Interaction Effects

What Are Interaction Effects?

An interaction effect occurs when the relationship between a predictor and the outcome depends on another variable. In disease forecasting, a common example is that rainfall's effect on disease may differ between regions -- heavy rainfall might strongly increase cases in lowland areas but have little effect in highlands.

In a linear regression without interactions, adding region indicators only shifts the baseline (intercept) per region. The slope of each predictor is the same everywhere:

cases = offset_region + b1 * rainfall + b2 * temperature

With an interaction term, the slope itself varies by region:

cases = offset_region + b1_region * rainfall + b2 * temperature

This is achieved by multiplying the region indicator with the predictor, creating a new feature: region_A * rainfall, region_B * rainfall, etc.

Regression Models Need Explicit Interactions

In linear regression (and generalized linear models), the model can only learn relationships that are explicitly encoded in the features. If the effect of rainfall differs between regions but the model has no interaction term, it is forced to find a single average effect -- which may be wrong for all regions.

Common interaction patterns in disease forecasting:

• Location x climate: different climate sensitivities per region
• Location x season: different seasonal patterns per region (as shown in the multi-region walkthrough)
• Season x climate: climate effects that vary by time of year

The downside of interactions is that they multiply the number of parameters. With 10 regions and 12 months, location x season creates 120 interaction features. With limited data, this can lead to overfitting.

Flexible ML Models Learn Interactions Implicitly

Tree-based models (Random Forest, XGBoost) and deep learning models can learn interaction effects without being told to look for them.

A decision tree naturally creates interactions through its branching structure. A split on "region = A" followed by a split on "rainfall > 100" effectively learns a region-specific rainfall threshold -- an interaction between region and rainfall.

Deep learning models learn interactions through their hidden layers. Nonlinear activation functions allow the model to combine inputs in complex ways without explicit feature engineering.

When to Use Explicit Interactions

Use explicit interactions when:

• Using linear regression or GLMs
• You have domain knowledge about which interactions matter
• The dataset is small enough that implicit learning would overfit

Rely on implicit interactions when:

• Using tree-based or deep learning models
• You have many potential interactions and want the model to discover which matter
• The dataset is large enough to support learning complex patterns

In practice, even with flexible models, adding known important interactions as explicit features can help -- it makes it easier for the model to find patterns that domain knowledge suggests should exist.