Multilevel Analysis/Hierarchical Linear Modeling
Last revised: August 30, 2016 General Information
Examples of Papers that Use Multilevel Models
Handy program and links
Questions or problems regarding this site should be sent to
There are 2 things that you need before you can do this:
General Information (MSword format):
- Aug 30: Homework is due at the beginning of lecture. If you are sick then give it to a friend or e-mail it to both
Wes and Carolyn.
- Aug 30: If you come to the lab session at 9am for an introduction to SAS, bring your laptop and put data file on
your remote desktop account (if using).
- Aug 25:
- Introduction to SAS will be Tuesday Sept 1, 9-10am in room 22 Education. Bring you laptop.
- The lab sessions when we have them will be 9-10:30 for R and 10:30-12 for SAS and mostly likely
be on Thursdays.
- Aug 25: See below for the first homework assignement, which is due Tuesday August 30.
- Aug 24: Those who came to class but weren't registered and signed the attendence sheet can all register.
You have to send me your UIN and netid so that I can put in a request for an override.
- Draft chapters on GLM, GLMM, and LLM (i.e., HLM).
- Resources for R users:
- Computing: We will be running statistical software (SAS) using remote desktop to a university server. Here are the instructions:
remote desktop connection. Here is the file referred to in the instructions as an RDP file. ---
Use "Save link as" when you download the RDP file and save it to a convient location (e.g., desktop).
When you run the RDP application and it will run remote desktop application and set up configurations such that you will be able to directly open and save files from the remote server to your computer (and visa versa).
If you don't want to do these things, just use your remote desktop program and enter "remote2.webstore.illinois.edu".
- Your computer must be hooked up to the internet. If you access the internet via campus wireless, home, hotel, Espresso Royal, or elsewhere), you will eed
to use VPN (Virtual Private Networking) to securely connect to the campus internet.
- You must be registered for the class. If you reccently registered, you may not yet have permission to login yet.
Lectures Notes: (I tend to up-date throughout the semester)
- Introduction ( up-dated Fall 2016).
SAS that generated (most of) the statistics and graphs in the lecture notes:
- Models for clustered data: Fixed and random
effects ANOVA and multiple regression. up-dated Fall 2016
SAS and R code that reproduces the statistics, graphs, etc. in the lecture notes:
- Optional: Introduction to SAS to be held....Tuesday Aug 30, 9am in room 22 Education.
- Random Intercept Models. up-dated Fall 2016
Fits ANCOVA model to NELS88, N=10 data (includes centering a variable, model
fitting using GLM, and SAS/GRAPH of model).
Creates SAS data set of level 1 data for the High School and Beyond data.
Creates SAS data set of level 2 data for the High School and Beyond data.
Merges level 1 and level 2 high school and beyond sas datasets.
SAS/GRAPHS for looking between and within variability of SES in the high
school and beyond data.
SAS PROC MIXED and fitting random intercept models (includes centering SES)...and some graphics.
- R: (New 2016)
- For the NELS example, use R from note on previous lecture on models for clustered data.
- HSB1data.txt. Student level data
- HSB2data.txt. School level data
- R_hsb_rand_intercept.txt. R code that
reproduces everything in lecture notes. You will need to change the "setwd" to where you put the data
and install package lmer, lattice and lmerTest.
- SAS for HLM and a little R.
These will be used in lecture (they can also be used to reproduce the models for HSB data in
the lecture notes on random intercept models):
- This is from the introduction to SAS session:
- R: See R code under Notes on Random Intercept Models
- Random Intercept and Slopes Models . (up-dated Fall 2016)
- Estimation of Marginal Model. (Up-dated fall 2016)
Statistical Inference: Marginal Model.
Model Building. (revision complete)
- New SAS programs:
- Longitudinal Data Analysis
- Lecture notes on Serial Correlation.. (not up-dated---may not cover)
- HLM for Riesby data. (data from Hedeker web-site plus additional
analyses I did).
- Error Structures Simulation:
Multilevel Logistic Regression.
Computer Lab Sessions: Bring laptop
- Homwork 1:
- Homwork 2:
- Final Exam and Projects: Hardcopy is due due TBA (offices are locked around 4:00pm).
Pentalty for late finals or projects is 10 points (out of 100 points) per weekday
(e.g., turn in Friday, 10 point deduction; turn in Monday 20 point, etc).
Examples of Papers that Use Multilevel Models
- Payne, B.R., Gao, X., Noh, S.R., Anderson, C.J., Stine-Morrow, E.A.L. (2011). The effects of print
exposure on sentence processing and memory in older adulats: Evidence for efficiency and reserve. Aging, Neuropsychology, and Cognition.
Some examples of crossed random effects, skewed responses (i.e., reaction times), and discrete response (i.e., Poisson).
- Segerstrom, S.C. & Sephton, S.E. (2010). Optimistic expectanices and cell-mediated immunity: The role
of positive affect. Psychological Science, 21, 448-455.
Example of where cluster centered level one variable is substantive (theoretical) interest. The response variable is numerical/continuous.
- Allen, N.E., Todd, N.R., Anderson, C.J., Davis, S.M., Javdani, Bruehler, V., & Dorsey, H.
(2013). Council-Based approaches to intimate partner violence: Evidence for distal change in system response. American Journal of Community
Psychology, 52, 1-12.
Example of a longitudinal study with creative centering of time. The response variable was a rate (probability).
- Poteat, V.P. & Anderson, C.J. (2012). Developmental changes in sexual prejudice from early to late
adolescence: The effects of gener, race, and ideology on different patterns of change. Developmental Psychology, 48, 1403-1415.
Example of an accelerated longitudinal design.
- Examples from Tom Snijders course web-page where multilevel models have been used. (click on "info course multilevel" on left and go to
bottom of page. These papers cover a range of topics (e.g., political science, sociology, school psychology, criminology, medicine, and others).
Example SAS Programs (ascii/text format):
Examples from Snijders & Bosker using SAS
Examples from Chapter 4 of Kreft & de Leeuw (provided and written
by Carol Nickerson):
Create SAS data for examples in Chapters 4 and 5.
Example 2-level analyses from Chapter 4 (random intercept models).
Example 2-level analyses from Chapter 5 (random intercept and
Examples analyses from Chapter 12 (longitudinal data analysis),
including creating sas dataset.
Handy Programs and Links:
SAS code that creates data set and fits models reported in Kreft &
Raw data file that is used as input to school23.sas.
Ones specific to multilevel modeling:
A FORTRAN program that computes large sample confidence intervals for a
A FORTRAN program that computes p-values and (bonferroni) critical values
for the standard normal, chi-squared, t, and F distributions (and for correlations).
For users of PC type computers,
is an executable (i.e. already compiled) program.