Categorical Predictor
Study guide: Exam MAS-I
A Categorical Predictor is an explanatory variable in a Generalized Linear Model whose values fall into a finite set of unordered groups (levels), such as territory or vehicle type — contrasted with an ordinal predictor (categories with a natural order, e.g., a credit tier) and a continuous predictor (a numeric variable, e.g., vehicle age).
| Predictor type | Example | How it enters the model |
|---|---|---|
| Categorical (nominal) | Territory, vehicle type | k-1 indicator variables for k levels |
| Ordinal | Credit tier, limit band | As categorical, or with order-preserving (e.g., banded numeric) coding |
| Continuous | Vehicle age, driver age | A single coefficient, or banded/transformed |
- A categorical predictor with
klevels is represented usingk-1indicator (dummy) variables; the omitted level is the reference level, absorbed into the intercept (see Parameter Estimate Tables) - Terminology differs between the MAS-I sources. The CAS outline lists categorical, ordinal and continuous predictors as three kinds, which is the sense used here. Dobson & Barnett call nominal and ordinal variables alike categorical; a qualitative explanatory variable is a factor and its categories are its levels
- An Interaction between two predictors allows the effect of one to differ across the levels of the other, e.g., the effect of vehicle age differing by territory
- Continuous predictors assume a smooth effect on the response (linear on the link scale unless transformed); banding a continuous variable into categories trades smoothness for flexibility at the cost of extra parameters
- Choosing the right type for each variable is part of selecting the Model Structure of an Extended Linear Model
Coding a Categorical Predictor with a Reference Level Territory has three levels: A, B, C. A Poisson GLM with a log link uses Territory A as the reference level and fits
\hat{\beta}_B = 0.20,\hat{\beta}_C = -0.10. Interpret the relativities for Territories B and C relative to A.Answer
\text{Relativity}_B = e^{0.20} \approx 1.22, \qquad \text{Relativity}_C = e^{-0.10} \approx 0.90Territory B's expected claim frequency is about 22% higher than Territory A, and Territory C's is about 10% lower, holding all else equal.