Generalized Linear Models (GLMs) are a versatile class of statistical models that extend the framework of traditional linear regression. The “model” in a GLM context refers to the relationship between a response variable and one or more predictor variables.
Key elements of a GLM:
- Link Function: GLMs accommodate various types of response variables (e.g., binary, count, continuous) by introducing a link function that connects the linear predictor to the expected value of the response. This link function accounts for the non-normal distribution of the response variable.
- Linear Predictor: Similar to linear regression, GLMs involve a linear combination of predictor variables, each weighted by its corresponding coefficient. However, the link function transforms this linear predictor to suit the distributional properties of the response variable.
- Family of Distributions: GLMs can handle a wide array of distributions for the response variable, such as Gaussian (normal), binomial, Poisson, and gamma distributions, among others. Each distribution within the GLM family has its own set of link functions.
- Estimation of Parameters: The parameters in a GLM, including coefficients for predictors and dispersion parameters, are typically estimated using maximum likelihood estimation or iteratively reweighted least squares, depending on the specific distributional assumptions.
Overall, GLMs offer a flexible framework for modeling relationships between variables in diverse settings where traditional linear regression might not be appropriate due to non-normality, heteroscedasticity, or other distributional issues in the response variable. They find extensive applications in fields such as healthcare, economics, biology, and social sciences