Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling

About the Book

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

Snijders and Bosker′s 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

• ecological fallacies

• 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 and survey weights

• Bayesian and MCMC estimation and latent-class models.

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

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

Tom A.B. Snijders is Professor of Statistics in the Social Sciences at the University of Oxford and Professor of Statistics and Methodology at the University of Groningen.

Roel J. Bosker is Professor of Education and Director of GION, Groningen Institute for Educational Research, at the University of Groningen.

Table of Contents:
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

Review :
′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. Too detailed and no IR Terrific book! Updated to provide current methods for multilevel models. This is a comprehensive textbook on multilevel analysis, with clear and basic background information on this particular statistical technique. This is a specialist book that provides clear guidance for doctoral researchers who are exploring complex nested relationships. This is a very advanced book. It is fondly theoretical, perfect for explaining the complex concept of multilevel analysis. This is the book!, however, the technical level is not appropriate to be adopted as a course material in my particular module. An excellent textbook which covers a broad range of pertinent issues for Multilevel modelling. Indeed, an essential read for those wanting to better grasp this powerful method of statistical analysis. This book provides a comprehensive coverage of multiple level theories and related models. Despite being an authoritative book in this field it should be used as a supplement for social science students because its content is not easily accessible. 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. 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. I found the book useful for researchers who want to know more about multi level statistics. A useful text for postgraduate students but I have to regard it only as a supplementary reading for my undergraduate students. One of the best textbooks on multilevel analysis! Strongly recommended to my students. This book provides a helpful and comprehensive introduction to the use of multi-level modelling.
The book is suitable for beginners due to the well understandable step by step explanations as well as advanced users due to deeper insight into specific topics and mathematical background. However more practical examples would benefit the learning. The book teaches more about the theoretical and statistical background and neglects the “how to” aspect. The online resources are rather scarce as well compared with other textbooks. Especially the lack of data files in different formats (e.g. for the HLM program) is a disadvantage. Well written textbook, however, due to its advanced statistical method, we only used it as supplemental reading for those students who were interested in some extra analysis. However, it makes a sophisticated method easier to understand and is a good alternative to Hox′ classic "Multilevel Analysis"." too technical language; should cater more for the needs of the "average" scientist and practitioner; definitely not recommended for newcomers to the subject" This impressively clear textbook achieves its title′s aim to be an introduction from basic to advanced multilevel modelling. Mathematical treatment is kept to the minimum to explain the differences between models, with an emphasis on intuitive understanding of concepts. This is very helpful to students who feel that moving up from regression/GLM to multilevel models is a big step.

I was especially impressed by the clear explanation of topics that are often described poorly by other authors, such as ICC and reliability, Hausman test (although the authors are unusual in never using the term ′endogeneity′), deviance tests and testing under ML/REML.

The ′Glommary′ at the end of each chapter is a nice mix of glossary and a recap of major points. The examples are clear, varied and motivating.

The only problem I have with the book is the lack of examples with software. Although these are prone to becoming out of date, having a chapter on software gives little information to the newcomer unless they can see for themselves how the software is not forbiddingly esoteric. Many students feel anxious about using software even after they have grasped the theory. Most readable book on multilevel analysis. Very good presenting of the complex topic of multilevel models. I recommended the book for every student interested in advanced methods. An excellent applied text, providing the basics and moving onto much more detailed multilevel analysis. A step by step introduction to multilevel analysis. A must have for studentents or researcher with an interesest in multilevel analyses Solid introduction even for newcomers to multilevel modeling. This is a very comprehensive book on multi-level analysis. The literature in this area is very scarce and often too specialised to give to students. I therefore welcome this book as an addition to teaching material. I recommend the book for master students who are already very advanced (often close to writing their dissertation) and whose master research deals with topics relevant for multi-level analysis. Very specialiced book. Only recommended for details. This is a thorough and approachable treatment of the topic, and the associated web resources are great. Very good, moderately technical introduction to multilevel modeling. Should be consulted by everyone using this technique in her own research.