A GLM hands you a column of coefficients. Your job is to translate those numbers into a sentence a pricing committee understands: which risks cost more, by how much, and whether the model is confident.
A generalized linear model links a predictor's characteristics to an expected outcome, usually frequency, severity, or pure premium. It writes the mean as a link function applied to a weighted sum of the risk factors. For ratemaking, the outcome is the loss cost the insurer expects from a policy with a given profile.
Multivariate methods replaced stacked one-way analyses for several reasons. They adjust for correlations between exposure characteristics, they separate real signal from random noise, they provide diagnostics on the quality of the fit, they allow interactions between factors, and they are transparent about the assumptions behind each estimate.
Three practical drivers pushed the industry to adopt them: cheaper computing power, data warehouses that made large policy files usable, and competitive pressure to price more finely than rivals.
Common mistakes
- Reading the raw coefficient as the relativity. A coefficient of 0.262 is a 1.30 factor, not a 0.262 factor. Always exponentiate under a log link.
- Adding relativities instead of multiplying. Log-link factors combine by multiplication. Summing 1.30 and 1.50 to get 2.80 instead of multiplying to 1.95 is wrong.
- Ignoring the base level. The reference level is 1.00 and already sits in the intercept. Applying an extra factor to a base-level risk double counts it.
Bottom line
- A GLM predicts expected loss through a linear predictor and a link function; the log link makes it multiplicative, so exponentiate a coefficient to read its relativity.
- The base level of every factor carries relativity 1.00, and the predicted value equals the base rate times the product of relativities across all factors.
- Standard errors, p-values, and confidence intervals separate signal from noise; a relativity interval containing 1.00 is not significant.
- Validate beyond significance: check that factor patterns stay consistent across years, and hold out data to compare expected versus actual by predicted band.
Exam shortcut
When you see a log-link coefficient, exponentiate immediately and read it as a percentage: 0.262 becomes , a 30% surcharge. Positive is a load, negative is a discount, zero is no effect. To price a full profile, start from and multiply one relativity per factor, including any interaction whose conditions both hold. Never add the relativities. For significance, exponentiate the coefficient's confidence interval.
The full lesson (about 3,156 words, 21 min read) adds 3 worked examples, all 8 common mistakes, a self-check, free in the app.
Learning objectives
- A15
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