Statistical Modeling & Regression · Generalized Linear Models (GLM)

Generalized linear models: structured models for correlated data

Public introduction · full guide in Eikos

Introduction

What this guide covers

A formal and rigorous mathematical approach to the analysis of non-independent observations using GEE, GLMM methodologies and transition models.

Overview

Topics covered

  • Introduction
  • Structured Models for Correlated Data
  • 1. From Independence to Correlation
  • One-Dimensional Exponential Family and Classical GLMs
  • The Breaking of Independence: Statistical Consequences
  • 2. Generalized Estimating Equations (GEE)

Related concepts

Main connections

  • Maximum likelihood estimation
  • Linear algebra & matrices
  • Variance & standard deviation
  • Mixed & multilevel models (GLMM)
  • Mean & expected value
  • Generalized linear models (GLM)

Compatible notation

Mathematical sample in LaTeX

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

f(yi;θi,ϕ)=exp{yiθi−b(θi)a(ϕ)+c(yi,ϕ)}
View LaTeX sourcef(y_i; \theta_i, \phi) = \exp \left\{ \frac{y_i \theta_i - b(\theta_i)}{a(\phi)} + c(y_i, \phi) \right\}