Location Specificity in Common Model Classes

Different model classes vary in how naturally they support region-specific effects versus sharing information across regions. This overview summarizes the main approaches.

Reference Table

Model class	Separate per region	Global (shared)	Semi-global / partial pooling
Linear regression	Yes (fit per region)	Yes (pooled)	Via mixed effects (e.g. lme4)
ARIMA	Yes (standard use)	Not typical	Not typical
ETS	Yes (standard use)	Not typical	Not typical
Hierarchical Bayesian	Yes	Yes	Yes (primary use case)
Random Forest / XGBoost	Yes	Yes (with region feature)	Via region feature
Deep learning (LSTM, etc.)	Yes	Yes (with embedding)	Via learned embeddings

Key Observations

Traditional time series models (ARIMA, ETS) are inherently single-series models. They fit one model per region by default and have no built-in mechanism for sharing information across regions.

Linear regression is flexible: it can be fit per region, pooled across regions, or extended with mixed effects (random intercepts/slopes per region) to partially pool. The walkthroughs in this session demonstrate these approaches using indicator variables and interaction terms.

Hierarchical Bayesian models (e.g. using PyMC, Stan, or INLA) are designed for partial pooling. Each region's parameters are drawn from a shared distribution, with the amount of shrinkage toward the group mean learned from data. This makes them well-suited for settings with many regions and limited data per region.

Tree-based models (Random Forest, XGBoost) can handle multiple regions by including a region identifier as a feature. The tree splits can then learn different patterns for different regions. This provides implicit partial pooling -- regions with similar patterns share tree structure.

Deep learning models typically handle multiple regions by learning region embeddings (dense vector representations). These embeddings allow the model to learn similarities between regions and share information accordingly, similar in spirit to partial pooling.

Which Approach Naturally Supports Borrowing Strength?

Borrowing strength (using data from all regions to improve estimates for each individual region) is most natural in:

• Hierarchical Bayesian models -- this is their primary design goal
• Tree-based models -- implicit through shared tree structure
• Deep learning -- through learned embeddings

It requires explicit setup in:

• Linear regression -- needs mixed-effects formulation or regularization
• ARIMA / ETS -- not naturally supported; requires external mechanisms like meta-learning or forecast combination