### About

Course Objectives

- To develop a critical approach to the analysis of contingency tables
- To examine the basic ideas and methods of generalized linear models
- To link logit and log-linear methods with generalized linear models
- To develop basic facility in the analysis of discrete data using SAS/R

### Course Topics

This graduate level course covers the following topics:

- Quick review of discrete probability distributions: binomial, multinomial, and Poisson.
- An introduction to the concept of likelihood.
- Implementing tests for one-way tables using Pearsons
*X*2 and likelihood-ratio*G*2 statistics. - Using contingency tables including 2 × 2 and
*r*×*c*tables, tests for independence and homogeneity of proportions, Fishers exact test, odds ratio and logit, other measures of association. - Using 3-way tables in full independence and conditional independence contexts, collapsing and understanding Simpson's paradox.
- Using generalized linear models in Poisson regression and logistic regression contexts for dichotomous response, including interpretation of coefficients, main effects and interactions, model selection, diagnostics, and assessing goodness of fit.
- Using polytomous logit models for ordinal and nominal response.
- Using loglinear models (and graphical models) for multi-way tables.
- And other topics as time permits (and due to the interests). These may include causality, repeated measures, generalized least squares, mixed models, latent-class models, missing data, and/or algebraic statistics approaches.

### Course Author(s)

Dr. Aleksandra Slavkovic is the primary author of these course materials and has taught this course for many semesters.

### Software

**SAS** (https://www.sas.com/), and/or **R** (https://www.cran.rproject.org/) are used in this course. You do not need both. See the Statistical Software page for more information about acquiring a copy of these applications.

SAS and R will be supported. Sample programs will be supplied **but students will be required to do some programing on their own**. Students should already feel comfortable using either SAS or R, or be a quick learner of software packages, or be able to figure out how to do the required analyses in another package of their choice. Due to different software versions and platforms there may be issues with running a code. Students should NOT wait to the point of frustration but must be proactive in seeking advice and help from appropriate sources including documentation resources, other students via the online discussion boards, the teaching assistant, instructor or helpdesk. Students who have no experience with programming or are anxious about being able to manipulate software code are strongly encouraged to take the one-credit courses in either SAS or R in order to establish this foundation before taking STAT 504.

### Textbook

Agresti, A. (2013). *Categorical Data Analysis*, 3rd Edition, Wiley.

This is the new and improved text of Agresti (1996). It is less theoretical and therefore less technical than Agresti (2002). Students are free to purchase either 2007 or 2002 text for this course. References are provided in the lesson materials for both texts.

### Prerequisites

STAT 460 or STAT 461 or STAT 502; Matrix Algebra (see Review). Basic knowledge of either SAS or R is strongly encouraged.