Applied Categorical Data Analysis
EdPsych/Psych/Soc 589
C.J. Anderson
Spring 2009

Last revised: May 4, 2009

General Information

Announcements

Lecture notes

Homework and Exams .

Example analyses

Handy program and links

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

General Information :

Syllabus (2009).
Course log. A record of what we actually did.

Announcements:

5/4/2009:
- The wrong dataset for problem 3 of the final was posted; the correct one is now posted.
- All homework answer keys and sas code are posted.
2/18/2009:
- Office hours canceled Wed Feb 18.
- Homework 4 is posted.
- Note that other computer labs that have SAS are the Foreign Language building, ALTAS (2nd floor Lincoln hall), the Union, the undergraduate library, and rm 15/17 Education bulidng.
- ALTAS is a statistics and GIS OPEN computer lab in 202 Lincoln Hall. Below are links to more information and services that they offer.
  - Their drop-in consulting hours are from 10 - 4 Monday through Wednesday, 11 - 4 Thursday, and 11 - 2 on Friday. .
  - SAS and other services offered by ATLAS computing lab. (fees for students are $15 and cover cost of materials)
  - The data service office hours in the library will be on Wednesday from 1:30-4:30. More details about this service can be found here.
  - If you have any questions about ATLAS's services or would like to make an appointment, please feel free to contact them at atlas-consult@illinois.edu
- Besides courses at ALTAS on SAS, the Statistics Department also have SAS instruction. For more information see http://www.stat.uiuc.edu/iso/training.htm (These cost $50 to $75).
2/2/2009: Homework 2 is posted.
1/28/2009: We have very good students this year who are catching various mistakes.
- The page numbers for the homework problems 2 & 3 in the first homework assignment have been corrected.
- The first set of notes now have all known errors taken out:
  - The computations for the probabilities for Poisson distribution are now correct
  - Although the SAS commands in the notes I gave in class and the SAS program online were correct, those in the online version of the lectures notes weren't. The latter has been corrected.
1/27/2009: An introduction to SAS was given in rm 15/17 Education building on Monday 9-10am.
1/21/2009: A student found some errors that I made in the example on Poisson regression. I've revised the SAS program (makes a much nicer graph too), and I added another one for this example. I'll also fix the notes.
1/8/2009: The course is full.

Lectures Notes:

Suggestion: Only print one or two lectures at a time. I often make changes to the notes.

Section 1. Introduction.
SAS code and Extra pages illustrating PROC FREQ using the BINOMIAL options:
- Poisson distribution: World Cup Soccer, 1994.
- Poisson distribution: World Cup Soccer, 1998.
- SAS commands.
- SAS output. (plain text file)

(date & time TBA) Optional: Introduction to SAS to be held in the computer lab. We will go over the first two items.
- Introduction to SAS notes..
- hsb-data.sas.
- Using SAS assist for graphics.
- Using SAS insight. (interactive data analysis)
Section 2. Two-way tables
- Introduction to 2-way tables.
- Chi-squared tests.
  Chi-square test of independence
  - French skiers and effectiveness of vitamin C in preventing colds.
  - FECHLD X MAPAID (GSS 1994 data).
- Tests of ordinal association.
  SAS (input and/or output):
  - Gender x Prestige (HSB data) with different scores.
  - FECHLD X MAPAID (GSS 1994 data).
  - School of Psychiatric Thought X Origin of schizophrenia (Agresti, 1990) with bad/wrong category scores.
  - Cochran-Armitage test using Framingham heart study data
    - SAS program . This SAS program also includes code for producing graphics using PROC GPLOT under SAS GRAPH.
- Exact tests for small samples.
Section 3. Three-way tables.
Section 4. Generalized linear models.
- Introduction to GLMs.
- Introduction to GLMS for Dichotomous data
- SAS programs used in these lecture notes:
  - T-cell and Hodgkin's disease.
    (various different GLMS)
  - Step and S shaped functions.
  - Plotting cummulative distribution functions (normal & logistic).
  - High School and Beyond linear, logit & probit to grouped data. Note: you need to first run the program that creates the data set (i.e., hsb-data.sas). For a description of the variables and coding see HSB file and coding.
Section 5. Regression Models for Counts.
- Poisson regression
- Inference and modeling checking.
- Extended Example, Negative Binomial and Zero Inflated Models. .
- SAS programs used in these lecture notes:
  - Deaths due to AIDS.
    (Poisson regression & transformation of x).
  - Crab data. (Poisson regression & outliers).
  - Lung Cancer.(Poisson regression with a few twists)
  - SAS program from lecture 2/28/2007 (show how to fit Poisson regression models, save fitted values and other statistics, plot data & fitted line using SAS/GRAPH
  - SAS: Bully nominations vs self report. (Poisson, NegBin, ZIP & SAS).
Section 6. Logistic Regression

Part 1 The basics
SAS programs used in these notes:
- High School & Beyond. (logistic regression & model checking).
- ESR data (regression diagnostics)
- SAS/MACRO for computing Range of Influence statistics using ESR data for illustration.
  (improved version)
Part 2 Added complexities of multiple explanatory & qualitative variables. (complete)

Section 7. Loglinear models for contingency tables

Lecture Notes
SAS Programs and Examples:
- GSS 1992 Presidential Election
- Blue Collar Worker data and how to compute the dissimilarity index in SAS

Section 8. Model building for logit and loglinear models.
- Model Building.
- SAS programs and examples:
  - Wickens Olzak data with SAS code (graphical models and linear by linear)
  - HSB example of linear by linear & uniform association models
  - SAS program showing effect of sampling 0's (hypothetical from Wickens)
  - Health concerns by genders (data from Fienberg). How to handle structural zeros & include indicators for specific cells
  - Fitting RC(1) to HSB using NLP...with & without ordinal restrictions, and other models too.
Section 9. Logit Models for multicategory variables
Extra reading: This site:
- Anderson & Rutkowski (2008). Multinomial Logistic Regression. In Osborne "Best Practices in Quantitative Methods".
- Anderson (in press). Categorical Data Analysis with a Psychometric Twist. In Milsap & Maydeu-Olivares "The Sage Handbook of Quantitative Psychology". 311-336.
Section 9. Models for matched pairs

Homework and Exams
Note: The SAS programs were ones that I used in creating the answer keys; that is, they're may be extra things in them that were not needed and I didn't write them with the intenion of posting them on the web.

Homework 1
- Homework assignment 1. (due Thursday Feb 5)
- Answer key for homework 1.
- SAS program for problem 1 (Agresti 1.8).
Homework 2
- Homework assignment 2. (due Thrusday Feb 12)
- Answer key for homework 2.
- SAS for Agresti (2007) 2.19.
- SAS for Agresti (2007) 2.27.
- SAS for Agresti (2007) 2.30.
Homework 3
- Homework assignment 3. (due Thursday Feb 19)
- Answer key for homework 3.
- SAS for Agresti (2007) 2.33.
- SAS for Agresti (1996) 3.8 and 3.9.
Homework 4
- Homework assignment 4. (due Thursday Feb 26)
- Answer key for homework 4.
- SAS for Agresti (2007) 3.11-3.12.
- SAS for Agresti (2007) 3.18.
- SAS problem 1.
Homework 5
- Homework assignment 5. (due Thursday March 5)
- Crab data (plus SAS).
- Answer key.
- SAS that produces results in answer key. note: dist=zip in GENMOD requires SAS v9.2 or later.
Midterm
- Midterm Exam. Due Thursday March 19 in class.
- Smallpox data.
- Cell differentiation data.
- Midterm Exam answer key.
Homework 6
- Homework assignment 6. (due April 9)
- Data for problem 1.
- SAS code for problem 1.
- SAS code for problem 2.
- Answer Key.
Homework 7
- Homework assignment 7. (Due Thursday April 16)
- Answer Key.
- Sas for 7.4.
- SAS for 7.15.
- SAS for 7.24.
Homework 8
Homework 9
- Homework assignment 7.
Final Exam or Project
- If you are doing a project here is a description of what to include in your project.
- If you are taking the final, (comming soon)
  - Final Exam.
  - SAS for Problem 2.
  - SAS for Problem 3. (the correct data set)
  - SAS for Problem 4.

Example SAS Programs (most are in ascii/text format):

Linear, logit and probit models of probiblities: model the probability of having attended academic program as a function of achievement test scores.
Dealing with overdispersion (SAS options and negative binomial): Poisson regression example of number of deaths due to AIDs.
- SAS program.
- Output from program in text format
- Output from program in postscript format
- Maybe add ZIP example
Multiple logistic regression
- SAS program to create HSB data set
- SAS program that performs multiple logistic regressions, etc.
Log-linear models and SAS:
- Computing the dissimilarity index
  - SAS program using Blue Collar data. (fits loglinear data, saves fitted values, merges output files, creates components of D index, and then sums to get the dissimilarity index).
  - SAS output.
- Log-linear/logit model connection
  - SAS program for 4-way table (Marital status x Gender x PMS x EMS). Two log-linear models are computed including one that is equivalent to a logit model, which is also fit directly as a logit model.
  - SAS output.
Example of linear by linear, uniform, and nominal by ordinal association models using SAS (high school and beyond SES X HSP).
- SAS input and output. (in postscript format)
- SAS input. (in text format)
Example of effect of sampling zeros used in lecture.
- SAS input and output. (in postscript format)
- SAS input. (in text format)
Generalized CMH tests for ordinal x ordinal, nominal x ordinal, and general association.
SAS input and output. (in text format)
Example of baseline/multinomial logistic response model, (output is in postscript format).
- baseline handout
- SAS program that fits baseline model and generates figures of fitted and observed values
Likelihood ratio tests of the equality of parameters over response options in the multinomial response model, (output is in postscript format).
- Multinomial logistic LR tests
- SAS program of Multinomial logistic regression and LR tests
Examples of conditional logit response model, (output is in postscript format).

Handy Programs and Links:

CIforP.f: A FORTRAN program that computes large sample confidence intervals for a proportion. For PC computers, a execultable version of CIforP (i.e., already complied)
pvalue.f: 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, pvalue.exe is an executable (i.e. already compiled) program.