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

Linear mixed models: Mathematical formulation and frequentist estimation

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction // Biostatistics and Econometrics · Advanced Level

Overview

Topics covered

  • Introduction
  • Mathematical Formulation of the Linear Mixed Model
  • Introduction and Context of Mixed Models
  • Laird-Ware Formulation and Matrix Notation
  • Fundamental Distributional Assumptions
  • The Structure of the G and R Matrices

Related concepts

Main connections

  • Variance & standard deviation
  • Linear algebra & matrices
  • Maximum likelihood estimation
  • Mixed & multilevel models (GLMM)
  • Residual analysis & diagnostics
  • 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}