Frequentist linear mixed models: estimation and inference

Introduction

What this guide covers

Linear mixed models (LMMs) constitute a generalization of the general linear model that allows incorporating fixed and random effects simultaneously. Within the methodological framework of frequentist inference, the accurate estimation of variance components and subsequent inference on fixed effects require sophisticated algebraic tools.

Overview

Topics covered

• Introduction
• Linear Mixed Models: Estimation and Frequentist Inference
• Historical perspective and limitations of least squares
• The Inadequacy of the Ordinary Least Squares (OLS) Method
• Formal mathematical formulation of the LMM
• Common Covariance Structures for G and R

Related concepts

Main connections

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

Compatible notation

Mathematical sample in LaTeX

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