glm.qmd

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title: "Generalized Linear Models"
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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. 

::: {.callout-tip}
## Learn more
  - @rstanarm rstanarm: {Bayesian} applied regression modeling via {Stan}.
  - @brms {brms}: An {R} Package for {Bayesian} Multilevel Models Using {Stan}.
  - @JSSv076i01 Stan: A Probabilistic Programming Language.
:::