What are the main ways to encode categorical variables for regression and when should I use each?

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AcadiFi · Accepted Answer

The right encoding depends on the model type and what you want the coefficients to mean. Four common choices: 1. Reference (dummy) coding. Drop one level; remaining coefficients compare each level to the reference. Clean interpretation and CFA-standard. Use for small-cardinality categories with a natural baseline. 2. Effect (deviation) coding. Code levels as +1, 0, −1 so coefficients represent deviations from the grand mean rather than from a reference. Useful when no natural baseline exists (e.g., geographic regions of equal standing). 3. One-hot encoding. Include all k dummies without an intercept, or use with regularized models like LASSO/ridge where multicollinearity is handled by the penalty. Standard in machine learning pipelines but unstable in ordinary OLS. 4. Target encoding. Replace each category with the mean of the target variable within that category. Compact for high-cardinality variables (e.g., ZIP code with 30,000 levels) but prone to target leakage; requires out-of-fold computation. ```mermaid flowchart TD A[Categorical
variable] --> B{How many
levels?} B -->|Few| C[Reference
or effect] B -->|Many| D[Target
encoding] A --> E{OLS or
ML model?} E -->|OLS| F[Reference
coding] E -->|Regularized| G[One-hot
OK] ``` For CFA exam purposes, stick with reference coding. In practice, choose based on model, interpretability needs, and cardinality.

What are the main ways to encode categorical variables for regression and when should I use each?

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