Appendix 1. Linear Mixed Model Theory

A1.1

Introduction

734

A1.2

Matrix Notation

734

A1.3

Formulation of the Mixed Model

735

 

A1.3.1

The General Linear Mixed Model

735

 

A1.3.2

Conditional and Marginal Distributions

736

 

A1.3.3

Example: Growth Curve with Compound Symmetry

737

 

A1.3.4

Example: Split-Plot Design

738

A1.4

Estimating Parameters, Predicting Random Effects

742

 

A1.4.1

Estimating β and Predicting u: The Mixed Model Equations

742

 

A1.4.2

Random Effects, Ridging, and Shrinking

743

 

A1.4.3

It’s All in the Sweep

744

 

A1.4.4

Maximum Likelihood and Restricted Maximum Likelihood for Covariance Parameters

746

A1.5

Statistical Properties

751

A1.6

Model Selection

752

 

A1.6.1

Model Comparisons via Likelihood Ratio Tests

752

 

A1.6.2

Model Comparisons via Information Criteria

753

A1.7

Inference ...

Get SAS for Mixed Models, Second Edition, 2nd Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.