**Resources for Multilevel Modeling**

Following is an extensive list of various types of resources related to
multilevel modeling including websites, books, journal articles,
software and related training, guide provides a set of resources to
those who are interested in learning more about multilevel modeling. The
guide is intended for those at all levels. Many of these materials were
obtained from the Web and the URLs are given in those instances.

**WEBSITES**

> 1\. Judith Singer (Ph.D., [Statistics, Harvard
> University](http://www.stat.harvard.edu/)) is the James Bryant Conant
> Professor of Education and former Academic Dean at the [Harvard
> Graduate School of Education](http://gseweb.harvard.edu/). One of the
> nation's leading applied statisticians, her professional life focuses
> on improving the quantitative methods used in social, educational and
> behavioral research. Singer is primarily known for her contributions
> to the practice of multilevel modeling, survival analysis, and
> individual growth modeling, and to making these and other statistical
> methods accessible to empirical researchers.

<http://gseweb.harvard.edu/~faculty/singer/>

2\. Centre for Multilevel Modeling, University of Bristol

> <http://www.mlwin.com/>

3\. Software Reviews of Multilevel Analysis Packages

> <http://www.mlwin.com/softrev/index.html>

4\. Are Multilevel Techniques Necessary? An overview, including
Simulation Studies Ita G.G. Kreft, California State University, Los
Angeles, June 25, 1996

> <http://www.calstatela.edu/faculty/ikreft/quarterly/quarterly.html>

5\. The Public Health Disparities Geocoding Project Monograph

> <http://www.hsph.harvard.edu/thegeocodingproject/webpage/monograph/multilevel.htm>

6\. The UCLA Academic Technology Services who maintain data and worked
examples in a number of different software packages for a number of
different multilevel textbooks\
[www.ats.ucla.edu/stat/examples/](http://www.ats.ucla.edu/stat/examples/)

**BOOKS**

1.  Luke DA. Multilevel Modeling: Quantitative Applications in the
    Social Sciences. July 2004 Sage Publications Inc.

2\. Snijders T., Bosker R. Multilevel Analysis: An Introduction to Basic
and Advanced Multilevel Modeling 1999. Sage Publications Inc.

3\. Kreft I.G., Leeuw Jd. Introducing Multilevel Modeling Jan. 1998.
Sage Publications Inc.

4**.** Heck R.H., Thomas S.L. An Introduction to Multilevel Modeling
Techniques. Dec. 1999 Lawrence Erlbaum Associates.

5\. Reise S.P., Duan N. Multilevel Modeling: Methodological Advances,
Issues and Applications Jan. 2003. Lawrence Erlbaum Associates.

6\. Raudenbush, S. W., and A. S. Bryk.. Heirarchical linear models:
Applications and data analysis methods. 2002 Thousand Oaks, CA: Sage.

**JOURNAL ARTICLES**

1.  Messer LC, Laraia BA, Kaufman JS, Eyster J, Holzman C, Culhane J,
    Elo I, Burke JG, O'Campo P. The development of a standardized
    neighborhood deprivation index. J Urban Health. 2006
    Nov;83(6):1041-62.

**SOFTWARE**

(The information in this section was obtained from the Centre for
Multilevel Modeling website http://www.mlwin.com/links/materials.shtml)

If you want to see how a particular model can be fitted in particular
software, there are resources in development at UCLA:\
[www.ats.ucla.edu/stat/examples/](http://www.ats.ucla.edu/stat/examples/)

For those wishing to analyze 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:\
[www.ats.ucla.edu/stat/examples/alda/](http://www.ats.ucla.edu/stat/examples/alda/)

### Training associated with software

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.

+-------+--------------------------------------------------------------+
| **    | **Training Material Description**                            |
| Softw |                                                              |
| are** |                                                              |
+-------+--------------------------------------------------------------+
| **    | Can be used to fit a range of multilevel models but has      |
| aML** | specific features for fitting multi-process or simultaneous  |
|       | equation models to hierarchical data where predictor         |
|       | variables may be non-random or endogenous, and other types   |
|       | of models used by economists such as a multilevel Heckman    |
|       | selection models\                                            |
|       | [www.applied-ml.com/product/multiproces                      |
|       | s.html](http://www.applied-ml.com/product/multiprocess.html) |
+-------+--------------------------------------------------------------+
| **    | The official site gives guidance at\                         |
| HLM** | [www.ssicentral.com/hlm/                                     |
|       | examples.html](http://www.ssicentral.com/hlm/examples.html)\ |
|       | \                                                            |
|       | There is very good introductory material on how to set up    |
|       | the models by Information Technology Services at the         |
|       | [University of                                               |
|       | Texas](http://www.utexas.edu/its/rc/tutorials/stat/hlm/)\    |
|       | \                                                            |
|       | Jason Newsom's [Multilevel Regression                        |
|       | cou                                                          |
|       | rse](http://www.upa.pdx.edu/IOA/newsom/mlrclass/default.htm) |
|       | that uses HLM, but covers a lot of other ground too (eg      |
|       | Distinguishing between random and fixed: variables, effects, |
|       | and coefficients; comparison of estimators, and kinks to     |
|       | SPSS Mixed)                                                  |
+-------+--------------------------------------------------------------+
| *     | You can download a version of the software, data and         |
| **MLw | training manuals from                                        |
| iN*** | [                                                            |
|       | TRAMMS](http://tramss.data-archive.ac.uk/Software/MLwiN.asp) |
|       | (Teaching Resources and Materials for Social Scientists)\    |
|       | \                                                            |
|       | The [manuals](http://www.mlwin.com/download/manuals.html)    |
|       | are a course in themselves\                                  |
|       | \                                                            |
|       | The substantial enhancement of the MCMC procedures in        |
|       | *MLwiN* is discussed in full in [*[MCMC Estimation in        |
|       | MLwiN]{.underline}*                                          |
|       | (pdf)](http://www.mlwin.com/download/MCMC est_2005.pdf)      |
|       | which is to be used with the version 2.0 of the program      |
+-------+--------------------------------------------------------------+
| **Mp  | This software allows structural equation modeling,           |
| lus** | multilevel modelling and mixture modelling; their web site,  |
|       | [www.statmodel.com](http://www.statmodel.com/) has training  |
|       | downloads and examples.                                      |
+-------+--------------------------------------------------------------+
| **    | [Judy Singer](http://gseweb.harvard.edu/~faculty/singer/)    |
| SAS** | has a pdf download that shows how to fit multilevel models   |
|       | in PROC MIXED; it is very well written.\                     |
|       | \                                                            |
|       | UCLA has implemented the Singer example in other software    |
|       | (eg R\\Splus, HLM, *MlwiN*, SPSS)\                           |
|       | [www.ats.ucla.edu/stat/paperexamples/singer/default.htm](ht  |
|       | tp://www.ats.ucla.edu/stat/paperexamples/singer/default.htm) |
|       |                                                              |
|       | C.J. Anderson has a lot of material for his course online    |
|       | at\                                                          |
|       | [www.ed.uiuc.edu/cour                                        |
|       | ses/EdPsy490CK/](http://www.ed.uiuc.edu/courses/EdPsy490CK/) |
|       |                                                              |
|       | Data and SAS related material are available for Applied      |
|       | Longitudinal Analysis by Garrett Fitzmaurice, Nan Laird,     |
|       | James Ware at\                                               |
|       | [biosun1.harvard.edu                                         |
|       | /\~fitzmaur/ala/](http://biosun1.harvard.edu/~fitzmaur/ala/) |
|       |                                                              |
|       | The code and data to fit the models contained in SAS System  |
|       | for Mixed Models (1996) by RC Littell, GA Milliken, WW       |
|       | Stroup, and RD Wolfinger, is to be found at\                 |
|       | <http://ftp.sas.com/samples/A55235>                          |
+-------+--------------------------------------------------------------+
| **S   | A useful discussion of the Linear Mixed Models procedure in  |
| PSS** | SPSS Advanced Models is to be found at                       |
|       | <http://www.spss.com/downloads/Papers.cfm> (search for       |
|       | Linear mixed-effects modeling in SPSS)                       |
|       |                                                              |
|       | also an [HTML downloadable                                   |
|       | tutorial](http://www.spss.com/down                           |
|       | loads/Papers.cfm?ProductID=00035&Name=SPSS_Base&DLType=Demo) |
|       | based on a set of case studies                               |
|       |                                                              |
|       | John Painter provides a clear guide on how to fit multilevel |
|       | models using SPPS mixed\                                     |
|       | [www.unc.edu/\~painter/](http://www.unc.edu/~painter/)       |
|       |                                                              |
|       | Another brief demonstration of SPSS Mixed in action is to be |
|       | found at\                                                    |
|       | [step.psy.cmu.edu/materials/spss/mixed.doc (word             |
|       | doc)](http://step.psy.cmu.edu/materials/spss/mixed.doc)      |
+-------+--------------------------------------------------------------+

## Freeware

There are a number of programs that are available at low or nil cost;
some of these are general (like
[R](http://www.mlwin.com/links/r.shtml)), 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.

+---------+------------------------------------------------------------+
| **Sof   | **Description**                                            |
| tware** |                                                            |
+---------+------------------------------------------------------------+
| **B     | has a number of distinctive features including handling    |
| AYESX** | 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\                  |
|         | [www.stat.uni-muenchen.de/\~lang/bayesx/bayesx.html]       |
|         | (http://www.stat.uni-muenchen.de/~lang/bayesx/bayesx.html) |
+---------+------------------------------------------------------------+
| *       | **B**ayesian inference **U**sing **G**ibbs **S**ampling is |
| *BUGS** | really a flexible language that allows the fitting of a    |
|         | very wide range of models using MCMC methods; this is a    |
|         | very rich site developed by the MRC Biostatistics Research |
|         | Unit in Cambridge which has lots of freely downloadable    |
|         | software and detailed manuals\                             |
|         | [www.                                                      |
|         | mrc-bsu.cam.ac.uk/bugs](http://www.mrc-bsu.cam.ac.uk/bugs) |
|         |                                                            |
|         | A number of courses using BUGS have been put online, a     |
|         | listing is given at\                                       |
|         | [                                                          |
|         | www.mrc-bsu.cam.ac.uk/bugs/weblinks/webresource.shtml](htt |
|         | p://www.mrc-bsu.cam.ac.uk/bugs/weblinks/webresource.shtml) |
|         |                                                            |
|         | Peter Congdon has written two books based around BUGS      |
|         | (Bayesian Statistical Modelling, and Applied Bayesian      |
|         | Modelling) data and programmes are available for both      |
|         | books at in zipped form, downloadable from                 |
|         |                                                            |
|         | <ftp://www.wiley.co.uk/pub/books/congdon/>                 |
+---------+------------------------------------------------------------+
| **Ge    | is an add-on to BUGS that has been developed by a team at  |
| oBUGS** | Imperial College to fit spatial models and produce a range |
|         | of maps as output\                                         |
|         | [www.mrc-bsu.cam.ac.uk/bugs/winbugs/geobugs.shtml          |
|         | ](http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/geobugs.shtml) |
+---------+------------------------------------------------------------+
| **G     | this software usefully undertakes multilevel latent class  |
| LLAMM** | 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; preferably STATA 8); 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/](http://www.gllamm.org/)                  |
+---------+------------------------------------------------------------+
| **MIX** | These 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](http://www.uic.edu/~hedeker/mix.html) |
+---------+------------------------------------------------------------+
| **R**   | is 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/](http://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&lsquo 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/](ht  |
|         | tp://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/](http://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\      |
|         | [psblade.ucdavis.edu/](http://psblade.ucdavis.edu/)        |
+---------+------------------------------------------------------------+

## Useful macros and other software

+-----------+----------------------------------------------------------+
| **S       | **Description**                                          |
| oftware** |                                                          |
+-----------+----------------------------------------------------------+
| **PreML** | There is a very useful utility written so as to export   |
|           | an SPSS file into a MLwiN worksheet, it is down-loadable |
|           | from Tom Snijders\' webpage\                             |
|           | <http://stat.gamma.rug.nl/snijders/PreML.inc>            |
+-----------+----------------------------------------------------------+
| **Diag    | Tom Snijders' homepage contains a set of MLwiN macros    |
| nostics** | for producing diagnostics and for fitting a social       |
|           | network model\                                           |
|           | [stat.gamma.rug.nl/snijders/m                            |
|           | lnmac.htm](http://stat.gamma.rug.nl/snijders/mlnmac.htm) |
+-----------+----------------------------------------------------------+
| **PINT**  | For determining appropriate required sample sizes and    |
|           | power in a two-level model; there is a manual            |
+-----------+----------------------------------------------------------+
| **OD**    | is another program for power analysis and optimal        |
|           | design, it has excellent graphical output, you will need |
|           | to read the published papers by Steve Raudenbush and     |
|           | Xiao-Feng Liu\                                           |
|           | [sitemaker.umich.                                        |
|           | edu/group-based](http://sitemaker.umich.edu/group-based) |
|           |                                                          |
|           | a manual has now appeared at Steve Raudenbush's          |
|           | [personal                                                |
|           | website](http://www-personal.umich.edu/~rauden/)         |
+-----------+----------------------------------------------------------+
| **Di      | is a public domain software for the statistical analysis |
| smapWin** | of epidemiological maps; it allows the analysis of       |
|           | unobserved heterogeneity using mixture models; the       |
|           | program offers a Poisson regression approach which links |
|           | disease and exposure data\                               |
|           | [www.medizin.fu-berlin.de/sozmed/DismapWin.html          |
|           | ](http://www.medizin.fu-berlin.de/sozmed/DismapWin.html) |
+-----------+----------------------------------------------------------+
| **PROC    | is a SAS® procedure, written by Bob Jones, that fits a   |
| TRAJ**    | discrete mixture model to longitudinal data, and thereby |
|           | implements Nagel's group trajectory model; a very useful |
|           | site for this type of model with downloads of papers is\ |
|           | [www.andrew.cmu.e                                        |
|           | du/user/bjones/](http://www.andrew.cmu.edu/user/bjones/) |
+-----------+----------------------------------------------------------+

**COURSES ON MULTILEVEL MODELING**

The multilevel website maintains a list of courses using MLwiN

<http://www.mlwin.com/support/workshop.html>

The Michigan-based Summer Program in Quantitative Methods of Social
Research usually has one or more courses

<http://www.icpsr.umich.edu/training/summer/>

There is a two-week long course by Kelvyn Jones and Myles Gould
consisting of 10 half-days at The Essex Summer School

<http://www.essex.ac.uk/methods/>

On a two year basis there is a week-long course by Kelvyn Jones and
Subramanian at the Swiss Summer School (based in Lugano)

<http://www.unige.ch/ses/sococ/ss/>

There is a unit at Brussels in December taught by Kelvyn Jones

<http://www.kubrussel.ac.be/english/index.htm>

Lemma will be providing introductory and advanced training on a regular
basis

<http://www.ncrm.ac.uk/nodes/lemma/training.php>