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Multilevel Analysis
An Introduction to Basic and Advanced Multilevel Modeling

Second Edition


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.


 
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

 
R

 
Stata

 
SPSS, commands VARCOMP and MIXED

 
 
Other multilevel software
PinT

 
Optimal Design

 
MLPowSim

 
Mplus

 
Latent Gold

 
REALCOM

 
WinBUGS

 
 
References
 
Index

Solid introduction even for newcomers to multilevel modeling.

Ms Freya Sukalla
Institut für Medien und Bildungstechnologie, Universität Augsburg
October 16, 2014

A step by step introduction to multilevel analysis. A must have for studentents or researcher with an interesest in multilevel analyses

Ms Claudia Schmidt
Educational Psychology , University of Oldenburg
August 1, 2014

This book provides a helpful and comprehensive introduction to the use of multi-level modelling.

Dr Peter Taylor
Division of Clinical Psychology, Liverpool University
February 19, 2014

too technical language; should cater more for the needs of the "average" scientist and practitioner; definitely not recommended for newcomers to the subject

Mr Joerg Wombacher
Business Administration , University of Applied Sciences Northwestern Switzerland
January 10, 2014

This is a comprehensive textbook on multilevel analysis, with clear and basic background information on this particular statistical technique.

Dr Elisabeth Dorant
Fac: Health, Medicine & Life Sciences, Maastricht University
December 16, 2013

This is a nice introductory book for multilevel analysis. It is writing in a very easy way to understand the principle of the multilevel research. The book covers the main analysis that student could need in for example a final posgrade dissertation or even at a level of PhD dissertation.

Dr Moises Betancort
Methodology, La Laguna University
October 15, 2013

This is a very advanced book. It is fondly theoretical, perfect for explaining the complex concept of multilevel analysis.

Dr Geronimo Maldonado-Martinez
Retrovirus Research Center, Universidad Central del Caribe
August 12, 2013

Terrific book! Updated to provide current methods for multilevel models.

Dr Bruce Cooper
School Of Nursing, University of California - San Fran
August 4, 2013

This is a very useful book in multilevel modelling. Even though our focus on Advanced Survey Methods is not multilevel, there is a particular chapter that helps the students see the connection between model and design- based approaches in advanced survey design, with emphasis on the role of weighting. Therefore, we introduced the book as an essential reading for this course.

Dr Maria Pampaka
Social Science , University of Manchester
June 28, 2013

Very good, moderately technical introduction to multilevel modeling. Should be consulted by everyone using this technique in her own research.

Professor Ingo Rohlfing
Political Science, University of Cologne
May 16, 2013

Sample Materials & Chapters

Chapter Two


For instructors

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