In contract a regular linear model where the response variable is assumed to be normally distributed, a generalized linear model (GLM) makes no such assumption. This allows GLMs to predict response variables with different distributions, e.g. Poisson, multinomial, etc.

GLMs are composed of three different parts: a linear predictor (\(ax_a + bx_b + cx_c\) …) similar to regular linear regression, a random component which describes the error in the distribution of the response variable, and a link function which describes how the linear component relates to the response variable.

These models are super useful, and as you may have noticed, occur all over the place; ‘GLM’ is something of a broad term. Many of the models we have gone over in this course are GLMs.

One of countless possible examples: Say we want to model the count of how many cars pass a traffic light within a certain amount of time given various conditions (time, weather, day, etc). We could initialize a GLM with a log link function (for integers), with errors that follow a Poisson distribution, and a linear component containing the independent variables variables. If that sounds like Poisson regression, it’s because it is; Poisson regression is one type of model GLMs include.

Helpful Sources:

https://towardsdatascience.com/linear-regression-or-generalized-linear-model-1636e29803d0

https://online.stat.psu.edu/stat504/lesson/6/6.1

https://www.researchgate.net/post/What_is_the_difference_between_the_general_linear_model_GLMand_generalized_linear_model_GZLM#:~:text=The%20general%20linear%20model%20requires,response%20variable%20follows%20different%20distributions.

https://en.wikipedia.org/wiki/Generalized_linear_model

https://stats.stackexchange.com/questions/7261/general-linear-model-vs-generalized-linear-model-with-an-identity-link-functio

https://www.quora.com/What-is-the-difference-between-general-linear-models-and-generalized-linear-models