Generalized Linear Models

Generalized Linear Models (GLMs) offer a versatile extension to ordinary linear regression, broadening its applicability to a wider range of data types and relationships. These models consist of three key components:

• Random Component: This specifies the probability distribution of the outcome variable, allowing for flexibility beyond the normal distribution assumed in ordinary linear regression.

• Linear Predictor: A familiar linear combination of covariates (independent variables) that contributes to explaining the outcome.

• Link Function: This crucial element connects the random component and linear predictor, transforming the linear combination to align with the scale and range of the outcome variable.

The following chapters will cover very simple, yet very useful, models. After you master the basics, you will probably want to write your own models from scratch.

Learn more

• Goodrich et al. (2020) rstanarm: {Bayesian} applied regression modeling via {Stan}.
• Bürkner (2017) {brms}: An {R} Package for {Bayesian} Multilevel Models Using {Stan}.
• Carpenter et al. (2017) Stan: A Probabilistic Programming Language.

Bürkner, Paul-Christian. 2017. “brms: An R Package for Bayesian Multilevel Models Using Stan.” Journal of Statistical Software 80 (1): 1–28. https://doi.org/10.18637/jss.v080.i01.

Carpenter, Bob, Andrew Gelman, Matthew D. Hoffman, Daniel Lee, Ben Goodrich, Michael Betancourt, Marcus Brubaker, Jiqiang Guo, Peter Li, and Allen Riddell. 2017. “Stan: A Probabilistic Programming Language.” Journal of Statistical Software 76 (1): 1–32. https://doi.org/10.18637/jss.v076.i01.

Goodrich, Ben, Jonah Gabry, Imad Ali, and Sam Brilleman. 2020. “Rstanarm: Bayesian Applied Regression Modeling via Stan.” https://mc-stan.org/rstanarm.