Glossary

Generalised Linear Model (GLM)

A flexible extension of ordinary linear regression that accommodates response variables with non-Normal error distributions (e.g., binomial, Poisson, gamma). A GLM is specified by three components: a probability distribution from the exponential family, a linear predictor, and...

Definition

A flexible extension of ordinary linear regression that accommodates response variables with non-Normal error distributions (e.g., binomial, Poisson, gamma). A GLM is specified by three components: a probability distribution from the exponential family, a linear predictor, and a link function connecting the mean of the distribution to the linear predictor. Logistic regression (binary outcomes) and Poisson regression (count data) are common special cases.

Why It Matters

GLMs allow researchers to model the wide variety of data structures encountered in practice — binary outcomes, count data, skewed continuous variables — within a single, coherent framework. Without GLMs, analysts would need ad hoc transformations or separate modelling traditions for each data type, making results harder to compare and communicate.

Example

A health researcher studying hospital readmission uses logistic regression (a GLM with a binomial distribution and logit link) to predict whether a patient is readmitted within 30 days, while an urban planner uses Poisson regression (a GLM with a Poisson distribution and log link) to model the number of traffic accidents at different intersections.

Related Terms

Software Notes

  • SPSS: Analyze > Generalized Linear Models > choose distribution and link
  • R: glm() with family argument; e.g., glm(y ~ x, family = binomial)
  • Stata: glm command or specific commands like logit, poisson