Statistical Modeling & Regression · Generalized Linear Models (GLM)

Generalized linear models (GLMs): inference and model comparison

Public introduction · full guide in Eikos

Introduction

What this guide covers

A comprehensive mathematical exposition of GLMs, from the internal geometry of the exponential family of dispersion and iterative estimation by IRLS, to asymptotic hypothesis testing, residual analysis and quasi-likelihood.

Overview

Topics covered

  • Introduction
  • Generalized Linear Models: Inference and Comparison
  • Fundamentals and Theoretical Introduction
  • Limitations of the Classical Linear Model
  • Definition and Three Components of the GLM
  • 1. The Random Component

Related concepts

Main connections

  • Maximum likelihood estimation
  • Linear algebra & matrices
  • Variance & standard deviation
  • Calculus & differentiation
  • Generalized linear models (GLM)
  • Residual analysis & diagnostics

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

𝐲=𝐗𝛃+ϵ
View LaTeX source\mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\epsilon}