Applied Categorical Data Analysis
EdPsych/Psych/Soc 589
C.J. Anderson
Fall 2022

Last revised:  June 2023

This course will be offered during the academic year 2024-2025 by Justin Kern of the Department of Educatonal Psychology.

This site is archived but should be available as an open access resource.

General Information

Announcements

Lecture notes

Homework and Exams 

Handy program and links

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

  General Information :

• Syllabus (2022). with correction (9/7/2022)
  
• Computing: You will have 2 options (i.e., I can provide help with):
  • SAS statistical software: 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 purchase a license from webstore.
  • R: It's free. There is more up-front learning with this and you will need to learn more packages and commands than SAS; however, you can't beat the graphics! I still consider myself a learner of R and will include R scripts to go with lectures; however, these will be rolled out as the semester progresses. There is also some online R information that goes with the Agresti text.
  
  

Announcements:

• Sept 7:  R script created in lecture for the practice problem.  I added to it some useful stuff.
  
• Aug 31:  I couldn't find and R function or package that computes the Adjusted Pearson (i.e., Haberman) residual so I wrote one.  This should work for 2-- and higher-3 way tables. 
  
• Aug 25:  changed due date for homework 1 to Wed Sept 7
  
• Graphing data but using text rather than points. The SAS and R code to do this. The data to use for SAS with code to create data file, and a text file for R.

Lectures Notes:

• Only print/download one lectures at a time because I may be making changes to them.
• Jumps to specific lectures and associated code are below.
  

• Introduction.
  • SAS:
    • Poisson distribution: World Cup Soccer, 1994.
    • Poisson distribution: World Cup Soccer, 1998.
    • Figure of Poisson Distribution.
    • Binomial example: Heights of candidates for US President for the candidates for US President.
    • For the peer nominations of bullies see Lecture below on Poisson regression.
  • R:
    • Figure of likelihood of binomial
    • Examples of Poisson distributions.
    • Poisson and world cup example.
    • Tests for proportion. (exact only)
    • Tests for proportion. (exact, asymptotic and more)
• Introduction to 2-way tables and basic measures of association
  
  • SAS:
    • Vitamin C x Colds
  • R:
    • Working with 2-way tables (uses cold data).
    • Tutorial: working 2-way tables and other stuff.


• Chi-square tests.
  
  • SAS:
    • Test of Independence: FECHLD X MAPAID (GSS 1994 data). (includes how to save standardized residuals to sas data set and then create a table of them).
    • Test of Independence: Admissions scandal.
    • Test of homogeneous distributions: French skiers and effectiveness of vitamin C in preventing colds.
    • Example of partitioning chi-square.
  • R:
    • Test of Independence in 4 x 5 table (GSS items on working moms):
      • Text file with GSS 1994 data.
      • R script for GSS test using multiple methods.
    • Test of Independence in 2 x 2 table (UofI Admission scandal)
    • Testing homogeneous distributions: French skiers and effectiveness of vitamin C in preventing colds (same as "Working with 2-way tables above).
    • Example of partitioning chi-square.
    • Function that computes Pearson and Adjusted Pearson ("haberman") residuals.  This reproduces what is in the lecture notes
    • R script solution to practice problem.  This is what was created in lecture, but I added to it and organized it a bit.


• Tests for Ordinal Association.
  
  • SAS:
    • Two "Likert" type items: FECHLD X MAPAID (GSS 1994 data).
    • A 2 x J table with ordered columns: Gender by Prestige using different scores.
    • A 3 x 3 table with with bad & good scores: School of Psychiatric Thought by Origin of schizophrenia (Agresti, 1990).
    • Power computation and plots: Power computation.
    • Test for trend: Cochran-Armitage of Framingham heart study data.
  • R:
    • Two "Likert" type items: 4 x 5 table (GSS items on working moms):
      • Text file with GSS 1994 data.
      • R script for Cochran-Mantel-Haenszel Test for ordinal association in 4 x 5
    • CHM for ordinal association in 3 x 3 table. (schools of psychiatric thoughts x origins of schizophrenia).
    • Trying different scores (Farmer et al. data). Includes how to get good scores from the data. (2 x 8 table).
    • Power of Mantel-Haenzel for ordinal association vs general test. Note: This include a function that I wrote that will compute power curves and tables. You can change the parameters input into the function for your own use....same and 1994 GSS example above.
    • Cochran-Armitage Trend test in (2 x J) tables. Note there are multiple ways to test this. There are limitations to the CochranArmitageTest( ) function (i.e., I can't figure out whether or how to change scores). I also include an example of prop.trend.test( ) function.
    • GSS Practice.  This is R script that inputs data and performs various tests.
    • GSS data for practice.  A text file that contains the data for the practice problem.
  
  
• Exact Tests for Small Samples.
  • SAS: Admissions scandal.
  • R: Admissions scandal.


• Three-way tables.
  • SAS:
    • Conditional independence & marginal dependence: Cal graduate admissions
    • Conditional independence & marginal dependence: Boy Scouts (hypothetical).
    • Conditional independence & marginal dependence: Blue collar workers x management x supervisor.
    • Conditional dependence & marginal independence: (Hypothetical) DIF.
    • Conditional dependence & marginal dependence: Age x Smoking x Breathing Test result.
    • Homogeneous association: Attitude toward media x year x race.
    • Hurricane_Katrina
  • R:
    • Conditional independence & marginal dependence: Data: Cal graduate admissions
    • Conditional independence & marginal dependence: R script: Cal graduate admissions
    • Conditional independence & marginal dependence: Data: Boy Scouts (hypothetical).
    • Conditional independence & marginal dependence: R script: Boy Scouts (hypothetical).
    • Conditional independence & marginal dependence: Blue collar workers x management x supervisor.
    • Conditional dependence & marginal independence: (Hypothetical) DIF.
    • Conditional dependence & marginal dependence: Age x Smoking x Breathing Test result.
    • Homogeneous association: Attitude toward media x year x race
    • In class set-up for practice


• Introduction to Generalized Linear Models (GLMs)
  
  • Supplemental reading on GLMs: Draft Chapter on GLMs from Anderson, Verkuilen & Johnson (in preparation). Applied Generalized Linear Mixed Models.
  • SAS:
    • Example of a variety of GLMS: T-cell and Hodgkin's disease.
    • SAS graph used to make figures in lectures: Step and S shaped functions.
      
    • More SAS graph (& data steps): Plotting cummulative distribution functions (normal & logistic).
      
  • R:
    • Example of a variety of GLMS: T-cell and Hodgkin's disease.




• Introduction to GLMS for Dichotomous data
  • For a description of the variables in the high school & beyond data: is here.
  • SAS:
    • hsb-data.sas.
    • Linear probability, logit & probit fit to grouped data: High School and Beyond.
      Note: you need to first run the program that creates the data set (i.e., hsb-data.sas)
    • High School and Beyond jittered data, loess and fitted values from logit model.
      Note: you need to first run the program that creates the data set (i.e., hsb-data.sas)
  • R:
    • hsb_data.csv.
    • Grouped data .
    • Linear, logit and probit models.
      
    • Data for Practice: Covid deaths and cases for Champaign County (May 15, 2021).
  • Graphing data, fitted values, loess in both SAS and R:
    • How to do jitter, loess and fitted for both R and SAS. (word document with SAS code and R script.
    • Donner Party data for SAS.
    • Donner Party data for R (plain text file)
  
  
• Poisson regression
  
  • SAS:
    • Deaths due to AIDS.
    • Crab data.
    • Lung Cancer.   This includes graphing using sgplot (data and model fitted values).
      
  • R:
    • Data: Deaths due to AIDS.
    • R script: Deaths due to AIDS.
    • Crab data.
    • R script for Poisson fit to Crab data.
    • Lung cancer data from Lindsey.
    • R script for models & graphs of lung cancer data.
    
    
• Statistical Inference & Model Checking for Poisson Regression.
  
  • SAS:
    • Deaths due to AIDS.
    • Lung Cancer.
    • Crab data.
    • Computing p-values for chisquares.
    • SAS: Bully nominations vs self report.
  • R:
    • Data: Deaths due to AIDS.
    • R script: Deaths due to AIDS.
    • Crab data.
    • R script for crab data.
    • Lung cancer data from Lindsey.
    • R script for models & graphs of lung cancer data.
    • Bully Example
      • Bully data.
      • Rmarkdown (html)
      • Rmarkdown (Rmd)
      • Rmarkdown (R)




• The Basics of Logistic Regression
  • SAS:
    • hsb-data.sas.
    • For a description of the variables, HSB coding.
    • Logistic regression and model checking: High School & Beyond.
    • Regression diagnositics: ESR data.
    • SAS/MACRO (& example) for computing Range of Influence statistics: RangeInfluence.sas
  • R:
    • HSB data in csv format: HSB data.
    • text file with ESR data.
    • R script for Logistic regression and model checking: High School & Beyond.  (up-dated 10/14/2021)
    • Rmarkdown for HSB example (posted 10/14/2021)
    • ESR example.
    • ROI function with examples.  (Range of influence R function for detecting possible miss-classification on the response/outcome/dependent variable)
  
  
• Multiple logistic Regression
  • SAS
    • hsb-data.sas. For a description of the variables, HSB coding.  
      
    • High School & Beyond.
    • csv file of Titanic passenger data..
    • SAS program that imports data (you need to change path to where you save the data).
    • SAS ESR Example of exact inference. This is OK to use.
  • R:
    • HSB Example:
      • HSB data in csv file.
      • HSB rmarkdown (html)
      • HSB source (rmd)
      • HSB script (r)
    • ESR example:
      • esr example.
      • text file with ESR data.
      • esr exact. Not recommended.
    • Titanic
      • Titanic data in csv format.
      • R script for Titanic data. 
        
    
    
  • Log-linear Models
    • SAS:
      • GSS 1992 Presidential Election
      • Blue Collar Worker data and how to compute the dissimilarity index in SAS
      • Revised GSS 1992 Presidential Election that shows linear x linear model and a nominal x linear model. These are topics that really will be talked about later.
      • SAS GENMOD example for doing Bayesian model fitting data-sf-ec-immutable="" (easy).
    • R:
      • Blue collar data
      • 4-way example:   .html     .Rmd   and   .R     (fixed 10/31/2022)
        
      • GSS Presidential election data
      • R code using package glmnet to do lasso in Poisson and logit regression. This is a small example, so really does not show the power of this method.
    
    
  • Model Building for Log-Linear & Logit models
    • Optional Additional Reading:
      • Anderson, C.J., Kateri, M., & Moustaki, I (forthcoming).  Log-linear and log-multiplicative association models for categorical data.  In M. Kateri and I Moustaki (eds) Trends and Challenages in Categorical Data. 
      • Pseudo-likelihood estimation of association models: the pleLMA package and r script from package vignette.
        
    • SAS
      • 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. This code with some minor changes can also be run in SAS/NLMIXED and probably HPNLMIX
    • R:
      • R for Wickens-Olzak (modeling signal detection data)
      • Text file of Wicken-Olzak data (signal detection)
      • R for linear x linear, RC(M) association model and correspondence analysis
      • Text file of HSB data for linear by linear models as well as RC(M) association and correspondence analysis.
      • Text file of HSB data
      • R for GSS data
      • Text file of GSS data
      • R for 4-way table
      • Text file 4-way data set (marital status x permatiral sex x extermatrial sex x gender).
      • R-code for dealing with zeros and modeling association.
      • How to draw graph using R:   .html      .Rmd     .r
    
    
  • Mulitnomial logit models (baseline and conditional)
    • Optional Extra reading:
      • Anderson & Rutkowski (2008). Mulitnomial logit models. (baseline and conditional) Multinomial Logistic Regression. In Osborne "Best Practices in Quantitative Methods".
      • Anderson (2009). Categorical Data Analysis with a Psychometric Twist. In Milsap & Maydeu-Olivares "The Sage Handbook of Quantitative Psychology". 311-336.
      • Anderson, Kim and Keller (2014) Multilevel Modeling of Categorical Response Variables. In Rutkowski, von Davier, & Rutkowski "A Handbook of International Large-Scale Assessment: Background, Techinical Issues, and Methods of Data Analysis.
    • SAS
      • High School and Beyond Data (and code to create plots).
      • Baseline logistic models for High School and Beyond Data.
      • Grouped NYLS data of employment x Father's education x Race. (to show connection between log-linear and logit models.)
      • Conditional logit model of choice of chocolate. (attributes of objects as predictors).
      • Conditional logit model of differenct combinations of choice set. (attributes of objects in sets as predictors).
      • Conditional logit model of model of transportation. (conditional logistic with predictors of the choice objects and predictors of individual making the choice.
    • R
      • HSB: Baseline logistic models
        • HSB r script for hsb example
        • Rmarkdown of HSB example.
      • Fathers and Sons: Logit and loglinear models.
      • Discrete choice models otherwise known as conditional multinomial logistic regression models:
        
      • discrete_choice_models.html  (nice for viewing)
        
      • discrete_choice_models.Rmd   (if you want to alter)
        
      • discrete_choice_models.r  (if you only want r script)
        
      • chocolates_data.txt Chocolates data (as text file)
      • brands_price_data.txt Brands-price data in format for glm
      • brands_mdc_data.txt Brands-price data in format for mlogit
      • transportation_data.txt Mode of transportation in format for mlogit
    
    
• Oridinal logit models
  
  • SAS:
    
    • High School and Beyond Data (and code to create plots).
    • HSB ordinal hsb logit model
    • Pirls modeling
    • Proportional (Cumulative) odds model for grouped data and continuation raios model.
    • Various models:Baseline, proporitional odds, adjcent categories and continuation ratios).
    • Adjacent categories model of Happiness.
  • R:
    • High School and Beyond Data  (text file)
    • Ordinal models fit to HSB data
    • Pirls data (text file)
    • R for Pirls data.
    • happiness data
    • Adjacent categories (and others) for happiness
    • Continuation Ratios example
  
  
• Models for matched pairs
  • SAS:
    • McNemar Test (Siskell & Ebert and cell phone use).
    • Proportional Log-linear models of quasi-independence, symmetry, quasi-symmetry and test of marginal homogenity
  • R:
    • McNemar Test & and various models. (Siskell & Ebert).
    • McNemar Test (cell phones while driving).
    • Models for square tables Uses migration data to illustrate models of quasi-independence, symmetry, quasi-symmetry, and marginal homodentiry.



Homework and Exams



• Homework 1
  • Homework Assignment 1    (due Wed Sept 7)
    
  • Answer key
  • R markdown for numerical results (html)
    
• Homework 2
  • Homework Assignment 2    (due Wed Sept 14)
    
  • Answer key
  • R markdown for answers
• Homework 3
  
  • Homework Assignment 3   (due Tuesday Sept 27)
  • Data for countries
  • Answer key
  • R markdown for computation (html)
  • Source (rmd)
  • R script (R)
• Homework 4
  
  • Homework Assignment 4   (due Wed October 5)
    
  • Data for problem 1
  • Answer key 4
    
  • R for computations  (html)
  • R for computations (Rmd)
  • R script (R)
• Homework 5
  • Homework Assignment 5-  Due Wed October 12
    
  • Data for problem 1  (soccer)
    
  • Data for problem 2 (crabs)
    
  • Computations in R (html)
  • Source (rmd)
  • R script of computations (R)
• Homework 6
  • Homework 6 assignment (the R script &/or markdown for lecture on binary logistic regression may help).   -- Due Octobe 26, 2022
    
  • Data for problem 1 (crabs)
    
  • Answer key 6
  • Rmarkdown homework 6 (html)
    
  • Source  homework 6 (rmd)
  • Rscript homework 6 (R)
• Homework 7
  • Homework Assignment 7    (Due Monday Nov 7)
    
  • Data: Table 5.12
  • Answer key will go here
  • R computations:   .html       .Rmd      .r
    
• Final project description