Multilevel modelling books

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In recent years, there have been a growing number of books explaining how to undertake multilevel modelling. Here we have grouped them into these broad categories. If there are any important ones that we have missed email us at info-cmm@bristol.ac.uk.

1. General books on multilevel modelling (aimed at a social science audience)
2. Books on longitudinal data analysis that emphasize (multilevel) random-coefficient models
3. More specialised books (that do spatial models, or are more technical accounts of mixed models, and so on)
4. Books that are linked to, or use, particular software
   • HLM
   • MLwiN
   • R and S-Plus
   • SAS
   • Stata
   • SPSS
   • WinBUGS
5. Books that discuss MCMC analysis

General books on multilevel modelling (aimed at a general social science audience)

• An important general site is the UCLA textbook examples site, which shows 'how to solve the examples using common statistical packages': www.ats.ucla.edu/stat/examples/default.htm. They cover the following books:
  • Introduction to Multilevel Modeling by Ita Kreft and Jan de Leeuw
  • Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling by Tom Snijders and Roel Bosker.
  • Multilevel Analysis: Techniques and Applications by Joop Hox
  • Multilevel Statistical Analysis by Harvey Goldstein
• Bickel, R. 2007. Multilevel Analysis for Applied Research: It's Just Regression. Guilford Press. There is an associated web site where you can download data at: www.itsjustregression.com/index.php
• Bressoux, P. (2008). Modélisation statistique appliquée aux sciences sociales. Bruxelles : De Boeck. 464 p. (Statistical modelling applied to social sciences). Book cover (PDF, 140kB), contents of chapters (PDF, 19kB)
• Gelman, A., and J. Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. www.stat.columbia.edu/~gelman/arm/
• Goldstein, H. 2003. Multilevel Statistical Models. Arnold. Some of the contents can be downloaded for from the following link, including updates and corrections: Multilevel Statistical Models (3rd Edition)
• Hox, J. J. 2002. Multilevel Analysis: Techniques and Applications. Lawrence Erlbaum Associates. joophox.net
• Leyland, A. H., and H. Goldstein. 2001. Multilevel Modelling of Health Statistics. Wiley.
• Longford, N. T. 1993. Random Coefficient Models. Oxford University Press.
• Luke, D. A. 2004. Multilevel Modeling. SAGE.
• Raudenbush, S. W., and A. S. Bryk. 2002. Hierarchical Linear Models: Applications and Data Analysis Methods. SAGE. Steve Raudenbush's personal web site has preprints and software for statistical power for multilevel models at http://sociology.uchicago.edu/people/faculty/raudenbush.shtml, while the HLM web site is at www.ssicentral.com/hlm/index.html
• Snijders, T. A. B., and R. J. Bosker. 1999. Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. SAGE. You can find datasets for some of the examples in this book, with MLwiN macros, corrections and updates, at: http://stat.gamma.rug.nl/multilevel.htm

Books on longitudinal data analysis that emphasize (multilevel) random-coefficient models

• Latent Curve Models: A Structural Equation Perspective by Kenneth A. Bollen and Patrick J. Curran
• Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence by Judith D. Singer and John B. Willett
• Applied Longitudinal Analysis by Garrett M. Fitzmaurice, Nan M. Laird and James H. Ware
• An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues and Applications by Duncan, Duncan, Strucker, Li and Alpert
• Modeling Longitudinal Data by Robert Weiss
• Fitzmaurice, G. M., N. M. Laird, and J. H. Ware. 2004. Applied Longitudinal Analysis. Wiley-IEEE. biosun1.harvard.edu/~fitzmaur/ala/
• Hedeker, D., and R. D. Gibbons. 2006. Longitudinal Data Analysis. Wiley-Interscience. There are a lot of useful downloads at tigger.uic.edu/~hedeker/ml.html
• Singer, J. D., and J. B. Willett. 2003. Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford University Press Inc, USA. gseacademic.harvard.edu/alda/

More specialised books (that do spatial models, or are more technical accounts of mixed models, and so on)

• Aerts, M. 2002. Topics in Modelling of Clustered Data. CRC Press. This book 'focuses on providing a comprehensive treatment of marginal, conditional, and random effects models using, among others, likelihood, pseudo-likelihood, and generalized estimating equations methods'
• Brown, H., and R. Prescott. 2006. Applied Mixed Models in Medicine. Wiley. This new edition presents an overview of the theory of mixed models applied to problems in medical research. There is a web site for the book at www.chs.med.ed.ac.uk/phs/mixed/main.html
• Clark, J. S., and A. E. Gelfand. 2006. Hierarchical Modelling for the Environmental Sciences: Statistical Methods. Oxford University Press. This edited collection deals with 'hierarchical Bayes and Markov Chain Monte Carlo methods for analysis …where information is heterogeneous and uncertain, processes are complex, and responses depend on scale'. Contains a number of chapters on spatial and spatial-temporal models
• Demidenko, E. 2005. Mixed Models: Theory and Applications. Wiley-IEEE. This book aims to provide 'in-depth mathematical coverage of …linear, generalized linear, and nonlinear mixed models, along with diagnostics at both a graduate-level text and a reference'
• Heck, R. H., and S. L. Thomas. 2000. An Introduction to Multilevel Modeling Techniques. Lawrence ErlbaumAssociates. This book deals with 'multilevel regression models and multilevel models for covariance structures using hierarchical linear modelling and structural equation modelling'
• Lawson, A. B., W. J. Browne, and C. L. V. Rodeiro. 2003. Disease Mapping with WinBUGS and MLwiN. John Wiley and Sons. This covers spatial models and how to fit the models in the named software. MLwiN Worksheets and macros at seis.bris.ac.uk/~frwjb/dm.html
• Little, T. D., K. U. Schnabel, and J. Baumert. 2000. Modeling Longitudinal and Multilevel Data: Practical Issues, Applied. Lawrence ErlbaumAssociates. This book aims to 'compare and contrast various analytic approaches to longitudinal and multiple-group data including SEM, Multi-level, LTA, and standard GLM techniques'
• Reise, S. P., and N. Duan. 2003. Multilevel Modeling: Methodological Advances, Issues, and Applications. Lawrence ErlbaumAssociates. This edited collection aims to 'critically examine the real problems that occur when trying to use MLMs in applied research, such as power, experimental design, and model violations … includes topics such as growth modeling, repeated measures analysis, nonlinear modeling, outlier detection, and meta analysis.'
• Skrondal, A., and S. Rabe-Hesketh. 2004. Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural equation models CRC Press. 'This book unifies and extends latent variable models, including multilevel or generalized linear mixed models, longitudinal or panel models, item response or factor models, latent class or finite mixture models, and structural equation models'. Web site: www.gllamm.org/

Books that are linked to, or use, particular software

HLM (HLM review)

• Raudenbush, S. W., and A. S. Bryk. 2002. Hierarchical Linear Models: Applications and Data Analysis Methods. SAGE. Steve Raudenbush's personal website has preprints and software for statistical power for multilevel models at http://sociology.uchicago.edu/people/faculty/raudenbush.shtml, while the HLM website is at www.ssicentral.com/hlm/index.html

MLwiN (MLwiN review)

Manuals

Web versions: Designed to be viewed electronically (either in your browser or after saving to your computer) and has coloured graphs and links for easy navigation round the document.

• A User's Guide to MLwiN, v2.31 (PDF, 4,138kB). Rasbash, J., Steele, F., Browne, W.J. and Goldstein, H. (2014) Centre for Multilevel Modelling, University of Bristol.
• Manual Supplement to MLwiN v2.31 (PDF, 1,847kB). Rasbash, J., Charlton, C., Jones, K.and Pillinger, R. (2014) Centre for Multilevel Modelling, University of Bristol,
• MCMC Estimation in MLwiN, v2.31 (PDF, 7.4 mb).  Browne, W.J. (2014) Centre for Multilevel Modelling, University of Bristol.

Print versions: use these links if you intend to print the manuals.

• A User's Guide to MLwiN, v2.31 (PDF, 4,777kB). Rasbash, J., Steele, F., Browne, W.J. and Goldstein, H. (2014) Centre for Multilevel Modelling, University of Bristol.
• Manual Supplement to MLwiN v2.31 (PDF, 1,775kB). Rasbash, J., Charlton, C., Jones, K.and Pillinger, R. (2014) Centre for Multilevel Modelling, University of Bristol.
• MCMC Estimation in MLwiN, v2.31 (PDF, 7.4 mb).  Browne, W.J. (2009) Centre for Multilevel Modelling, University of Bristol.

• Lawson, A. B., W. J. Browne, and C. L. V. Rodeiro. 2003. Disease Mapping with WinBUGS and MLwiN. John Wiley and Sons. This covers spatial models and how to fit the models in the MLwiN.. Worksheets and macros at seis.bris.ac.uk/~frwjb/dm.html

R and S-Plus (R review and S-Plus review)

• Albert, J. 2007. Bayesian Computation with R. Springer-Verlag New York Inc. Discusses the R to WinBugs interface
• Faraway, J. J. 2006. Extending the Linear Model with R: Generalized Linear, Mixed Effects and. CRC Press.
• Gelman, A., and J. Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. Web site: www.stat.columbia.edu/~gelman/arm/
• Pinheiro, J. C., and D. M. Bates. 2000. Mixed-Effects Models in S and S-Plus. Springer. There is an additional support for this book at http://stat.bell-labs.com/NLME/index.html
• Rossi, P. E., G. M. Allenby, and R. E. McCulloch. 2005. Bayesian Statistics and Marketing. Wiley.
• Venables, W. N., and B. D. Ripley. 2002. Modern Applied Statistics with S. Springer. Chapter 10 deals with random and mixed effects models including for discrete responses, the object glmmPQL . There is online support for the book at www.stats.ox.ac.uk/pub/MASS4/

SAS (SAS review)

• Fitzmaurice, G. M., N. M. Laird, and J. H. Ware. 2004. Applied Longitudinal Analysis. Wiley-IEEE. Web site including SAS macros is biosun1.harvard.edu/~fitzmaur/ala/
• Hedeker, D., and R. D. Gibbons. 2006. Longitudinal Data Analysis. Wiley-Interscience. There are a lot of useful downloads including examples in SAS at tigger.uic.edu/~hedeker/ml.html
• Littell, R. C. 2006. SAS for Mixed Models. SAS Publishing.
• Brown, H., and R. Prescott. 2006. Applied Mixed Models in Medicine. Wiley. This new edition presents an overview of the theory of mixed models applied to problems in medical research. Web site - www.chs.med.ed.ac.uk/phs/mixed/main.html
• Verbeke, G., and G. Molenberghs. 1997. Linear Mixed Models in Practice: An SAS-oriented Approach. Springer.

Stata (Stata review)

• Rabe-Hesketh, S., and A. Skrondal. 2005. Multilevel and longitudinal modeling using STATA. Stata Press.
• Skrondal, A., and S. Rabe-Hesketh. 2004. Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural equation models. CRC Press. Web site - www.gllamm.org/
• Go to our online course materials - incuding multilevel modelling using Stata, starting with Regression with a Single Continuous Explanatory Variable. Note - please register to use these materials. We require you to register so that we can collect data to help us to conduct and publish research into the learning of multilevel methodology and applications. The course is free.

SPSS (SPSS review)

• Bickel, R. 2007. Multilevel Analysis for Applied Research: It's Just Regression. Guilford Press. There is an associated web site where you can download data at www.itsjustregression.com/index.php
• Hedeker, D., and R. D. Gibbons. 2006. Longitudinal Data Analysis. Wiley-Interscience. There are a lot of useful downloads, including examples in SPSS at tigger.uic.edu/~hedeker/ml.html

WinBUGS (WinBUGS review)

• Albert, J. 2007. Bayesian Computation with R. Springer-Verlag New York Inc. Discusses the R to WinBugs interface
• Gelman, A., and J. Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. The Web site www.stat.columbia.edu/~gelman/arm/
• Lawson, A. B., W. J. Browne, and C. L. V. Rodeiro. 2003. Disease Mapping with WinBUGS and MLwiN. John Wiley and Sons. This covers spatial models and how to fit the models in WinBUGS
• Spiegelhalter, D. J., K. R. Abrams, and J. P. Myles. 2004. Bayesian Approaches to Clinical Trials and Health-Care Evaluation. John Wiley and Sons. Downloads for examples that use WinBugs and Excel worksheets at www.mrc-bsu.cam.ac.uk/bayeseval/

Books that discuss MCMC analysis

• Albert, J. 2007. Bayesian Computation with R. Springer-Verlag New York Inc.
• Browne, W.J. (2009) MCMC Estimation in MLwiN, v2.10 (PDF, 7.4 mb). Centre for Multilevel Modelling, University of Bristol.
• Carlin, B. P., and T. A. Louis. 2000. Bayes and Empirical Bayes Methods for Data Analysis. CRC Press.
• Chen, M., Q. Shao, and J. G. Ibrahim. 2000. Monte Carlo Methods in Bayesian Computation. Springer.
• Clark, J. S., and A. E. Gelfand. 2006. Hierarchical Modelling for the Environmental Sciences: Statistical Methods. Oxford University Press. This edited collection deals with 'hierarchical Bayes and Markov Chain Monte Carlo methods for analysis …where information is heterogeneous and uncertain, processes are complex, and responses depend on scale'. Contains a number of chapters on spatial and spatial-temporal models
• Gamerman, D., and H. F. Lopes. 2006. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. CRC Press
• Gelman, A. et al 2004. Bayesian Data Analysis. CRC Press
• Gelman, A., and J. Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. The Web site www.stat.columbia.edu/~gelman/arm/
• Gelman, A., and X. Meng. 2004. Applied Bayesian Modeling and Causal Inference from Incomplete-Data. John Wiley and Sons.
• Gilks, W. R., S. Richardson, and D. J. Spiegelhalter. 1996. Markov Chain Monte Carlo in Practice. CRC Press
• Gill, J. 2007. Bayesian Methods: A Social and Behavioral Sciences Approach 2nd ed. CRC Press
• Goldstein, H. 2003. Multilevel Statistical Models. Arnold. Some of the contents can be downloaded for from the following link, including updates and corrections: Multilevel Statistical Models (3rd Edition). Chapter 2 deals with MCMC estimation
• Green, P. J., N. L. Hjort, and S. Richardson. 2003. Highly Structured Stochastic Systems. Oxford University Press.
• Hox, J. J. 2002. Multilevel Analysis: Techniques and Applications. Lawrence Erlbaum Associates. The Web site: is http://joophox.net. Chapter 11 deals with MCMC.
• Koop, G., D. J. Poirier, and J. L. Tobias. 2007. Bayesian Econometric Methods. Cambridge UniversityPress.
• Lancaster, T. 2004. An Introduction to Modern Bayesian Econometrics. Blackwell Publishing.
• Lawson, A. B., W. J. Browne, and C. L. V. Rodeiro. 2003. Disease Mapping with WinBUGS and MLwiN. John Wiley and Sons. This covers spatial models and how to fit the models in the named software. MLwiN Worksheets and macros at seis.bris.ac.uk/~frwjb/dm.html
• Robert, C. P., and G. Casella. 2004. Monte Carlo Statistical Methods. Springer.
• Rossi, P. E., G. M. Allenby, and R. E. McCulloch. 2005. Bayesian Statistics and Marketing. Wiley.
• Spiegelhalter, D. J., K. R. Abrams, and J. P. Myles. 2004. Bayesian Approaches to Clinical Trials and Health-Care Evaluation. John Wiley and Sons. Downloads for examples that use WinBugs and Excel worksheets at www.mrc-bsu.cam.ac.uk/bayeseval