Statistical Modeling & Regression · Mixed & Multilevel Models (GLMM)

Generalized linear mixed models (GLMM) — Advanced statistical treatise

Public introduction · full guide in Eikos

Introduction

What this guide covers

Theoretical rigor, mathematical formulation of random effects in non-Gaussian exponential families, numerical approximation techniques and advanced frequentist inference methodologies.

Overview

Topics covered

  • Introduction
  • Generalized Linear Mixed Models
  • Statistical Fundamentals and Transition from LMM to GLMM
  • Formulation of the Mathematical Structure of GLMMs
  • Common Exponential Families and Link Functions
  • Conditional Effects vs. Marginal Effects (Population)

Related concepts

Main connections

  • Mixed & multilevel models (GLMM)
  • Variance & standard deviation
  • Maximum likelihood estimation
  • Linear algebra & matrices
  • Poisson distribution
  • Calculus & differentiation

Compatible notation

Mathematical sample in LaTeX

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

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