Web resources for multilevel modelling

Compiled by Kelvyn Jones, Myles Gould and SV Subramanian.

Books and related downloads and materials

A selection here, but for a full list, go to useful books

  • Go to taster of Goldstein's classic text in its 3rd edition on multilevel statistical models ( Goldstein H, 2003, Multilevel statistical models, London, Arnold Publishers)
  • The second edition of Multilevel statistical models can also be downloaded
  • Supplementary material for Tom Snijders and Roel Bosker textbook – Snijders T, Bosker R, 1999 Multilevel analysis: an introduction to basic and advanced multilevel modeling, London, Sage, including updates and corrections, data sets used in examples, with set-ups for running the examples in MLwiN and in HLM, and an introduction to MLwiN can be found at http://stat.gamma.rug.nl/multilevel.htm
  • Supplementary material for Joop Hox's textbook – Hox J, 2002, Multilevel analysis: techniques and applications, Mahwah, NJ, Lawrence Erlbaum – can be found at www.ats.ucla.edu/stat/examples/ma_hox/default.htm
  • The complete content of Hox J, 1995, Applied multilevel analysis, Amsterdam: TT-Publikaties can be downloaded at Hox's website
  • Supplementary material to Skrondal, A. and Rabe-Hesketh, S. (2004). Generalized Latent Variable Modeling: Multilevel, Longitudinal and Structural Equation Models. Chapman and Hall/CRC. can be found at www.gllamm.org/
  • Supplementary material to Garrett Fitzmaurice, Nan Laird, James Ware (2004) Applied Longitudinal Analysis Wiley is to be found at www.hsph.harvard.edu/fitzmaur/ala/
  • Supplementary material to Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence by Judy Singer and John Wilett (2003) Oxford University Press, can be found at: gseacademic.harvard.edu/~alda/
  • For those interested in the analysis of spatial data, there is Andrew B. Lawson, William J. Browne, Carmen L. Vidal Rodeiro (2003) Disease Mapping with WinBUGS and MLwiN, Wiley and its associated website http://seis.bris.ac.uk/~frwjb/dm.html
  • To read a comparison of multilevel modelling with traditional approaches to running ANOVA, regression, and logistic regression with memories/events being "nested" within people/testing session see Wright DB, 1998, Modelling clustered data in autobiographical memory research: the multilevel approach, Applied Cognitive Psychology, 12, 339-357 at: http://www2.fiu.edu/~dwright/pdf/multil.pdf
  • To keep up to date with developments in the field join the CMM newsletter

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Reference lists about multilevel modelling

Publications by the CMM team, and associates, can be accessed via the CMM Members page.

Wolfgang Ludwig-Mayerhofer's annotated references on multilevel modelling: wlm.userweb.mwn.de/wlmmule.htm

There is a structured list of references (based on different types of model) at the HLM website www.ssicentral.com/hlm/references.html#r7

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Software in general

The CMM maintains reviews of some of the packages available for multilevel modelling. These reviews contain syntax for fitting a range of multilevel models to example datasets.

If you want to see how a particular model can be fitted in particular software, there are the developing resources at UCLA www.ats.ucla.edu/stat/examples/

For those wishing to analyse longitudinal data, software instructions in a wide range of programs is provided by UCLA to accompany the textbook Singer JD, Willett JB, 2003 Applied longitudinal data analysis: modeling change and event occurrence, New York, Oxford University Press, at:

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Training associated with software packages

A growing amount of web-based (or at least downloadable) training materials are being developed. We have organized this section by the particular software that is being used, and rather arbitrarily separated commercial software from the freeware that follows

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Free software

There are a number of programs that are available at low or nil cost; some of these are general (like R), others are more specific but can have special features that make them particularly attractive; we have tried to identify these special features below. We have also pointed to some appropriate training resources.

    • Has a number of distinctive features including handling structured (correlated) and/or unstructured (uncorrelated) effects of spatial covariates (geographical data) and unstructured random effects of unordered group indicators. It allows non-parametric relationships between the response and the predictors (generalized additive models) and does this for continuous and discrete outcomes, it can manipulate and display geographical maps http://www.bayesx.org/
  • BUGS
  • GeoBUGS
    • GLLAMM usefully undertakes multilevel latent class and factor analysis, adapative quadrature to derive the full likelihood with discrete and normal response, and has facilities for fitting non-parametric models in which the distribution at the higher level can be non-normal (you need STATA to run this software; this software is particularly useful for the models listed above, but can be slow to converge. This site is also a rich one with growing number of downloads of lectures and papers showing how the approach can be used in practice www.gllamm.org/

      You can download materials from a multilevel modelling course taught at Lancaster University which includes examples of using GLLAMM for continuous and discrete responses.
  • MIX
    • MIX are a set of stand-alone programs that fit a number of specific models including mixed-effects linear regression, mixed-effects logistic regression for nominal or ordinal outcomes, mixed-effects probit regression for ordinal outcomes, mixed-effects Poisson regression, and mixed-effects grouped-time survival analysis. They have a common interface, and importantly they calculate the likelihood directly so allowing comparison of the change in deviance for nested models. The are versions for Windows as well as for PowerMac and Solaris www.uic.edu/~hedeker/mix.html
  • R
    • R is a complete system for statistical computation and graphics, it can be seen as an Open Source implementation of the S language which in turn underlies the S-Plus software. It is distributed freely under the GNU General Public License and can be used for commercial purposes. It operates across a very wide range of platforms. The latest version and documentation can be obtained via CRAN, the Comprehensive R Archive Network cran.r-project.org/
  • R/S
    • Normal-theory models are fitted in R using lme and nlme functions described in full in 'Mixed-effects models in S and S-PLUS by J. C. Pinheiro and D. M. Bates (2000), there is an additional support for this book at cm.bell-labs.com/cm/ms/departments/sia/project/nlme/

      for discrete responses there is the function glmmPQL which is discussed in the 4th edition of Modern applied statistics with S W. N. Venables and B. D. Ripley; the book also covers normal theory models; there is online support for the book at www.stats.ox.ac.uk/pub/MASS4/

      Jeff Gill maintains a website that provides help, tutorials and references for those who want to use R

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Useful software and macros

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Experts' Websites

Douglas Bates who developed the LME and NLME functions in R and S-plus has a website at www.stat.wisc.edu/~bates/bates.html

Bill Browne (who has made major contributions to the MCMC component of MLwiN) has a large number of downloadable papers at seis.bris.ac.uk/~frwjb/bill.html

David Draper has a lot of material about the Bayesian approach to hierarchical models on his web site: www.cse.ucsc.edu/~draper/

Tony Fielding has useful material on ordered categorical variables, endogeneity and instrumental variables including MLwiN macros on his web site

Andrew Gelman has lots of downloadable papers and presentations on multilevel modelling with a strong Bayesian flavour www.stat.columbia.edu/~gelman/

Harvey Goldstein, who is the instigator of the MLwiN software has a number of downloadable papers at his web site

Don Hedeker who has been behind the MIX set of programs has lecture transparencies and class notes on longitudinal analysis at Don Hedeker's web site

Joop Hox's web site has papers, programs and lectures to download at http://joophox.net

Alastair Leyland has extensively used multilevel modelling in public health

Bengt Muthen who is the developer of Mplus which allows multilevel factor analysis has a site at https://gseis.ucla.edu/directory/bengt-muthen/

Jason Newsom's multilevel web site has discussion of topics like centering, and how to distinguish between fixed and random effects http://web.pdx.edu/~newsomj/

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David Rogosa has useful links to his course Education 260 on Popular Methods (including multilevel modeling, and causal inference) and Education 351 on Longitudinal analysis www.stanford.edu/~rag/

Steve Raudenbush's LAMMP website has publications and pre-prints and links to the projects he is currently working on www-personal.umich.edu/~rauden/

Tom Snijder's web site www.stats.ox.ac.uk/~snijders/

Subramanian's research papers on using multilevel models in social epidemiology and health as well training resources related to the concepts and application of multilevel statistical methods can be found at http://www.hsph.harvard.edu/faculty/venkata-sankaranarayanan/.

The Office of Behavioral and Social Sciences Research (OBSSR) have some great interactive Multilevel Modeling Materials.

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Examples of multilevel modelling

For an interesting discussion about what multilevel models can (and cannot do) see the interchange at www.stat.columbia.edu

For the use of multilevel models in social network analysis, see www.stats.ox.ac.uk/~snijders/socnet.htm

For papers using multilevel modelling, see the Gallery of published examples, searchable by model type.

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Tutorials in MCMC estimation

MCMC estimation is increasingly being used to estimate complex models; there are number of sites with really helpful resources to get you started:

Simon Jackman's Estimation and Inference via Markov chain Monte Carlo: a resource for social scientists tamarama.stanford.edu/mcmc/

Jeff Gill's web site is a mine of information in this area, it includes some down-loadable chapters from his 2002 book Bayesian Methods for the Social and Behavioral Sciences which is to be thoroughly recommended http://jgill.wustl.edu/Site/Homepage.html

There is a useful website for David Spiegelhalter, Keith Abrams and Jonathan Myles (2003) Bayesian approaches to clinical trials and health-care evaluation, Wiley; it contains downloads for the examples that use WinBugs and Excel worksheets that allow simple analysis of odds-ratio and hazard ratio models on the basis of normal priors and likelihoods www.mrc-bsu.cam.ac.uk/bayeseval/

Sujjit Sahu's tutorial on MCMC www.maths.soton.ac.uk/staff/Sahu/utrecht/

Harold Lehmann Bayesian Communication prototypes Bayesian analysis on-line www.hopkinsmedicine.org/Bayes/PrimaryPages/Index.cfm

A Brief Introduction to Graphical Models and Bayesian Networks is to be found at http://www.cs.ubc.ca/~murphyk/Bayes/bayes.html

For software to determine sample-size requirements using prior opinion see Lawrence Joseph's Bayesian software site www.medicine.mcgill.ca/epidemiology/Joseph/

To keep up to date in this area, you can visit the MCMC preprint service www.statslab.cam.ac.uk/~mcmc/

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Causal analysis

Introductory sites

Christopher Winship's Counterfactual Causal Analysis in Sociology website provides a good introduction to developments in this area www.wjh.harvard.edu/~cwinship/cfa.html

Harvard School of Public Health PROGRAM ON CAUSAL INFERENCE in Epidemiology and Allied Sciences www.hsph.harvard.edu/causal/index.htm

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Experts on causal analysis

Judea Pearl has a large number of downloads of lectures and papers ayes.cs.ucla.edu/jp_home.html

Guido Imbens - ideas.repec.org/e/pim4.html

David Harding - www-personal.umich.edu/~dharding/

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Software for causal analysis with observational data

for R-based matching software which uses a wide range of techniques see Gary King's site sekhon.berkeley.edu/matching/

there is a SPSS syntax file for propensity scoring available at John Painter's site www.unc.edu/~painter/SPSSsyntax/propen.txt

facilities in R for Multivariate and Propensity Score Matching Software written by Jasjeet Sekhon sekhon.berkeley.edu/matching/

and Stata programs for ATT estimation based on propensity score matching www.sobecker.de/pscore.html

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Multilevel modelling and causal analysis

The "Columbia group on Bayesian statistics, multilevel modelling, causal inference, and social networks" have a site at www.stat.columbia.edu/~sam/MultilevelModeling/

There are pre-prints and publications on Steve Raudenbush's site - search for 'causal'.

Tony Fielding has material on endogeneity and instrumental variables including MLwiN macros, at Tony Fielding

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Missing data

Missing data are a persistent problem in social and other datasets. The Centre for Multilevel Modelling's (CMM) Missing Data webpage details functionality the CMM team, together wtih colleagues, have developed to handle complex datasets with missing data via the software packages REALCOM-IMPUTE and Stat-JR.

Note that further guidance on handling missing data can also be found at http://missingdata.lshtm.ac.uk, and also in Module 14 of the free LEMMA online multilevel modelling course.

Note: some of the documents on this page are in PDF format. In order to view a PDF you will need Adobe Acrobat Reader

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