Multilevel Analysis
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Multilevel Analysis
An Introduction to Basic and Advanced Multilevel Modeling

Second Edition


© 2012 | 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.


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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  
R  
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

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 24, 2016

Good book on multilevel modeling

Professor Jost Sieweke
Business Administration , Heinrich Heine University
April 1, 2016

The content of the textbook is great. However, the text is very difficult to follow when students do not have a very strong background on statistics.

Dr Bruno Schivinski
Nottingham Business School, Nottingham Trent University
November 8, 2015

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ISBN: 9781849202015
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