Course Description
This course is designed as a broad, applied introduction to the
statistical analysis of categorical (or discrete) data, such as counts,
proportions, nominal variables, ordinal variables, discrete variables
with few values, continuous variables grouped into a small number of
categories, etc.
The course begins with methods designed for cross-classified
table of counts, (i.e., contingency tables), using simple chi
square-based methods.
It progresses to generalized linear models, for which log-linear
models provide a natural extension of simple chi square-based
methods.
This framework is then extended to comprise logit and logistic
regression models for binary responses and generalizations of these
models for polytomous (multicategory) outcomes.
Throughout, there is a strong emphasis on associated
graphical methods for visualizing categorical data,
checking model assumptions, etc. Lab sessions will familiarize the
student with software using R for carrying out these analyses.
Course and lecture topics are listed below, in a visual overview.
Overview & Introduction

Topics:
- Course outline, books, R
- What is categorical data?
- Categorical data analysis: methods & models
- Graphical methods
Discrete Distributions

Topics:
- Discrete distributions: Basic ideas
- Fitting discrete distributions
- Graphical methods: Rootograms, Ord plots
- Robust distribution plots
- Looking ahead
Two-way Tables

Topics:
- Overview: \(2 \times 2\), \(r \times c\), ordered tables
- Independence
- Visualizing association
- Ordinal factors
- Square tables: Observer agreement
- Looking ahead: models
Loglinear models & mosaic displays

Topics:
- Mosaic displays: Basic ideas
- Loglinear models
- Model-based methods: Fitting & graphing
- Mosaic displays: Visual fitting
- survival on the Titanic
- Sequential plots & models
Correspondence Analysis

Topics:
- CA: Basic ideas
- Singular value decomposition (SVD)
- Optimal category scores
- Multiway tables: MCA
Logistic regression

Topics:
- Model-based methods: Overview
- Logistic regression: one predictor, multiple predictors,
fitting
- Visualizing logistic regression
- Effect plots
- Case study: Racial profiling
- Model diagnostics
Logistic regression: Extensions

Topics:
- Case study: Survival in the Donner party
- Polytomous response models
- Proportional odds model
- Nested dichotomies
- Multinomial models
Extending loglinear models

Topics:
- Logit models for response variables
- Models for ordinal factors
- RC models, estimating row/col scores
- Models for square tables
- More complex models
GLMs for count data

Topics:
- Generalized linear models: Families & links
- GLMs for count data
- Model diagnostics
- Overdispersion
- Excess zeros
Copyright © 2018 Michael Friendly. All rights reserved. ||
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orcid.org/0000-0002-3237-0941