Multilevel Analysis
An Introduction to Basic and Advanced Multilevel Modeling

Second Edition

Tom A B Snijders - University of Groningen, Netherlands
Roel J Bosker - University of Groningen, Netherlands

Courses:
Statistics - General Interest | Structural Equation Modeling, Hierarchical Linear Modeling, & Multilevel Modeling

December 2011 | 368 pages | SAGE Publications Ltd

The Second Edition of this classic text introduces the main methods, techniques, and issues involved in carrying out multilevel modeling and analysis.

Snijders and Boskers' book is an applied, authoritative, and accessible introduction to the topic, providing readers with a clear conceptual and practical understanding of all the main issues involved in designing multilevel studies and conducting multilevel analysis.

This book provides step-by-step coverage of:

Multilevel theories
Multi-stage sampling
The hierarchical linear model
Testing and model specification
Heteroscedasticity
Study designs
Longitudinal data
Multivariate multilevel models
Discrete dependent variables

There are also new chapters on:

Missing data
Multilevel Modeling for Surveys
Bayesian and MCMC estimation and latent-class models.

This book has been comprehensively revised and updated since the last edition, and now includes guides to modeling using HLM, MLwiN, SAS, Stata including GLLAMM, R, SPSS, Mplus, WinBugs, Latent Gold, and Mix.

This is a must-have text for any student, teacher, or researcher with an interest in conducting or understanding multilevel analysis.

Available Formats

ISBN: 9781849202008	Hardcover	Suggested Retail Price: $220.00	Bookstore Price: $176.00
ISBN: 9781849202015	Paperback	Suggested Retail Price: $73.00	Bookstore Price: $58.40
ISBN: 9781446289600	Electronic Version	Suggested Retail Price: $66.00	Bookstore Price: $52.80

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Preface second edition

Preface to first edition

Introduction

Multilevel analysis

Probability models

This book

Prerequisites

Notation

Multilevel Theories, Multi-Stage Sampling and Multilevel Models

Dependence as a nuisance

Dependence as an interesting phenomenon

Macro-level, micro-level, and cross-level relations

Glommary

Statistical Treatment of Clustered Data

Aggregation

Disaggregation

The intraclass correlation

Within-group and between group variance

Testing for group differences

Design effects in two-stage samples

Reliability of aggregated variables

Within-and between group relations

Regressions

Correlations

Estimation of within-and between-group correlations

Combination of within-group evidence

Glommary

The Random Intercept Model

Terminology and notation

A regression model: fixed effects only

Variable intercepts: fixed or random parameters?

When to use random coefficient models

Definition of the random intercept model

More explanatory variables

Within-and between-group regressions

Parameter estimation

'Estimating' random group effects: posterior means

Posterior confidence intervals

Three-level random intercept models

Glommary

The Hierarchical Linear Model

Random slopes

Heteroscedasticity

Do not force ?01 to be 0!

Interpretation of random slope variances

Explanation of random intercepts and slopes

Cross-level interaction effects

A general formulation of fixed and random parts

Specification of random slope models

Centering variables with random slopes?

Estimation

Three or more levels

Glommary

Testing and Model Specification

Tests for fixed parameters

Multiparameter tests for fixed effects

Deviance tests

More powerful tests for variance parameters

Other tests for parameters in the random part

Confidence intervals for parameters in the random part

Model specification

Working upward from level one

Joint consideration of level-one and level-two variables

Concluding remarks on model specification

Glommary

How Much Does the Model Explain?

Explained variance

Negative values of R2?

Definition of the proportion of explained variance in two-level models

Explained variance in three-level models

Explained variance in models with random slopes

Components of variance

Random intercept models

Random slope models

Glommary

Heteroscedasticity

Heteroscedasticity at level one

Linear variance functions

Quadratic variance functions

Heteroscedasticity at level two

Glommary

Missing Data

General issues for missing data

Implications for design

Missing values of the dependent variable

Full maximum likelihood

Imputation

The imputation method

Putting together the multiple results

Multiple imputations by chained equations

Choice of the imputation model

Glommary

Assumptions of the Hierarchical Linear Model

Assumptions of the hierarchical linear model

Following the logic of the hierarchical linear model

Include contextual effects

Check whether variables have random effects

Explained variance

Specification of the fixed part

Specification of the random part

Testing for heteroscedasticity

What to do in case of heteroscedasticity

Inspection of level-one residuals

Residuals at level two

Influence of level-two units

More general distributional assumptions

Glommary

Designing Multilevel Studies

Some introductory notes on power

Estimating a population mean

Measurement of subjects

Estimating association between variables

Cross-level interaction effects

Allocating treatment to groups or individuals

Exploring the variance structure

The intraclass correlation

Variance parameters

Glommary

Other Methods and Models

Bayesian inference

Sandwich estimators for standard errors

Latent class models

Glommary

Imperfect Hierarchies

A two-level model with a crossed random factor

Crossed random effects in three-level models

Multiple membership models

Multiple membership multiple classification models

Glommary

Survey Weights

Model-based and design-based inference

Descriptive and analytic use of surveys

Two kinds of weights

Choosing between model-based and design-based analysis

Inclusion probabilities and two-level weights

Exploring the informativeness of the sampling design

Example: Metacognitive strategies as measured in the PISA study

Sampling design

Model-based analysis of data divided into parts

Inclusion of weights in the model

How to assign weights in multilevel models

Appendix. Matrix expressions for the single-level estimators

Glommary

Longitudinal Data

Fixed occasions

The compound symmetry models

Random slopes

The fully multivariate model

Multivariate regression analysis

Explained variance

Variable occasion designs

Populations of curves

Random functions

Explaining the functions 27415.2.4

Changing covariates

Autocorrelated residuals

Glommary

Multivariate Multilevel Models

Why analyze multiple dependent variables simultaneously?

The multivariate random intercept model

Multivariate random slope models

Glommary

Discrete Dependent Variables

Hierarchical generalized linear models

Introduction to multilevel logistic regression

Heterogeneous proportions

The logit function: Log-odds

The empty model

The random intercept model

Estimation

Aggregation

Further topics on multilevel logistic regression

Random slope model

Representation as a threshold model

Residual intraclass correlation coefficient

Explained variance

Consequences of adding effects to the model

Ordered categorical variables

Multilevel event history analysis

Multilevel Poisson regression

Glommary

Software

Special software for multilevel modeling

HLM

MLwiN

The MIXOR suite and SuperMix

Modules in general-purpose software packages

SAS procedures VARCOMP, MIXED, GLIMMIX, and NLMIXED

Stata

SPSS, commands VARCOMP and MIXED

Other multilevel software

PinT

Optimal Design

MLPowSim

Mplus

Latent Gold

REALCOM

WinBUGS

References

Index

'Overall, Snijders and Bosker provide an accessible and readable text on the subject of multilevel analysis. It is as much tailored to the needs of advanced quantitative researchers, as to relative beginners in the field. As a reader with limited experience in quantitative research, but an interest in advancing my knowledge and understanding of multilevel analysis, I found this text an ideal introduction to the area' -
Emma Smith
Methodspace Book Reviews Club

This new edition is still intended for students, teachers, or researchers with an interest in conducting or understanding multilevel analysis. The book is definitely an excellent reference book for researchers working in social sciences, education, environmental sciences, and economic, biological, medical, and health disciplines.

Yuehua Wu

York University, Toronto

Zentralblatt Math

I found the book useful for researchers who want to know more about multi level statistics.

Dr Muhammet Mustafa Alpaslan

Education, Mugla Sitki Kocman Universitesi

July 10, 2017

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This is one the most comprehensive books about multilevel analysis. It's like a "must have" book for those who want to have a deep understanding of different aspects of multilevel analysis.

Dr Amin Mousavi

Educational Psychology , University Of Saskatchewan

September 7, 2016

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Good book on multilevel modeling

Professor Jost Sieweke

Business Administration , Heinrich Heine University

January 18, 2016

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A must for scholars engaged in multilevel research. High on analytical treatment.

Professor Israr Qureshi

Business Administration , IE Business School