Course Description
Categorical data analysis with emphasis on practical applications in educational research and on the use of computing packages for analysis of such data. Topics include contingency table analyses, generalized linear models, logistic regression, and loglinear models. These techniques are applied to data sets from educational research.
Athena Title
Categorical Data Analysis Edu
Prerequisite
ERSH 8320 or ERSH 8320E
Semester Course Offered
Offered every year.
Grading System
A - F (Traditional)
Student learning Outcomes
- Students will be able to analyze two-way and three-way contingency tables.
- Students will be able to relate components of a generalized linear model.
- Students will be able to interpret logistic regression models and item response models.
- Students will be able to analyze contingency table data using log-linear models.
- Students will be able to apply nominal and graded response models to educational test data.
- Students will be able to perform data analyses using computers for practical applications in education.
Topical Outline
- I. Introduction to Categorical Data Analysis
a. Binomial and Poisson Distribution
b. Large-Sample Inference
- II. Two-Way Contingency Tables (Objective 1)
a. Comparing Proportions in Two-by-Two Tables
b. Odds Ratios and Log Odds Ratio
c. Chi-Square Tests of Independence
d. Fisher's Exact Test
- III. Three-Way Contingency Tables (Objective 1)
a. Conditional Independence
b. Mantel-Haenszel Test of Differential Item Functioning
c. Test of Homogeneity of Odds Ratios
- IV. Generalized Linear Models (Objective 2)
a. Components of a Generalized Linear Model
b. Wald, Likelihood-Ratio, Score Test Triad
- V. Logistic Regression (Objective 3)
a. Model Checking
b. Logit Models and Item Response Models
- VI. Loglinear Models for Contingency Tables (Objective 4)
a. Analysis of Tables via Loglinear Models
b. Loglinear-Logit Connection
- VII. Applying Logit and Loglinear Models (Objective 4)
a. Association Graphs and Collapsibility
b. Modeling of Ordinal Association
c. Effects of Sparse Data
- VIII. Multicategorical Logit Models (Objective 5)
a. Bock's Nominal Response Model
b. Samejima's Graded Response Model
- IX. Models for Matched Pairs (Objective 6)
a. Rasch Model
b. Symmetry and Quasi-Symmetry Models
- X. Historical Development and Current Applications (Objective 6)
a. Historical Development
b. Applications in Educational Research
