# Ed Psych 587

Edpsych/Psych/Stat 587

C.J. Anderson

Spring 2019

*Last revised: Feb 19, 2019*

**Site under re-construction**

**General Information**

**Announcements**

**Course Resources (computing mostly)**

**Lecture notes**

**Computer Lab**To R users, there is a correction to computer lab 2 and information about convergence posted below.

**Homework**

**Examples of Papers that Use Multilevel Models**

**Example analyses**

**Handy program and links**

Questions or problems regarding this site should be sent to cja@illinois.edu.

**Announcements**:

- 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.

**Computing and Other Resources**:

**SAS:**- 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
- Introduction to SAS notes..
- hsb1.sas. Creates SAS data set of level 1 data for the High School and Beyond data.
- Using SAS assist for graphics.
- Slick online SAS training from SAS.com

**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).**

**Lecture Notes**: (Up-dated throughout the semester)

**Introduction****Models for clustered data: Fixed and random effects ANOVA and multiple regression.**- SAS
- NELS data for 10 schools. Run this program before the next one.
- Generates statistics, fits models & produces graphics.

- R

- SAS
**Random Intercept Models.**- SAS
**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.

- R:
- 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
. These will be described and used in lecture:**SAS and R for HLM**- SAS:
- HSB1 data. (level 1 data -- students)
- HSB2 data (level 2 data -- schools)
- SAS code to be discussed in lecture.
- Using SAS assist for graphics.

- This is from the introduction to SAS session (won't be covered):
- R:
- HSB1data.txt. Student level data
- HSB2data.txt. School level data
- The R code in the notes.

- SAS:
**Random Intercept and Slopes Models**.- SAS
- 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.

- R
- 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**.- SAS:
- 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:
- R code for graphs illustrating MLE
- R for simulating HLM data. New Spring 2019

- SAS:
**Statistical Inference: Marginal Model**.- SAS:
- 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.

- R:
- 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).

- SAS:

**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).

- SAS:
- 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).

- R:
- 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.**

- New SAS programs:
- 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:
- HSB1 data. (level 1 data -- students)
- HSB2 data (level 2 data -- schools)

- Old SAS programs:
- eda.sas SAS program including commands for exploratory data analyses (SAS/GRAPH, R^2meta, R^2_j, means structure, etc).
- Simulations.sas. SAS program running first simulation and exploration of random structure.
- Simulation_long.sas. SAS program running second simulation and exploration of random structure. This has a different sigma^2's and tau's.
- New Variance EDA.sas. Exploratory data analyses of random structure for example given in class.
- SAS v9.1 experimental diagnostics..

- R: (new fall 2016)
- R code for graphics and more, including some tests, and some graphics not covered in lecture (described in lme4 mannual).
- nels data used by R code.

**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.**.

- SAS:
- Multilevel Logistic Regression. (up-dated 2017)
- SAS:
- 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.

- R: (revised 2017)

**Computer Lab Sessions: Bring laptop**

- Computer Lab Session 1: (bring laptop)
- Computer Lab Session 2: (bring laptop) Thursday Feb 14 -->

- SAS:
- R:
- R instructions for computer lab 4 with some example graphs.

**Homework**

- Homework 1:
- Homework assignment 1 Due Tuesday, January 29, 2019.

- Homework 2:
- Homework 2 Due Thursday January 31, 2019
- Answer key.

- Homework 3:
- Homework 3 Due February 7, 2019
- SAS:
- R

- Homework 4:

**(e.g., turn in Friday, 10 point deduction; turn in Monday 20 point, etc).**

**Final Exam and Projects**: Hardcopy is due**4:30 pm Friday May 3, 2019 (offices in Education are locked around 4:00pm)**. Pentalty for late finals or projects is 10 points (out of 100 points) per weekday.- Final Exam and data
- with SAS code to create data set:
- as plain txt file for R or other programs:

- What to include in a Final Project.

**(e.g., turn in Friday, 10 point deduction; turn in Monday 20 point, etc).**

**Final Exam and Projects**: Hardcopy is due**4:30 pm Friday May 3, 2019 (offices in Education are locked around 4:00pm)**. Pentalty for late finals or projects is 10 points (out of 100 points) per weekday.- Final Exam and data
- with SAS code to create data set:
- as plain txt file for R or other programs:

- What to include in a Final Project.

-->;

**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. - 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 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.

**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.

**Handy Programs and Links:**

**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.