Useful books

In your search for publications, if you work in a university you may be able to access Web of Knowledge (subscribable service) or, use Google Scholar from here (enter title, author and/or other key words):

Google Scholar

In recent years, there have been a growing number of books explaining how to undertake multilevel modeling. Here we have grouped them quite crudely into five broad categories:

  1. General books on multilevel modeling (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, etc.)
  4. Books that are linked to, or use, particular software
  5. Books that discuss MCMC analysis

Deliberately some books appear in more than one category. We have also provided specific links to Google books so that you can inspect a proportion of the text and the contents, and to any author web sites that provide additional material.

If there are any important ones we have missed please let us know. (our contact details)

Last updated by Kelvyn Jones, January 2008.

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

Bickel, R. 2007. Multilevel Analysis for Applied Research: It's Just Regression. Guilford Press. Google Books. There is an associated web site where you can download data at: http://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). pdf image Book cover, pdf image contents of chapters

Gelman, A., and J. Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. Google Books. The home page for this book is http://www.stat.columbia.edu/~gelman/arm/

Goldstein, H. 2003. Multilevel Statistical Models. Arnold. Google Books. 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. Google Books. The home page for this book is http://www.geocities.com/joophox/mlbook/leabook.htm

Leyland, A. H., and H. Goldstein. 2001. Multilevel Modelling of Health Statistics. Wiley. Google Books

Longford, N. T. 1993. Random Coefficient Models. Oxford University Press. Google Books

Luke, D. A. 2004. Multilevel Modeling. SAGE. Google Books

Raudenbush, S. W., and A. S. Bryk. 2002. Hierarchical Linear Models: Applications and Data Analysis Methods. SAGE. Google Books. Steve Raudenbush's personal web site has preprints and software for statistical power for multilevel models at http://www-personal.umich.edu/~rauden/, while the HLM web site is at http://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. Google Books. Datasets for some of the examples in this book, with MLwiN macros, corrections and updates, can be found at: stat.gamma.rug.nl/snijders/multilevel.htm

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

Fitzmaurice, G. M., N. M. Laird, and J. H. Ware. 2004. Applied Longitudinal Analysis. Wiley-IEEE. Google Books. home page for this book is http://biosun1.harvard.edu/~fitzmaur/ala/

Hedeker, D., and R. D. Gibbons. 2006. Longitudinal Data Analysis. Wiley-Interscience. Google Books. There are a lot of useful downloads at http://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. The home page of the book is at http://gseacademic.harvard.edu/alda/

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

We have given very short summaries of distinctive features.

Aerts, M. 2002. Topics in Modelling of Clustered Data. CRC Press. Google Books. 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. Google Books. This new edition 'presents an overview of the theory of mixed models applied to problems in medical research'. There is a home page for the book at http://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. Google Books. 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. Google Books.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. Google Books. 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. Google Books. This covers spatial models and how to fit the models in the named software. MLwiN Worksheets and macros at http://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. Google Books. 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. Google Books. 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. Google Books. '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'. Extensive home page at http://www.gllamm.org/

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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. Google Books Steve Raudenbush’s personal website has preprints and software for statistical power for multilevel models at http://www-personal.umich.edu/~rauden/, while the HLM website is at http://www.ssicentral.com/hlm/index.html

MLwiN

MLwiN review

Manuals: (Click titles to download for free - or you can also go to our order form to purchase)

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.

printer image Print versions (use these links if you intend to print the manuals)

The print version has been optimised for black and white printing. However the content (and page numbering) is the same as the web versions.

*The MCMC manual included in the MLwiN 2.13 installation (and which can be reached by clicking Start -> All Programs -> Centre for Multilevel Modelling -> MCMC Manual) is entitled 'MCMC estimation in MLwiN version 2.10' whereas the version of the manual that can be downloaded from the website is entitled 'MCMC estimation in MLwiN version 2.13'. This is due to an oversight: despite the mistake in the title, the MCMC manual included with the software is the correct manual for version 2.13, and is identical to the version that can be downloaded above. The manual contains the documentation of the new MCMC methodology features that appears in version 2.13.

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

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R and S-Plus

R review

S-Plus review

Albert, J. 2007. Bayesian Computation with R. Springer-Verlag New York Inc. Google Books. Discusses the R to WinBugs interface 

Faraway, J. J. 2006. Extending the Linear Model with R: Generalized Linear, Mixed Effects and. CRC Press. Google Books

Gelman, A., and J. Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. Google Books. The home page for this book is http://www.stat.columbia.edu/~gelman/arm/

Pinheiro, J. C., and D. M. Bates. 2000. Mixed-Effects Models in S and S-Plus. Springer. Google Books. There is an additional support for this book at http://cm.bell-labs.com/cm/ms/departments/sia/project/nlme/

Rossi, P. E., G. M. Allenby, and R. E. McCulloch. 2005. Bayesian Statistics and Marketing. Wiley. Google Books. Extensive discussion of MCMC implemented in  R code at http://faculty.chicagogsb.edu/peter.rossi/research/bsm.html

Venables, W. N., and B. D. Ripley. 2002. Modern Applied Statistics with S. Springer. Google Books. Chapter 10 deals with random and mixed effects models including for discrete responses, the object glmmPQL . There is online support for the book at http://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. Google Books. Home page for this book, including SAS macros  is http://biosun1.harvard.edu/~fitzmaur/ala/

Hedeker, D., and R. D. Gibbons. 2006. Longitudinal Data Analysis. Wiley-Interscience. Google Books There are a lot of useful downloads including  examples in SAS at http://tigger.uic.edu/~hedeker/ml.html

Littell, R. C. 2006. SAS for Mixed Models. SAS Publishing. Google Books.

Brown, H., and R. Prescott. 2006. Applied Mixed Models in Medicine. Wiley. Google Books. This new edition 'presents an overview of the theory of mixed models applied to problems in medical research'. There is a home page for the book at  http://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. Google Books

STATA

STATA review

Rabe-Hesketh, S., and A. Skrondal. 2005. Multilevel and longitudinal modeling using STATA. Stata Press. Google Books

Skrondal, A., and S. Rabe-Hesketh. 2004. Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural equation models. CRC Press. Google Books. Extensive home page at http://www.gllamm.org/

SPSS

SPSS review

Bickel, R. 2007. Multilevel Analysis for Applied Research: It's Just Regression. Guilford Press. Google Books.  There is an associated web site where you can download data at http://www.itsjustregression.com/index.php

Hedeker, D., and R. D. Gibbons. 2006. Longitudinal Data Analysis. Wiley-Interscience. Google Books. There are a lot of useful downloads, including  examples in SPSS,  at http://tigger.uic.edu/~hedeker/ml.html

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WinBugs

WinBugs review

Albert, J. 2007. Bayesian Computation with R. Springer-Verlag New York Inc. Google Books. Discusses the R to WinBugs interface 

Gelman, A., and J. Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. Google Books. The home page for this book is http://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. Google Books. 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. Google Books. Downloads for examples that use WinBugs and Excel worksheets at  http://www.mrc-bsu.cam.ac.uk/bayeseval

An important general site is the UCLA textbook examples site, which shows 'how to solve the examples using common statistical packages': http://www.ats.ucla.edu/stat/examples/default.htm

They cover the following books

Multilevel Modeling

Longitudinal Data Analysis

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Books that discuss MCMC analysis

Albert, J. 2007. Bayesian Computation with R. Springer-Verlag New York Inc. Google Books

Browne, W.J. (2009) pdf logo MCMC Estimation in MLwiN, v2.10.  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. Google Books

Chen, M., Q. Shao, and J. G. Ibrahim. 2000. Monte Carlo Methods in Bayesian Computation. Springer. Google Books

Clark, J. S., and A. E. Gelfand. 2006. Hierarchical Modelling for the Environmental Sciences: Statistical Methods. Oxford University Press. Google Books. 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. Google Books

Gelman, A. et al  2004. Bayesian Data Analysis. CRC Press. Google Books

Gelman, A., and J. Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. Google Books. The home page for this book is http://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. Google Books

Gilks, W. R., S. Richardson, and D. J. Spiegelhalter. 1996. Markov Chain Monte Carlo in Practice. CRC Press. Google Books.

Gill, J. 2007. Bayesian Methods: A Social and Behavioral Sciences Approach 2nd ed. CRC Press. Google Books

Goldstein, H. 2003. Multilevel Statistical Models. Arnold. Google Books. 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. Google Books

Hox, J. J. 2002. Multilevel Analysis: Techniques and Applications. Lawrence Erlbaum Associates. Google Books. The home page for this book is http://www.geocities.com/joophox/mlbook/leabook.htm.  Chapter 11 deals with MCMC.

Koop, G., D. J. Poirier, and J. L. Tobias. 2007. Bayesian Econometric Methods. Cambridge UniversityPress. Google Books

Lancaster, T. 2004. An Introduction to Modern Bayesian Econometrics. Blackwell Publishing. Google Books

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

Robert, C. P., and G. Casella. 2004. Monte Carlo Statistical Methods. Springer. Google Books

Rossi, P. E., G. M. Allenby, and R. E. McCulloch. 2005. Bayesian Statistics and Marketing. Wiley. http://books.google.co.uk/books?id=z9w6AAAACAAJ&dq=Bayesian&lr=. Extensive discussion of MCMC implemented in R code at http://faculty.chicagogsb.edu/peter.rossi/research/bsm.html

Spiegelhalter, D. J., K. R. Abrams, and J. P. Myles. 2004. Bayesian Approaches to Clinical Trials and Health-Care Evaluation. John Wiley and Sons. Google Books. Downloads for examples that use WinBugs and Excel worksheets at  http://www.mrc-bsu.cam.ac.uk/bayeseval

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