Last revised: May 7, 2019
Questions or problems regarding this site should be sent to firstname.lastname@example.org. Announcements :
- April 5:
- Computer Lab 4 will be continued on Tuesday where
- SAS group 10:00-10:55am
- R group 10:55-11:50am
- SAS and R created in Lab 4 on Thursday at posted here and below:
- New due date for homework 6: Tuesday April 16
- Newer version of R computer lab 4 instructions posted (the same as what was distributed in lab on Thursday
- Link to data for R lab fixed....same as lab 3 data
- Computer Lab 4 will be continued on Tuesday where
- March 29:
- All lectures notes are posted (2 on longitudinal data and one on logistic regression
- R,SAS and answer keys for Homework 5 have been posted
- Materials for Lab 4 are posted.
- Lab 4 will be held Thursday April 4 and homework will be due 1 week later (Thursday April 11th).
- After turning in Homework 6, you should be working on your projects/finals if you have not already started them
- March 25: First set of notes on longitudinal data are posted.
- March 13: I have posted a description what you should report if you are doing a project. I have also posted a final "exam" and data, which is basically just a project but with data and questions that I provide. For the final, I have provide 4 options: Choose just one.
- March 12: The following are now posted:
- Answer keys for homework 4 are posted, as well as SAS and R scripts for lab 2.
- SAS and R scripts from today's lab are posted under "Computer Lab 3"
- SAS macro hlmRsq.sas works on my office and laptop computer, but only for random intercept & slope models. It is not working for random intercept models, but these are easy to compute.
- Feb 19: The following are now posted:
- Answer keys for homework 3. (For R there is a separate document with an up-dated summary table.)
- SAS and R to estimate the models from computer Lab 1.
- SAS and R developed in Lab2.
- Feb 14: Addendum to R Computer lab 2 and Homework 4.
- Feb 11: Computer lab 2 materials are posted along with homework #4.
- Feb 7: Change of due data for homework 3: Tue Feb 12.
- Jan 29: SAS and R done in lab are posted below (under computer lab 1).
- Jan 18: Homework assignment is posted below and is due Tuesday Jan 29.
- Jan 18: Last year's instructions on graphics are posted under computer lab 4.
- Nov 16: When we have computer labs, SAS will run 9:00 to 10:30am and R will run from 10:30=1:50am
- Nov 7: I have started to re-construct this site. Work will be complete by the end of Spring semester.
- You can obtain a free educational versions from SAS.com. Look for "SAS Software for Learning". There is a University Edition and an OnDemand version. The latter requires an internet connection but it also includes more procedures (e.g., GRAPH, ETS and OR). Alternatively, you can obtain a lisence from webstore, which when I last checked (Jan 2, 2019) was $0.00, yes no cost. You can either borrow, download or purchase the program (media) from webstore. With the 2nd option, you should get more procedures and packages.
- Introduction to SAS
- Resources for R users:
- You can download (for free) R and Rstudio from the internet.
- Introduction to Multilevel Modeling in R by Grover, Guillermono and Hudson (2015). This document uses the high school and beyond data set to illustrate a lot about how to do data management, HLM models and analyses, and graphics. If you are using R, I highly recommend this.
- Doing scatter-plots with lattice.
- A Brief Introduction to R, the multilevel package and the nlme package by Paul Bliese (2016). This includes some introductory material on R and how to do multilevel modeling.
- Lecture notes by Kyle Roberts. I included these because there is a nice R code section
- Resources for STATA users:
- Slides on Bayesian estimation of multilevel models by Chuck Huber.
- do file.
- Draft chapters on GLM, GLMM, and LLM (i.e., HLM).
- Models for clustered data: Fixed and random effects ANOVA and multiple regression.
- NELS data for 10 schools. Run this program before the next one.
- Generates statistics, fits models & produces graphics.
- Random Intercept Models.
- ANCOVA.sas. Fits ANCOVA model to NELS88, N=10 data (includes centering a variable, model fitting using GLM, and SAS/GRAPH of model).
- hsb1.sas. Creates SAS data set of level 1 data for the High School and Beyond data.
- hsb2.sas. Creates SAS data set of level 2 data for the High School and Beyond data.
- hsball.sas. Merges level 1 and level 2 high school and beyond sas datasets.
- betwithin.sas. SAS/GRAPHS for looking between and within variability of SES in the high school and beyond data.
- randomintercepts.sas. SAS PROC MIXED and fitting random intercept models (includes centering SES)...and some graphics.
- 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 packages lmer, lattice and lmerTest.
- Little R function that computes the ICC.
- SAS and R for HLM.
These will be described and used in lecture:
- This is from the introduction to SAS session (won't be covered):
- Random Intercept and Slopes Models .
- text file of data. NELS88 data for N=23 school.
- school23.sas. SAS program that creates SAS data set for NEL88 data for N=23 school.
- NELS23.sas. SAS program that fits various random intercept and slope models to the NEL88 data for N=23 school.
- Centering & NELS data. Illustrates effects of different kinds of centering -- NEL88 data for N=23 school.
- NELS23 data in txt format.
- R code for NELS for 23 schools. Including among other things, code for data manipulation, creating variables, doing some graphics, model fitting using lmer.
- Student level HSB data in txt format.
- School level HSB data in txt format.
- R code for HSB. Code for data manipulation, creating variables, doing some graphics, model fitting using lmer. Not all the graphics code is here, but the R code for Nels (23 schools) has examples of similar graphics.
- Estimation of Marginal Model.
- Graphs showling likeihood of normal distribution.
- How to simulate HLM (in SAS).
- SAS: Simulation study on MLE vs REML and different N.
- SAS: For those who might want to use Bayesian estimation, I worked up a small example for the empty model,random intercept with one predictor, and a random intercept and slope model. I also included SAS PROC MIXED code if you want to compare results. You can change the seed to "-1" and run the mcmc code a few times and compare results.
- R code for graphs illustrating MLE
- R for simulating HLM data. New Spring 2019
- The brms package to fit multilevel model (i.e., Bayesian estimation) New Spring 2019 This example uses the nels23 data, which you can find on this web-site (e.g., under model building). In terms of specify the basic model, the model syntax is very similar to lmer.
- Statistical Inference: Marginal Model.
- SAS commands for ddfm (Simulation to show what different choices for df yield).
- HSB1 data. (level 1 data -- students)
- HSB2 data (level 2 data -- schools)
- hlmrsq.sas SAS macro that computes R_1^2 and R_2^2.
- Recchia JSS paper describing the hlmrsq.sas macro and how to use it.
- SAS for fixed effects & Rsq. Illustrates various things.
- hsb1.txt Can use to try out functions.
- hsb2.txt Can use to try out functions.
- hsb.sas This SAS code can used to compare results of R and SAS.
- robust. This R code is a function that computes robust ("sandwiche") standard errors for fixed effects. Be sure to read comments at the top regarding use. I am still working on betwee/within numerator degrees of freedom options (the residual df are fine, but between/within ones for cross-random effects are a bit "off" relative to SAS/MIXED).
- hlmRsq. This R code is a function that takes results from lmer and computes R1sq and R2sq as described in Snijders, TAB, Bosker, RJ (1994). Modeled variance in two-level models." Sociological Methods & Research, 22, 342-363. This works for both random intercept and random intercept and slope models. Be sure to read comments at the top before use.
- contrast.txt This R code is a function does contrasts. It takes as input model and a vector/matrix of contrasts and computes both F and Wald test statistics.
- Illustrates some of things done in lecture (i.e., computing roubst se, computing R squares, and finding mixture p-values).
- Random Effects.
- Power and sample size:
- Xiaofeng Steven Liu (2014). Statistical Power Analysis for the Social and Behavioral Sciences: Basic and Advanced Techinques. Routledge: NY. This book contains explanation of procedures and code for R, SAS and SPSS. If you search google scholar
- Optimal Design Software Program and documenation from Raudenbush group. (PC only)
- PINT Program and documentation from Snijders. (PC only)
- Google "Xiaofeng Liu power hlm", you will find some of his papers on power and HLM (I think he was a student of Raudenbush).
- HSB1 data. (level 1 data -- students)
- HSB2 data (level 2 data -- schools)
- SAS program and EB estimates of U's.
- SAS commands for mini-study on micro sample size on U's.
- SAS commands for mini-study on macro sample size on estimates.
- SAS commands for mini-study on effects of non-normality on the distribution of EB estimates.
- Using SAS/ASSIST to produce graphics. (Alternatives given in next lecture).
- High School and Beyond data. (level 1 and level 2 in one file).
- R that goes with lecture
- Function to simulate simple HLM with mixture of 2 normals for Uoj with examples. This also includes easier ways to plot histograms and qqplots of estimated random effects. The function can be modified to fit more complex models.
- Model Building.
- SAS programs:
li>NELS data for N=23 schools (from Kreft & de Leeuw).
- SAS data set NELS data for N=23 schools (from Kreft & de Leeuw).
- SAS Exploratory data analysis: Fixed Effects
- SAS Exploratory data analysis: Random Effects
- Modeling the data & diagnostics.
- Assessing homogeneity variance assumption (and modeling level 1 variance as random ). You will need the high school and beyond data for this:
- SAS programs:
- Longitudinal Data and HLM. Note that data in this lecture and next is from data from Hedeker web-site and web-site for Hedeker & Gibbons book on longitudinal data analysis.
- Serial Correlation..
- Multilevel Logistic Regression.
- Longitudinal study on depression. (data from Agresti, 2002)
- Longitudinal study on respiratory infections. (data from Skrondal & Rabe-Hesketh,2004)
- Simmulation study & demonstration.
- I will not be posting the Rodkin et al. data set or SAS code.
- Rasch and 2pl model fit to LSAT6.
- Rasch and 2pl model fit to General Social Suvery Vocabulary items with covariate.
- SAS for plotting item response curves for GSS data.
- Computer Lab Session 1: (bring laptop)
- Computer Lab Session 2: (bring laptop)
- Computer Lab Session 3: (bring laptop)
- Computer Lab Session 4:
- Homework 1:
- Homework 2:
- Homework 3:
- Homework 4:
- Homework 5:
- Homework 6:
- Final Exam and Projects: Hardcopy is due .....
Pentalty for late finals or projects is 10 points (out of 100 points) per weekday.
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 adults: 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.
- Steen-Baker, A.A., Ng, Shukhan, Payne, B.R., Anderson, C.J., Federmeier, K.D., & Stine-Morrow, E.A.L (2017). The effects of context on processing words during sentence reading among adults varying in age and literacy skills. Psychology and Aging, 32, 460-472.
Example cross-random effects in an study using eye-tracking data. Data were skewed so first log-transformed and then used HLM (i.e., a log-normal model).
- 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 (1st edition) using SAS
- MLbook.sas. Create SAS data for examples in Chapters 4 and 5.
- Ch4_examples.sas. Example 2-level analyses from Chapter 4 (random intercept models).
- Ch5_examples.sas. Example 2-level analyses from Chapter 5 (random intercept and slopes).
- Ch12_examples.sas. Examples analyses from Chapter 12 (longitudinal data analysis), including creating sas dataset.
- 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 adults: Evidence for efficiency and reserve. Aging, Neuropsychology, and Cognition.
- Examples from Chapter 4 of Kreft & de Leeuw (provided and written by Carol Nickerson):
- School23.sas. SAS code that creates data set and fits models reported in Kreft & de Leeuw.
- school23.dat. Raw data file that is used as input to school23.sas.
- Ones specific to multilevel modeling:
- Centre for Multilevel Modelling. This site includes trainting materials, publications, reviews of multilevel software, data sets, a BBC audio program featuring Harvey Goldstein, and more..
- Tom Snijders' multilevel web-site. This has data & various material that's used in Snijders & Bosker An Introduction to Basic and Advanced Multilevel Modeling as well as other multilevel stuff.
- Scientific software international home page. Student version of HLM program can be downloaded from this site.
- NELS88 data: various data sets used in Kreft & de Leeuw (Introducing heirarchical linear modeling)
- Using SAS PROC MIXED to fit multilevel, heirarchical models, and individual growth models. Downloadable paper by Judith Singer. Other papers also downloadable.
Lecture Notes : (Up-dated throughout the semester)
Computer Lab Sessions: Bring laptop