Course 9 Generalized Linear Models

The Generalized Linear Model (GLM) extends the linear regression framework to accommodate response variables that are not normally distributed, making it a powerful tool for modeling a wide range of data types. GLMs unify various statistical models, including linear regression, logistic regression, and Poisson regression, under a single framework by introducing a link function that relates the linear predictor to the expected value of the response variable. This flexibility allows GLMs to effectively handle binary, count, and categorical data. The model consists of three key components: the random component describing the distribution of the response variable, the systematic component representing the linear predictor, and the link function connecting the mean of the response to the linear predictor. Understanding GLMs provides a foundation for advanced statistical modeling and is essential for epidemiology, social sciences, and machine learning.