HLM 5: Concepts and Background

The theoretical chapters from the HLM 5 manual are available here as a service to both current and potential users who wish to familiarize them with the concepts used and theoretical aspects of features available in this hierarchical linear and non-linear modeling program.

For a brief introduction to HLM, see the introductory section.
For information on the background for general 2-level models, see Chapter 1.
Background for general 3-level models is provided in Chapter 3.
Models for the analysis of dichotomous and count data are discussed in Chapter 5.
Chapter 7 provides background for the hierarchical multivariate linear models than can be fitted using HLM.

Introduction to HLM

Chapter 1: Background for general 2-level models

Chapter 1: Contents
1.1 The general two-level model
1.2 Parameter estimation
1.3 Hypothesis testing
1.4 Restricted versus full maximum likelihood
1.5 Generalized Estimating Equations

Chapter 3: Background for general 3-level models

Chapter 3: Contents
Conceptual and statistical background for three-level models
3.1 The general three-level model
3.2 Parameter estimation
3.3 Hypothesis testing


Chapter 5: Background for HGLM

Chapter 5: Contents
Conceptual and statistical background for Hierarchical Generalized Linear Models (HGLM)
5.1 The two-level HLM as a special case of HGLM
5.2 Two- and three-level models for binary outcomes
5.3 The model for count data
5.4 The model for multinomial data
5.5 The model for ordinal data
5.6 Parameter estimation
5.6.1 Estimation via PQL
5.6.2 Properties of the estimators
5.6.3 Parameter estimation: A high-order Laplace approximation of maximum likelihood
5.7 Unit-specific and population-average models
5.8 Over-dispersion and under-dispersion
5.9 Restricted versus full PQL versus full ML
5.10 Hypothesis testing

Chapter 7: Background for HMLM and HMLM2

Chapter 7:Contents
Chapter 7 Conceptual background for Hierarchical Multivariate Linear Models (HMLM)
7.1 Unrestricted model
7.2 Standard HLM with homogenous level-1 variance
7.3 HLM with varying level-1 variance
7.4 HLM with a log-linear model for the level-1 variance
7.5 First-order auto-regressive model at level-1
7.6 HMLM2: A multilevel, multivariate model