + temporal lags apply to:
    • Transit ridership
    • Crime monitoring
    • Housing dynamics
    • Health and education outcomes
    • Environmental monitoring

12. Core Concepts Recap

  1. Panel data tracks the same spatial units over time.
  2. Temporal lags encode short- and long-term persistence.
  3. Temporal validation ensures realistic performance testing.
  4. Station fixed effects handle unobserved spatial heterogeneity.
  5. Space-time error analysis diagnoses model bias.
  6. Equity assessment is essential for deployment decisions.